From dfc0f0c7b9990632690f342b201d927155ebb041 Mon Sep 17 00:00:00 2001 From: Uzair Mohammed Date: Wed, 20 Mar 2024 16:21:15 -0700 Subject: [PATCH] Completed HW2 --- hw2/gameTree.png | Bin 0 -> 51736 bytes hw2/hw2.pdf | Bin 0 -> 353050 bytes .../__pycache__/grader_util.cpython-312.pyc | Bin 0 -> 24936 bytes hw2/ints/__pycache__/logic.cpython-312.pyc | Bin 0 -> 59652 bytes .../__pycache__/submission.cpython-312.pyc | Bin 0 -> 2834 bytes hw2/ints/examples.py | 26 + hw2/ints/grader.py | 109 ++ hw2/ints/grader_util.py | 448 +++++++ hw2/ints/logic.py | 1084 +++++++++++++++++ hw2/ints/models/4a-0.pklz | Bin 0 -> 395 bytes hw2/ints/models/4a-1.pklz | Bin 0 -> 381 bytes hw2/ints/models/4a-2.pklz | Bin 0 -> 131396 bytes hw2/ints/models/4a-3.pklz | Bin 0 -> 129509 bytes hw2/ints/models/4a-4.pklz | Bin 0 -> 194567 bytes hw2/ints/models/4a-5.pklz | Bin 0 -> 2071 bytes hw2/ints/models/4a-all.pklz | Bin 0 -> 1081 bytes hw2/ints/submission.py | 42 + hw2/knights/__pycache__/logic.cpython-312.pyc | Bin 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zW)bUWXho~pW|8G!_27%*!-^^;WAYKQm)XM$tAViM;yCWPfVj7QL}e?lRdKIhmnZy_ V6 datetime.timedelta(seconds=self.max_seconds + 1): + raise TimeoutFunctionException() + return result + # End modification for Windows here + signal.signal(signal.SIGALRM, self.handle_max_seconds) + signal.alarm(self.max_seconds + 1) + result = self.function(*args) + signal.alarm(0) + return result + + +class Part: + def __init__(self, number, grade_func, max_points, max_seconds, extra_credit, description, basic): + if not isinstance(number, str): + raise Exception("Invalid number: %s" % number) + if grade_func is not None and not callable(grade_func): + raise Exception("Invalid grade_func: %s" % grade_func) + if not isinstance(max_points, int) and not isinstance(max_points, float): + raise Exception("Invalid max_points: %s" % max_points) + if max_seconds is not None and not isinstance(max_seconds, int): + raise Exception("Invalid max_seconds: %s" % max_seconds) + if not description: + print('ERROR: description required for part {}'.format(number)) + # Specification of part + self.number = number # Unique identifier for this part. + self.description = description # Description of this part + self.grade_func = grade_func # Function to call to do grading + self.max_points = max_points # Maximum number of points attainable on this part + self.max_seconds = max_seconds # Maximum allowed time that the student's code can take (in seconds) + self.extra_credit = extra_credit # Whether this is an extra credit problem + self.basic = basic + # Grading the part + self.points = 0 + self.side = None # Side information + self.seconds = 0 + self.messages = [] + self.failed = False + + def fail(self): + self.failed = True + + def is_basic(self): + return self.grade_func is not None and self.basic + + def is_hidden(self): + return self.grade_func is not None and not self.basic + + def is_auto(self): + return self.grade_func is not None + + def is_manual(self): + return self.grade_func is None + + +class Grader: + def __init__(self, args=None): + if args is None: + args = sys.argv + self.parts = [] # Parts (to be added) + self.useSolution = False # Set to true if we are actually evaluating the hidden test cases + + parser = argparse.ArgumentParser() + parser.add_argument('--js', action='store_true', help='Write JS file with information about this assignment') + parser.add_argument('--json', action='store_true', + help='Write JSON file with information about this assignment') + parser.add_argument('--summary', action='store_true', help='Don\'t actually run code') + parser.add_argument('remainder', nargs=argparse.REMAINDER) + self.params = parser.parse_args(args[1:]) + + args = self.params.remainder + if len(args) < 1: + self.mode = AUTO_MODE + self.selectedPartName = None + else: + if args[0] in [BASIC_MODE, AUTO_MODE, ALL_MODE]: + self.mode = args[0] + self.selectedPartName = None + else: + self.mode = AUTO_MODE + self.selectedPartName = args[0] + + self.messages = [] # General messages + self.currentPart = None # Which part we're grading + self.fatalError = False # Set this if we should just stop immediately + + def add_basic_part(self, number, grade_func, max_points=1, max_seconds=default_max_seconds, extra_credit=False, + description=""): + """Add a basic test case. The test will be visible to students.""" + self.assert_new_number(number) + part = Part(number, grade_func, max_points, max_seconds, extra_credit, description, basic=True) + self.parts.append(part) + + def add_hidden_part(self, number, grade_func, max_points=1, max_seconds=default_max_seconds, extra_credit=False, + description=""): + """Add a hidden test case. The output should NOT be visible to students + and so should be inside a BEGIN_HIDE block.""" + self.assert_new_number(number) + part = Part(number, grade_func, max_points, max_seconds, extra_credit, description, basic=False) + self.parts.append(part) + + def add_manual_part(self, number, max_points, extra_credit=False, description=""): + """Add a manual part.""" + self.assert_new_number(number) + part = Part(number, None, max_points, None, extra_credit, description, basic=False) + self.parts.append(part) + + def assert_new_number(self, number): + if number in [part.number for part in self.parts]: + raise Exception("Part number %s already exists" % number) + + # Try to load the module (submission from student). + def load(self, module_name): + try: + return __import__(module_name) + except Exception as e: + self.fail("Threw exception when importing '%s': %s" % (module_name, e)) + self.fatalError = True + return None + except: + self.fail("Threw exception when importing '%s'" % module_name) + self.fatalError = True + return None + + def grade_part(self, part): + print('----- START PART %s%s: %s' % ( + part.number, ' (extra credit)' if part.extra_credit else '', part.description)) + self.currentPart = part + + start_time = datetime.datetime.now() + try: + TimeoutFunction(part.grade_func, part.max_seconds)() # Call the part's function + except KeyboardInterrupt: + raise + except MemoryError: + signal.alarm(0) + gc.collect() + self.fail('Memory limit exceeded.') + except TimeoutFunctionException: + signal.alarm(0) + self.fail('Time limit (%s seconds) exceeded.' % part.max_seconds) + except Exception as e: + signal.alarm(0) + self.fail('Exception thrown: %s -- %s' % (str(type(e)), str(e))) + self.print_exception() + except SystemExit: + # Catch SystemExit raised by exit(), quit() or sys.exit() + # This class is not a subclass of Exception and we don't + # expect students to raise it. + self.fail('Unexpected exit.') + self.print_exception() + end_time = datetime.datetime.now() + part.seconds = (end_time - start_time).seconds + ###### quick fix to pacman problem 4 ###### + if part.seconds > part.max_seconds: + signal.alarm(0) + self.fail('Time limit (%s seconds) exceeded.' % part.max_seconds) + ###### quick fix to pacman problem 4 ###### + if part.is_hidden() and not self.useSolution: + display_points = '???/%s points (hidden test ungraded)' % part.max_points + else: + display_points = '%s/%s points' % (part.points, part.max_points) + print('----- END PART %s [%s]' % ( + part.number, display_points)) + print() + + def get_selected_parts(self): + parts = [] + for part in self.parts: + if self.selectedPartName is not None and self.selectedPartName != part.number: + continue + if self.mode == BASIC_MODE: + if part.is_basic(): + parts.append(part) + elif self.mode == AUTO_MODE: + if part.is_auto(): + parts.append(part) + elif self.mode == ALL_MODE: + parts.append(part) + else: + raise Exception("Invalid mode: {}".format(self.mode)) + return parts + + def grade(self): + parts = self.get_selected_parts() + + result = {'mode': self.mode} + + # Grade it! + if not self.params.summary and not self.fatalError: + print('========== START GRADING') + for part in parts: + self.grade_part(part) + + # When students have it (not useSolution), only include basic tests. + active_parts = [part for part in parts if self.useSolution or part.basic] + + total_points = sum(part.points for part in active_parts if not part.extra_credit) + extra_credit = sum(part.points for part in active_parts if part.extra_credit) + max_total_points = sum(part.max_points for part in active_parts if not part.extra_credit) + max_extra_credit = sum(part.max_points for part in active_parts if part.extra_credit) + + print('========== END GRADING [%s/%s points + %s/%s extra credit]' % + (total_points, max_total_points, extra_credit, max_extra_credit)) + + result_parts = [] + leaderboard = [] + for part in parts: + r = {'number': part.number, 'name': part.description} + + if self.params.summary: + # Just print out specification of the part + r['description'] = part.description + r['max_seconds'] = part.max_seconds + r['max_points'] = part.max_points + r['extra_credit'] = part.extra_credit + r['basic'] = part.basic + else: + r['score'] = part.points + # Force max_score to be 0 for extra credits for displaying correct total points on Gradescope + r['max_score'] = 0 if (part.extra_credit and self.mode == AUTO_MODE) else part.max_points + r["visibility"] = "after_published" if part.is_hidden() else "visible" + r['seconds'] = part.seconds + if part.side is not None: + r['side'] = part.side + r['output'] = "\n".join(part.messages) + + if part.side is not None: + for k in part.side: + leaderboard.append({"name": k, "value": part.side[k]}) + result_parts.append(r) + result['tests'] = result_parts + result['leaderboard'] = leaderboard + + self.output(self.mode, result) + + def display(name, select_extra_credit): + parts_to_display = [p for p in self.parts if p.extra_credit == select_extra_credit] + max_basic_points = sum(p.max_points for p in parts_to_display if p.is_basic()) + max_hidden_points = sum(p.max_points for p in parts_to_display if p.is_hidden()) + max_manual_points = sum(p.max_points for p in parts_to_display if p.is_manual()) + max_total_points_found = max_basic_points + max_hidden_points + max_manual_points + print("Total %s (basic auto/coding + hidden auto/coding + manual/written): %d + %d + %d = %d" % + (name, max_basic_points, max_hidden_points, max_manual_points, max_total_points_found)) + if not select_extra_credit and max_total_points_found != 75: + print('WARNING: max_total_points = {} is not 75'.format(max_total_points_found)) + + if self.params.summary: + display('points', False) + display('extra credit', True) + + def output(self, mode, result): + if self.params.json: + path = 'grader-{}.json'.format(mode) + with open(path, 'w') as out: + print(json.dumps(result), file=out) + print('Wrote to %s' % path) + if self.params.js: + path = 'grader-{}.js'.format(mode) + with open(path, 'w') as out: + print('var ' + mode + 'Result = ' + json.dumps(result) + ';', file=out) + print('Wrote to %s' % path) + + # Called by the grader to modify state of the current part + + def add_points(self, amt): + self.currentPart.points += amt + + def assign_full_credit(self): + if not self.currentPart.failed: + self.currentPart.points = self.currentPart.max_points + return True + + def assign_partial_credit(self, credit): + self.currentPart.points = credit + return True + + def set_side(self, side): + self.currentPart.side = side + + @staticmethod + def truncate_string(string, length=200): + if len(string) <= length: + return string + else: + return string[:length] + '...' + + def require_is_numeric(self, answer): + if isinstance(answer, int) or isinstance(answer, float): + return self.assign_full_credit() + else: + return self.fail("Expected either int or float, but got '%s'" % self.truncate_string(answer)) + + def require_is_one_of(self, true_answers, pred_answer): + if pred_answer in true_answers: + return self.assign_full_credit() + else: + return self.fail("Expected one of %s, but got '%s'" % ( + self.truncate_string(true_answers), self.truncate_string(pred_answer))) + + def require_is_equal(self, true_answer, pred_answer, tolerance=TOLERANCE): + if is_equal(true_answer, pred_answer, tolerance): + return self.assign_full_credit() + else: + return self.fail("Expected '%s', but got '%s'" % ( + self.truncate_string(str(true_answer)), self.truncate_string(str(pred_answer)))) + + def require_is_less_than(self, less_than_quantity, pred_answer): + if pred_answer < less_than_quantity: + return self.assign_full_credit() + else: + return self.fail("Expected to be < %f, but got %f" % (less_than_quantity, pred_answer)) + + def require_is_greater_than(self, greater_than_quantity, pred_answer): + if pred_answer > greater_than_quantity: + return self.assign_full_credit() + else: + return self.fail("Expected to be > %f, but got %f" % + (greater_than_quantity, pred_answer)) + + def require_is_true(self, pred_answer): + if pred_answer: + return self.assign_full_credit() + else: + return self.fail("Expected to be true, but got false") + + def fail(self, message): + print('FAIL:', message) + self.add_message(message) + if self.currentPart: + self.currentPart.points = 0 + self.currentPart.fail() + return False + + def print_exception(self): + tb = [item for item in traceback.extract_tb(sys.exc_info()[2]) if not is_traceback_item_grader(item)] + for item in traceback.format_list(tb): + self.fail('%s' % item) + + def add_message(self, message): + if not self.useSolution: + print(message) + if self.currentPart: + self.currentPart.messages.append(message) + else: + self.messages.append(message) diff --git a/hw2/ints/logic.py b/hw2/ints/logic.py new file mode 100644 index 0000000..ed99c9d --- /dev/null +++ b/hw2/ints/logic.py @@ -0,0 +1,1084 @@ +# Simple logical inference system: resolution and model checking for first-order logic. +# @author Percy Liang + +import collections + + +# Recursively apply str inside map +def rstr(x): + if isinstance(x, tuple): return str(tuple(map(rstr, x))) + if isinstance(x, list): return str(list(map(rstr, x))) + if isinstance(x, set): return str(set(map(rstr, x))) + if isinstance(x, dict): + newx = {} + for k, v in list(x.items()): + newx[rstr(k)] = rstr(v) + return str(newx) + return str(x) + + +class Expression: + # Helper functions used by subclasses. + def ensureType(self, arg, wantedType): + if not isinstance(arg, wantedType): + raise Exception('%s: wanted %s, but got %s' % (self.__class__.__name__, wantedType, arg)) + return arg + + def ensureFormula(self, arg): + return self.ensureType(arg, Formula) + + def ensureFormulas(self, args): + for arg in args: self.ensureFormula(arg) + return args + + def isa(self, wantedType): + return isinstance(self, wantedType) + + def join(self, args): + return ','.join(str(arg) for arg in args) + + def __eq__(self, other): + return str(self) == str(other) + + def __hash__(self): + return hash(str(self)) + + # Cache the string to be more efficient + def __repr__(self): + if not self.strRepn: self.strRepn = self.computeStrRepn() + return self.strRepn + + +# A Formula represents a truth value. +class Formula(Expression): pass + + +# A Term coresponds to an object. +class Term(Expression): pass + + +# Variable symbol (must start with '$') +# Example: $x +class Variable(Term): + def __init__(self, name): + if not name.startswith('$'): raise Exception('Variable must start with "$", but got %s' % name) + self.name = name + self.strRepn = None + + def computeStrRepn(self): return self.name + + +# Constant symbol (must be uncapitalized) +# Example: john +class Constant(Term): + def __init__(self, name): + if not name[0].islower(): raise Exception('Constants must start with a lowercase letter, but got %s' % name) + self.name = name + self.strRepn = None + + def computeStrRepn(self): return self.name + + +# Predicate symbol (must be capitalized) applied to arguments. +# Example: LivesIn(john, palo_alto) +class Atom(Formula): + def __init__(self, name, *args): + if not name[0].isupper(): raise Exception('Predicates must start with a uppercase letter, but got %s' % name) + self.name = name + self.args = list(map(toExpr, args)) + self.strRepn = None + + def computeStrRepn(self): + if len(self.args) == 0: return self.name + return self.name + '(' + self.join(self.args) + ')' + + +def toExpr(x): + if isinstance(x, str): + if x.startswith('$'): return Variable(x) + return Constant(x) + return x + + +AtomFalse = False +AtomTrue = True + + +# Example: Not(Rain) +class Not(Formula): + def __init__(self, arg): + self.arg = self.ensureFormula(arg) + self.strRepn = None + + def computeStrRepn(self): return 'Not(' + str(self.arg) + ')' + + +# Example: And(Rain,Snow) +class And(Formula): + def __init__(self, arg1, arg2): + self.arg1 = self.ensureFormula(arg1) + self.arg2 = self.ensureFormula(arg2) + self.strRepn = None + + def computeStrRepn(self): return 'And(' + str(self.arg1) + ',' + str(self.arg2) + ')' + + +# Example: Or(Rain,Snow) +class Or(Formula): + def __init__(self, arg1, arg2): + self.arg1 = self.ensureFormula(arg1) + self.arg2 = self.ensureFormula(arg2) + self.strRepn = None + + def computeStrRepn(self): return 'Or(' + str(self.arg1) + ',' + str(self.arg2) + ')' + + +# Example: Implies(Rain,Wet) +class Implies(Formula): + def __init__(self, arg1, arg2): + self.arg1 = self.ensureFormula(arg1) + self.arg2 = self.ensureFormula(arg2) + self.strRepn = None + + def computeStrRepn(self): return 'Implies(' + str(self.arg1) + ',' + str(self.arg2) + ')' + + +# Example: Exists($x,Lives(john, $x)) +class Exists(Formula): + def __init__(self, var, body): + self.var = self.ensureType(toExpr(var), Variable) + self.body = self.ensureFormula(body) + self.strRepn = None + + def computeStrRepn(self): return 'Exists(' + str(self.var) + ',' + str(self.body) + ')' + + +# Example: Forall($x,Implies(Human($x),Alive($x))) +class Forall(Formula): + def __init__(self, var, body): + self.var = self.ensureType(toExpr(var), Variable) + self.body = self.ensureFormula(body) + self.strRepn = None + + def computeStrRepn(self): return 'Forall(' + str(self.var) + ',' + str(self.body) + ')' + + +# Take a list of conjuncts / disjuncts and return a formula +def AndList(forms): + result = AtomTrue + for form in forms: + result = And(result, form) if result != AtomTrue else form + return result + + +def OrList(forms): + result = AtomFalse + for form in forms: + result = Or(result, form) if result != AtomFalse else form + return result + + +# Return list of conjuncts of |form|. +# Example: And(And(A, Or(B, C)), Not(D)) => [A, Or(B, C), Not(D)] +def flattenAnd(form): + if form.isa(And): + return flattenAnd(form.arg1) + flattenAnd(form.arg2) + else: + return [form] + + +# Return list of disjuncts of |form|. +# Example: Or(Or(A, And(B, C)), D) => [A, And(B, C), Not(D)] +def flattenOr(form): + if form.isa(Or): + return flattenOr(form.arg1) + flattenOr(form.arg2) + else: + return [form] + + +# Syntactic sugar +def Equiv(a, b): return And(Implies(a, b), Implies(b, a)) + + +def Xor(a, b): return And(Or(a, b), Not(And(a, b))) + + +# Special predicate which is used internally (e.g., in propositionalization). +def Equals(x, y): return Atom('Equals', x, y) + + +# Given a predicate name (e.g., Parent), return a formula that asserts that +# that predicate is anti-reflexive +# (e.g., Not(Parent(x,x))). +def AntiReflexive(predicate): + # return Forall('$x', Not(Atom(predicate, '$x', '$x'))) + # Force Equals() to be used and show up in the models. + return Forall('$x', Forall('$y', Implies(Atom(predicate, '$x', '$y'), + Not(Equals('$x', '$y'))))) + + +############################################################ +# Simple inference rules + +# A Rule takes a sequence of argument Formulas and produces a set of result +# Formulas (possibly [] if the rule doesn't apply). +class Rule: + pass + + +class UnaryRule(Rule): + def applyRule(self, form): raise Exception('Override me') + + +class BinaryRule(Rule): + def applyRule(self, form1, form2): raise Exception('Override me') + + # Override if rule is symmetric to save a factor of 2. + def symmetric(self): return False + + +############################################################ +# Unification + +# Mutate |subst| with variable => bindings +# Return whether unification was successful +# Assume forms are in CNF. +# Note: we don't do occurs check because we don't have function symbols. +def unify(form1, form2, subst): + if form1.isa(Variable): return unifyTerms(form1, form2, subst) + if form1.isa(Constant): return unifyTerms(form1, form2, subst) + if form1.isa(Atom): + return form2.isa(Atom) and form1.name == form2.name and len(form1.args) == len(form2.args) and \ + all(unify(form1.args[i], form2.args[i], subst) for i in range(len(form1.args))) + if form1.isa(Not): + return form2.isa(Not) and unify(form1.arg, form2.arg, subst) + if form1.isa(And): + return form2.isa(And) and unify(form1.arg1, form2.arg1, subst) and unify(form1.arg2, form2.arg2, subst) + if form1.isa(Or): + return form2.isa(Or) and unify(form1.arg1, form2.arg1, subst) and unify(form1.arg2, form2.arg2, subst) + raise Exception('Unhandled: %s' % form1) + + +# Follow multiple links to get to x +def getSubst(subst, x): + while True: + y = subst.get(x) + if y == None: return x + x = y + + +def unifyTerms(a, b, subst): + # print 'unifyTerms', a, b, rstr(subst) + a = getSubst(subst, a) + b = getSubst(subst, b) + if a == b: return True + if a.isa(Variable): + subst[a] = b + elif b.isa(Variable): + subst[b] = a + else: + return False + return True + + +# Assume form in CNF. +def applySubst(form, subst): + if len(subst) == 0: return form + if form.isa(Variable): + # print 'applySubst', rstr(form), rstr(subst), rstr(subst.get(form, form)) + # return subst.get(form, form) + return getSubst(subst, form) + if form.isa(Constant): return form + if form.isa(Atom): return Atom(*[form.name] + [applySubst(arg, subst) for arg in form.args]) + if form.isa(Not): return Not(applySubst(form.arg, subst)) + if form.isa(And): return And(applySubst(form.arg1, subst), applySubst(form.arg2, subst)) + if form.isa(Or): return Or(applySubst(form.arg1, subst), applySubst(form.arg2, subst)) + raise Exception('Unhandled: %s' % form) + + +############################################################ +# Convert to CNF, Resolution rules + +def withoutElementAt(items, i): return items[0:i] + items[i + 1:] + + +def negateFormula(item): + return item.arg if item.isa(Not) else Not(item) + + +# Given a list of Formulas, return a new list with: +# - If A and Not(A) exists, return [AtomFalse] for conjunction, [AtomTrue] for disjunction +# - Remove duplicates +# - Sort the list +def reduceFormulas(items, mode): + for i in range(len(items)): + for j in range(i + 1, len(items)): + if negateFormula(items[i]) == items[j]: + if mode == And: + return [AtomFalse] + elif mode == Or: + return [AtomTrue] + else: + raise Exception("Invalid mode: %s" % mode) + items = sorted(set(items), key=str) + return items + + +# Generate a list of all subexpressions of a formula (including terms). +# Example: +# - Input: And(Atom('A', Constant('a')), Atom('B')) +# - Output: [And(Atom('A', Constant('a')), Atom('B')), Atom('A', Constant('a')), Constant('a'), Atom('B')] +def allSubexpressions(form): + subforms = [] + + def recurse(form): + subforms.append(form) + if form.isa(Variable): + pass + elif form.isa(Constant): + pass + elif form.isa(Atom): + for arg in form.args: recurse(arg) + elif form.isa(Not): + recurse(form.arg) + elif form.isa(And): + recurse(form.arg1); recurse(form.arg2) + elif form.isa(Or): + recurse(form.arg1); recurse(form.arg2) + elif form.isa(Implies): + recurse(form.arg1); recurse(form.arg2) + elif form.isa(Exists): + recurse(form.body) + elif form.isa(Forall): + recurse(form.body) + else: + raise Exception("Unhandled: %s" % form) + + recurse(form) + return subforms + + +# Return a list of the free variables in |form|. +def allFreeVars(form): + variables = [] + + def recurse(form, boundVars): + if form.isa(Variable): + if form not in boundVars: variables.append(form) + elif form.isa(Constant): + pass + elif form.isa(Atom): + for arg in form.args: recurse(arg, boundVars) + elif form.isa(Not): + recurse(form.arg, boundVars) + elif form.isa(And): + recurse(form.arg1, boundVars); recurse(form.arg2, boundVars) + elif form.isa(Or): + recurse(form.arg1, boundVars); recurse(form.arg2, boundVars) + elif form.isa(Implies): + recurse(form.arg1, boundVars); recurse(form.arg2, boundVars) + elif form.isa(Exists): + recurse(form.body, boundVars + [form.var]) + elif form.isa(Forall): + recurse(form.body, boundVars + [form.var]) + else: + raise Exception("Unhandled: %s" % form) + + recurse(form, []) + return variables + + +# Return |form| with all free occurrences of |var| replaced with |obj|. +def substituteFreeVars(form, var, obj): + def recurse(form, boundVars): + if form.isa(Variable): + if form == var: return obj + return form + elif form.isa(Constant): + return form + elif form.isa(Atom): + return Atom(*[form.name] + [recurse(arg, boundVars) for arg in form.args]) + elif form.isa(Not): + return Not(recurse(form.arg, boundVars)) + elif form.isa(And): + return And(recurse(form.arg1, boundVars), recurse(form.arg2, boundVars)) + elif form.isa(Or): + return Or(recurse(form.arg1, boundVars), recurse(form.arg2, boundVars)) + elif form.isa(Implies): + return Implies(recurse(form.arg1, boundVars), recurse(form.arg2, boundVars)) + elif form.isa(Exists): + if form.var == var: return form # Don't substitute inside + return Exists(form.var, recurse(form.body, boundVars + [form.var])) + elif form.isa(Forall): + if form.var == var: return form # Don't substitute inside + return Forall(form.var, recurse(form.body, boundVars + [form.var])) + else: + raise Exception("Unhandled: %s" % form) + + return recurse(form, []) + + +def allConstants(form): + return [x for x in allSubexpressions(form) if x.isa(Constant)] + + +class ToCNFRule(UnaryRule): + def __init__(self): + # For standardizing variables. + # For each existing variable name, the number of times it has occurred + self.varCounts = collections.Counter() + + def applyRule(self, form): + newForm = form + + # Step 1: remove implications + def removeImplications(form): + if form.isa(Atom): return form + if form.isa(Not): return Not(removeImplications(form.arg)) + if form.isa(And): return And(removeImplications(form.arg1), removeImplications(form.arg2)) + if form.isa(Or): return Or(removeImplications(form.arg1), removeImplications(form.arg2)) + if form.isa(Implies): return Or(Not(removeImplications(form.arg1)), removeImplications(form.arg2)) + if form.isa(Exists): return Exists(form.var, removeImplications(form.body)) + if form.isa(Forall): return Forall(form.var, removeImplications(form.body)) + raise Exception("Unhandled: %s" % form) + + newForm = removeImplications(newForm) + + # Step 2: push negation inwards (de Morgan) + def pushNegationInwards(form): + if form.isa(Atom): return form + if form.isa(Not): + if form.arg.isa(Not): # Double negation + return pushNegationInwards(form.arg.arg) + if form.arg.isa(And): # De Morgan + return Or(pushNegationInwards(Not(form.arg.arg1)), pushNegationInwards(Not(form.arg.arg2))) + if form.arg.isa(Or): # De Morgan + return And(pushNegationInwards(Not(form.arg.arg1)), pushNegationInwards(Not(form.arg.arg2))) + if form.arg.isa(Exists): + return Forall(form.arg.var, pushNegationInwards(Not(form.arg.body))) + if form.arg.isa(Forall): + return Exists(form.arg.var, pushNegationInwards(Not(form.arg.body))) + return form + if form.isa(And): return And(pushNegationInwards(form.arg1), pushNegationInwards(form.arg2)) + if form.isa(Or): return Or(pushNegationInwards(form.arg1), pushNegationInwards(form.arg2)) + if form.isa(Implies): return Or(Not(pushNegationInwards(form.arg1)), pushNegationInwards(form.arg2)) + if form.isa(Exists): return Exists(form.var, pushNegationInwards(form.body)) + if form.isa(Forall): return Forall(form.var, pushNegationInwards(form.body)) + raise Exception("Unhandled: %s" % form) + + newForm = pushNegationInwards(newForm) + + # Step 3: standardize variables: make sure all variables are different + # Don't modify subst; return a new version where var is mapped onto + # something that hasn't been seen before. + def updateSubst(subst, var): + self.varCounts[var.name] += 1 + newVar = Variable(var.name + str(self.varCounts[var.name])) + return dict(list(subst.items()) + [(var, newVar)]) + + def standardizeVariables(form, subst): + if form.isa(Variable): + if form not in subst: raise Exception("Free variable found: %s" % form) + return subst[form] + if form.isa(Constant): return form + if form.isa(Atom): return Atom(*([form.name] + [standardizeVariables(arg, subst) for arg in form.args])) + if form.isa(Not): return Not(standardizeVariables(form.arg, subst)) + if form.isa(And): return And(standardizeVariables(form.arg1, subst), standardizeVariables(form.arg2, subst)) + if form.isa(Or): return Or(standardizeVariables(form.arg1, subst), standardizeVariables(form.arg2, subst)) + if form.isa(Exists): + newSubst = updateSubst(subst, form.var) + return Exists(newSubst[form.var], standardizeVariables(form.body, newSubst)) + if form.isa(Forall): + newSubst = updateSubst(subst, form.var) + return Forall(newSubst[form.var], standardizeVariables(form.body, newSubst)) + raise Exception("Unhandled: %s" % form) + + newForm = standardizeVariables(newForm, {}) + + # Step 4: replace existentially quantified variables with Skolem functions + def skolemize(form, subst, scope): + if form.isa(Variable): return subst.get(form, form) + if form.isa(Constant): return form + if form.isa(Atom): return Atom(*[form.name] + [skolemize(arg, subst, scope) for arg in form.args]) + if form.isa(Not): return Not(skolemize(form.arg, subst, scope)) + if form.isa(And): return And(skolemize(form.arg1, subst, scope), skolemize(form.arg2, subst, scope)) + if form.isa(Or): return Or(skolemize(form.arg1, subst, scope), skolemize(form.arg2, subst, scope)) + if form.isa(Exists): + # Create a Skolem function that depends on the variables in the scope (list of variables) + # Example: + # - Suppose scope = [$x, $y] and form = Exists($z,F($z)). + # - Normally, we would return F(Z($x,$y)), where Z is a brand new Skolem function. + # - But since we don't have function symbols, we replace with a Skolem predicate: + # Forall($z,Implies(Z($z,$x,$y),F($z))) + # Important: when doing resolution, need to catch Not(Z($z,*,*)) as a contradiction. + if len(scope) == 0: + subst[form.var] = Constant('skolem' + form.var.name) + return skolemize(form.body, subst, scope) + else: + skolem = Atom(*['Skolem' + form.var.name, form.var] + scope) + return Forall(form.var, Or(Not(skolem), skolemize(form.body, subst, scope))) + if form.isa(Forall): + return Forall(form.var, skolemize(form.body, subst, scope + [form.var])) + raise Exception("Unhandled: %s" % form) + + newForm = skolemize(newForm, {}, []) + + # Step 5: remove universal quantifiers [note: need to do this before distribute, unlike Russell/Norvig book] + def removeUniversalQuantifiers(form): + if form.isa(Atom): return form + if form.isa(Not): return Not(removeUniversalQuantifiers(form.arg)) + if form.isa(And): return And(removeUniversalQuantifiers(form.arg1), removeUniversalQuantifiers(form.arg2)) + if form.isa(Or): return Or(removeUniversalQuantifiers(form.arg1), removeUniversalQuantifiers(form.arg2)) + if form.isa(Forall): return removeUniversalQuantifiers(form.body) + raise Exception("Unhandled: %s" % form) + + newForm = removeUniversalQuantifiers(newForm) + + # Step 6: distribute Or over And (want And on the outside): Or(And(A,B),C) becomes And(Or(A,C),Or(B,C)) + def distribute(form): + if form.isa(Atom): return form + if form.isa(Not): return Not(distribute(form.arg)) + if form.isa(And): return And(distribute(form.arg1), distribute(form.arg2)) + if form.isa(Or): + # First need to distribute as much as possible + f1 = distribute(form.arg1) + f2 = distribute(form.arg2) + if f1.isa(And): + return And(distribute(Or(f1.arg1, f2)), distribute(Or(f1.arg2, f2))) + if f2.isa(And): + return And(distribute(Or(f1, f2.arg1)), distribute(Or(f1, f2.arg2))) + return Or(f1, f2) + if form.isa(Exists): return Exists(form.var, distribute(form.body)) + if form.isa(Forall): return Forall(form.var, distribute(form.body)) + raise Exception("Unhandled: %s" % form) + + newForm = distribute(newForm) + + # Post-processing: break up conjuncts into conjuncts and sort the disjuncts in each conjunct + # Remove instances of A and Not(A) + conjuncts = [OrList(reduceFormulas(flattenOr(f), Or)) for f in flattenAnd(newForm)] + # print rstr(form), rstr(conjuncts) + assert len(conjuncts) > 0 + if any(x == AtomFalse for x in conjuncts): return [AtomFalse] + if all(x == AtomTrue for x in conjuncts): return [AtomTrue] + conjuncts = [x for x in conjuncts if x != AtomTrue] + results = reduceFormulas(conjuncts, And) + if len(results) == 0: results = [AtomFalse] + # print 'CNF', form, rstr(results) + return results + + +class ResolutionRule(BinaryRule): + # Assume formulas are in CNF + # Assume A and Not(A) don't both exist in a form (taken care of by CNF conversion) + def applyRule(self, form1, form2): + items1 = flattenOr(form1) + items2 = flattenOr(form2) + results = [] + # print 'RESOLVE', form1, form2 + for i, item1 in enumerate(items1): + for j, item2 in enumerate(items2): + subst = {} + if unify(negateFormula(item1), item2, subst): + newItems1 = withoutElementAt(items1, i) + newItems2 = withoutElementAt(items2, j) + newItems = [applySubst(item, subst) for item in newItems1 + newItems2] + + if len(newItems) == 0: # Contradiction: False + results = [AtomFalse] + break + + # print 'STEP: %s %s => %s %s' % (form1, form2, rstr(newItems), rstr(subst)) + result = OrList(reduceFormulas(newItems, Or)) + + # Not(Skolem$x($x,...)) is a contradiction + if isinstance(result, Not) and result.arg.name.startswith('Skolem'): + results = [AtomFalse] + break + + # Don't add redundant stuff + if result == AtomTrue: continue + if result in results: continue + + results.append(result) + if results == [AtomFalse]: break + + # print 'RESOLUTION: %s %s => %s' % (form1, form2, rstr(results)) + return results + + def symmetric(self): + return True + + +############################################################ +# Model checking + +# Return the set of models +def performModelChecking(allForms, findAll, objects=None, verbose=0): + if verbose >= 3: + print(('performModelChecking', rstr(allForms))) + # Propositionalize, convert to CNF, dedup + allForms = propositionalize(allForms, objects) + # Convert to CNF: actually makes things slower + # allForms = [f for form in allForms for f in ToCNFRule().applyRule(form)] + # if any(x == AtomFalse for x in allForms): return [] + # if all(x == AtomTrue for x in allForms): return [set()] + # allForms = [x for x in allForms if x != AtomTrue] + # allForms = reduceFormulas(allForms, And) + allForms = [universalInterpret(form) for form in allForms] + allForms = list(set(allForms) - set([AtomTrue, AtomFalse])) + if verbose >= 3: + print(('All Forms:', rstr(allForms))) + + if allForms == []: return [set()] # One model + if allForms == [AtomFalse]: return [] # No models + + # Atoms are the variables + atoms = set() + for form in allForms: + for f in allSubexpressions(form): + if f.isa(Atom): atoms.add(f) + atoms = list(atoms) + + if verbose >= 3: + print(('Atoms:', rstr(atoms))) + print(('Constraints:', rstr(allForms))) + + # For each atom, list the set of formulas + # atom index => list of formulas + atomForms = [ + (atom, [form for form in allForms if atom in allSubexpressions(form)]) \ + for atom in atoms \ + ] + # Degree heuristic + atomForms.sort(key=lambda x: -len(x[1])) + atoms = [atom for atom, form in atomForms] + + # Keep only the forms for an atom if it only uses atoms up until that point. + atomPrefixForms = [] + for i, (atom, forms) in enumerate(atomForms): + prefixForms = [] + for form in forms: + useAtoms = set(x for x in allSubexpressions(form) if x.isa(Atom)) + if useAtoms <= set(atoms[0:i + 1]): + prefixForms.append(form) + atomPrefixForms.append((atom, prefixForms)) + + if verbose >= 3: + print('Plan:') + for atom, forms in atomForms: + print((" %s: %s" % (rstr(atom), rstr(forms)))) + assert sum(len(forms) for atom, forms in atomPrefixForms) == len(allForms) + + # Build up an interpretation + N = len(atoms) + models = [] # List of models which are true + model = set() # Set of true atoms, mutated over time + + def recurse(i): # i: atom index + if not findAll and len(models) > 0: return + if i == N: # Found a model on which the formulas are true + models.append(set(model)) + return + atom, forms = atomPrefixForms[i] + result = universalInterpretAtom(atom) + if result == None or result == False: + if interpretForms(forms, model): recurse(i + 1) + if result == None or result == True: + model.add(atom) + if interpretForms(forms, model): recurse(i + 1) + model.remove(atom) + + recurse(0) + + if verbose >= 5: + print('Models:') + for model in models: + print((" %s" % rstr(model))) + + return models + + +# A model is a set of atoms. +def printModel(model): + for x in sorted(map(str, model)): + print(('*', x, '=', 'True')) + print(('*', '(other atoms if any)', '=', 'False')) + + +# Convert a first-order logic formula into a propositional formula, assuming +# database semantics. +# Example: Forall becomes And over all objects +# - Input: form = Forall('$x', Atom('Alive', '$x')), objects = ['alice', 'bob'] +# - Output: And(Atom('Alive', 'alice'), Atom('Alive', 'bob')) +# Example: Exists becomes Or over all objects +# - Input: form = Exists('$x', Atom('Alive', '$x')), objects = ['alice', 'bob'] +# - Output: Or(Atom('Alive', 'alice'), Atom('Alive', 'bob')) +def propositionalize(forms, objects=None): + # If not specified, set objects to all constants mentioned in in |form|. + if objects == None: + objects = set() + for form in forms: + objects |= set(allConstants(form)) + objects = list(objects) + else: + # Make sure objects are expressions: Convert ['a', 'b'] to [Constant('a'), Constant('b')] + objects = [toExpr(obj) for obj in objects] + + # Recursively convert |form|, which could contain Exists and Forall, to forms that don't contain these quantifiers. + # |subst| is a map from variables to constants. + def convert(form, subst): + if form.isa(Variable): + if form not in subst: raise Exception("Free variable found: %s" % form) + return subst[form] + if form.isa(Constant): return form + if form.isa(Atom): + return Atom(*[form.name] + [convert(arg, subst) for arg in form.args]) + if form.isa(Not): return Not(convert(form.arg, subst)) + if form.isa(And): return And(convert(form.arg1, subst), convert(form.arg2, subst)) + if form.isa(Or): return Or(convert(form.arg1, subst), convert(form.arg2, subst)) + if form.isa(Implies): return Implies(convert(form.arg1, subst), convert(form.arg2, subst)) + if form.isa(Exists): + return OrList([convert(form.body, dict(list(subst.items()) + [(form.var, obj)])) for obj in objects]) + if form.isa(Forall): + return AndList([convert(form.body, dict(list(subst.items()) + [(form.var, obj)])) for obj in objects]) + raise Exception("Unhandled: %s" % form) + + # Think of newForms as conjoined + newForms = [] + # Convert all the forms + for form in forms: + newForm = convert(form, {}) + if newForm == AtomFalse: return [AtomFalse] + if newForm == AtomTrue: continue + newForms.extend(flattenAnd(newForm)) + return newForms + + +# Some atoms have a fixed value, so we should just evaluate them. +# Assumption: atom is propositional logic. +def universalInterpretAtom(atom): + if atom.name == 'Equals': + return AtomTrue if atom.args[0] == atom.args[1] else AtomFalse + return None + + +# Reduce the expression (e.g., Equals(a,a) => True) +# Assumption: atom is propositional logic. +def universalInterpret(form): + if form.isa(Variable): return form + if form.isa(Constant): return form + if form.isa(Atom): + result = universalInterpretAtom(form) + if result != None: return result + return Atom(*[form.name] + [universalInterpret(arg) for arg in form.args]) + if form.isa(Not): + arg = universalInterpret(form.arg) + if arg == AtomTrue: return AtomFalse + if arg == AtomFalse: return AtomTrue + return Not(arg) + if form.isa(And): + arg1 = universalInterpret(form.arg1) + arg2 = universalInterpret(form.arg2) + if arg1 == AtomFalse: return AtomFalse + if arg2 == AtomFalse: return AtomFalse + if arg1 == AtomTrue: return arg2 + if arg2 == AtomTrue: return arg1 + return And(arg1, arg2) + if form.isa(Or): + arg1 = universalInterpret(form.arg1) + arg2 = universalInterpret(form.arg2) + if arg1 == AtomTrue: return AtomTrue + if arg2 == AtomTrue: return AtomTrue + if arg1 == AtomFalse: return arg2 + if arg2 == AtomFalse: return arg1 + return Or(arg1, arg2) + if form.isa(Implies): + arg1 = universalInterpret(form.arg1) + arg2 = universalInterpret(form.arg2) + if arg1 == AtomFalse: return AtomTrue + if arg2 == AtomTrue: return AtomTrue + if arg1 == AtomTrue: return arg2 + if arg2 == AtomFalse: return Not(arg1) + return Implies(arg1, arg2) + raise Exception("Unhandled: %s" % form) + + +def interpretForm(form, model): + if form.isa(Atom): return form in model + if form.isa(Not): return not interpretForm(form.arg, model) + if form.isa(And): return interpretForm(form.arg1, model) and interpretForm(form.arg2, model) + if form.isa(Or): return interpretForm(form.arg1, model) or interpretForm(form.arg2, model) + if form.isa(Implies): return not interpretForm(form.arg1, model) or interpretForm(form.arg2, model) + raise Exception("Unhandled: %s" % form) + + +# Conjunction +def interpretForms(forms, model): + return all(interpretForm(form, model) for form in forms) + + +############################################################ + +# A Derivation is a tree where each node corresponds to the application of a rule. +# For any Formula, we can extract a set of categories. +# Rule arguments are labeled with category. +class Derivation: + def __init__(self, form, children, cost, derived): + self.form = form + self.children = children + self.cost = cost + self.permanent = False # Marker for being able to extract. + self.derived = derived # Whether this was derived (as opposed to added by the user). + + def __repr__(self): return 'Derivation(%s, cost=%s, permanent=%s, derived=%s)' % ( + self.form, self.cost, self.permanent, self.derived) + + +# Possible responses to queries to the knowledge base +ENTAILMENT = "ENTAILMENT" +CONTINGENT = "CONTINGENT" +CONTRADICTION = "CONTRADICTION" + + +# A response to a KB query +class KBResponse: + # query: what the query is (just a string description for printing) + # modify: whether we modified the knowledge base + # status: one of the ENTAILMENT, CONTINGENT, CONTRADICTION + # trueModel: if available, a model consistent with the KB for which the the query is true + # falseModel: if available, a model consistent with the KB for which the the query is false + def __init__(self, query, modify, status, trueModel, falseModel): + self.query = query + self.modify = modify + self.status = status + self.trueModel = trueModel + self.falseModel = falseModel + + def show(self, verbose=1): + padding = '>>>>>' + print(padding + ' ' + self.responseStr()) + if verbose >= 1: + print(('Query: %s[%s]' % ('TELL' if self.modify else 'ASK', self.query))) + if self.trueModel: + print('An example of a model where query is TRUE:') + printModel(self.trueModel) + if self.falseModel: + print('An example of a model where query is FALSE:') + printModel(self.falseModel) + + def responseStr(self): + if self.status == ENTAILMENT: + if self.modify: + return 'I already knew that.' + else: + return 'Yes.' + elif self.status == CONTINGENT: + if self.modify: + return 'I learned something.' + else: + return 'I don\'t know.' + elif self.status == CONTRADICTION: + if self.modify: + return 'I don\'t buy that.' + else: + return 'No.' + else: + raise Exception("Invalid status: %s" % self.status) + + def __repr__(self): + return self.responseStr() + + +def showKBResponse(response, verbose=1): + if isinstance(response, KBResponse): + response.show(verbose) + else: + items = [(obj, r.status) for ((var, obj), r) in list(response.items())] + print(('Yes: %s' % rstr([obj for obj, status in items if status == ENTAILMENT]))) + print(('Maybe: %s' % rstr([obj for obj, status in items if status == CONTINGENT]))) + print(('No: %s' % rstr([obj for obj, status in items if status == CONTRADICTION]))) + + +# A KnowledgeBase is a set collection of Formulas. +# Interact with it using +# - addRule: add inference rules +# - tell: modify the KB with a new formula. +# - ask: query the KB about +class KnowledgeBase: + def __init__(self, standardizationRule, rules, modelChecking, verbose=0): + # Rule to apply to each formula that's added to the KB (None is possible). + self.standardizationRule = standardizationRule + + # Set of inference rules + self.rules = rules + + # Use model checking as opposed to applying rules. + self.modelChecking = modelChecking + + # For debugging + self.verbose = verbose + + # Formulas that we believe are true (used when not doing model checking). + self.derivations = {} # Map from Derivation key (logical form) to Derivation + + # Add a formula |form| to the KB if it doesn't contradict. Returns a KBResponse. + def tell(self, form): + return self.query(form, modify=True) + + # Ask whether the logical formula |form| is True, False, or unknown based + # on the KB. Returns a KBResponse. + def ask(self, form): + return self.query(form, modify=False) + + def dump(self): + print(('==== Knowledge base [%d derivations] ===' % len(self.derivations))) + for deriv in list(self.derivations.values()): + print((('-' if deriv.derived else '*'), deriv if self.verbose >= 2 else deriv.form)) + + ####### Internal functions + + # Returns a KBResponse or if there are free variables, a mapping from (var, obj) => query without that variable. + def query(self, form, modify): + # print 'QUERY', form + # Handle wh-queries: try all possible values of the free variable, and recurse on query(). + freeVars = allFreeVars(form) + if len(freeVars) > 0: + if modify: + raise Exception("Can't modify database with a query with free variables: %s" % form) + var = freeVars[0] + allForms = AndList([deriv.form for deriv in list(self.derivations.values())]) + if allForms == AtomTrue: return {} # Weird corner case + objects = allConstants(allForms) + # Try binding |var| to |obj| + response = {} + for obj in objects: + response[(var, obj)] = self.query(substituteFreeVars(form, var, obj), modify) + return response + + # Assume no free variables from here on... + formStr = '%s, standardized: %s' % (form, rstr(self.standardize(form))) + + # Models to serve as supporting evidence + falseModel = None # Makes the query false + trueModel = None # Makes the query true + + # Add Not(form) + if not self.addAxiom(Not(form)): + self.removeTemporary() + status = ENTAILMENT + else: + # Inconclusive... + falseModel = self.consistentModel + self.removeTemporary() + + # Add form + if self.addAxiom(form): + if modify: + self.makeTemporaryPermanent() + else: + self.removeTemporary() + trueModel = self.consistentModel + status = CONTINGENT + else: + self.removeTemporary() + status = CONTRADICTION + + return KBResponse(query=formStr, modify=modify, status=status, trueModel=trueModel, falseModel=falseModel) + + # Apply the standardization rule to |form|. + def standardize(self, form): + if self.standardizationRule: + return self.standardizationRule.applyRule(form) + return [form] + + # Return whether adding |form| is consistent with the current knowledge base. + # Add |form| to the knowledge base if we can. Note: this is done temporarily! + # Just calls addDerivation. + def addAxiom(self, form): + self.consistentModel = None + for f in self.standardize(form): + if f == AtomFalse: return False + if f == AtomTrue: continue + deriv = Derivation(f, children=[], cost=0, derived=False) + if not self.addDerivation(deriv): return False + return True + + # Return whether the Derivation is consistent with the KB. + def addDerivation(self, deriv): + # Derived a contradiction + if deriv.form == AtomFalse: return False + + key = deriv.form + oldDeriv = self.derivations.get(key) + maxCost = 100 + if oldDeriv == None and deriv.cost <= maxCost: + # if oldDeriv == None or (deriv.cost < oldDeriv.cost and (deriv.permanent >= oldDeriv.permanent)): + # print 'UPDATE %s %s' % (deriv, oldDeriv) + # self.dump() + # Something worth updating + self.derivations[key] = deriv + if self.verbose >= 3: print(('add %s [%s derivations]' % (deriv, len(self.derivations)))) + + if self.modelChecking: + allForms = [deriv.form for deriv in list(self.derivations.values())] + models = performModelChecking(allForms, findAll=False, verbose=self.verbose) + if len(models) == 0: + return False + else: + self.consistentModel = models[0] + + # Apply rules forward + if not self.applyUnaryRules(deriv): return False + for key2, deriv2 in list(self.derivations.items()): + if not self.applyBinaryRules(deriv, deriv2): return False + if not self.applyBinaryRules(deriv2, deriv): return False + + return True + + # Raise an exception if |formulas| is not a list of Formulas. + def ensureFormulas(self, rule, formulas): + if isinstance(formulas, list) and all(formula == False or isinstance(formula, Formula) for formula in formulas): + return formulas + raise Exception('Expected list of Formulas, but %s returned %s' % (rule, formulas)) + + # Return whether everything is okay (no contradiction). + def applyUnaryRules(self, deriv): + for rule in self.rules: + if not isinstance(rule, UnaryRule): continue + for newForm in self.ensureFormulas(rule, rule.applyRule(deriv.form)): + if not self.addDerivation(Derivation(newForm, children=[deriv], cost=deriv.cost + 1, derived=True)): + return False + return True + + # Return whether everything is okay (no contradiction). + def applyBinaryRules(self, deriv1, deriv2): + for rule in self.rules: + if not isinstance(rule, BinaryRule): continue + if rule.symmetric() and str(deriv1.form) >= str(deriv2.form): continue # Optimization + for newForm in self.ensureFormulas(rule, rule.applyRule(deriv1.form, deriv2.form)): + if not self.addDerivation( + Derivation(newForm, children=[deriv1, deriv2], cost=deriv1.cost + deriv2.cost + 1, + derived=True)): + return False + return True + + # Remove all the temporary derivations from the KB. + def removeTemporary(self): + for key, value in list(self.derivations.items()): + if not value.permanent: + del self.derivations[key] + + # Mark all the derivations marked temporary to permanent. + def makeTemporaryPermanent(self): + for deriv in list(self.derivations.values()): + deriv.permanent = True + + +# Create an empty knowledge base equipped with the usual inference rules. +def createResolutionKB(): + return KnowledgeBase(standardizationRule=ToCNFRule(), rules=[ResolutionRule()], modelChecking=False) + + +def createModelCheckingKB(): + return KnowledgeBase(standardizationRule=None, rules=[], modelChecking=True) diff --git a/hw2/ints/models/4a-0.pklz b/hw2/ints/models/4a-0.pklz new file mode 100644 index 0000000000000000000000000000000000000000..411c8fa0088410675609f97f7e4b153aa2887df2 GIT binary patch literal 395 zcmV;60d)Q!iwFpH@p@wd|1@DOFfMRwYmiBWEDYP97*QA%-T?1~&9?xSH_GL6*Y|@sjyf1K zt!C#X#&`o0fBR2S7$?n;sgukoC`<{mDCZ6HaGZ2x@E)Q_xo(Sezoam&`*|u-zS|0@ z=uQ215mCJsxi)5aUT2zBnA7uP#GdnlN>oVMacfcC#=`GTSz)oivm}gfMPXTMS@zBH zTq%X(80QsE^@UZ5HR3m|3z{|1s=`Jex+$nYmGtnAjV(4PGh|z0M?-|55h@#ut+3n2 z?CEGv?EW|Hhn9B9a)pejRbmX0JGE!8!*7td8V?sHEBRZ{=tm_MBw?wQ27hFs_i ptK_nDDRHHxYt40y)s4ihmhQBBPr8?Q2)^-n@B=#nKO=hr005vxz2yJ^ literal 0 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zJjqgDuuNmQ6`U;fBqQo!!3w_4Z8(K+s^Sel%~5@7Kn<$2TBI_@X{E;LwudvMheUJ_ zJnkw#eO%*A(U@CY?R6a7BA0v?gGKG1sdNc8ap8u4=F=2v-VrRe+^^ zaGbB+gRUlMfv$;$#(ZouVT)i}!>^8v!8sy=Jd5g;a7F8L#op6UhcM2rPfQ7slAkbZey9K%@fV^!C zJKamTPoVpQxF!@hJwSL+pohHCgSRY^!IOKK@Q7fKwqsuNP3$qk$aNO(!mm)p@6PlLWfcvaBXJoNu= z;&s9sg1y;_Wm-Yw_!i-9LEj0`bO;Wk?-Je<^!-jWDBMFoAbcq3N8ux-Bhilup9uPC zt8451c<5(@&jtOW)inzJlJJ$FUxyp$+{SMR-wO6!7|XPS#_@Z?4}$*KIcKmS9{LmE zXF-1n&)K= Tuple[List[Formula], Formula]: + def Even(x): return Atom('Even', x) # whether x is even + + def Odd(x): return Atom('Odd', x) # whether x is odd + + def Successor(x, y): return Atom('Successor', x, y) # whether x's successor is y + + def Larger(x, y): return Atom('Larger', x, y) # whether x is larger than y + + # Note: all objects are numbers, so we don't need to define Number as an + # explicit predicate. + # + # Note: pay attention to the order of arguments of Successor and Larger. + # Populate `formulas` with the 6 laws above. + # + # Hint: You might want to use the Equals predicate, defined in logic.py. This + # predicate is used to assert that two objects are the same. + formulas = [] + formulas.append(Forall('$x', Exists('$y', And(Successor('$x', '$y'), And(Not(Equals('$x', '$y')), Forall('$z', Implies(Not(Equals('$z', '$y')), Not(Successor('$x', '$z'))))))))) + formulas.append(Forall('$x', Or(And(Even('$x'), Not(Odd('$x'))), And(Odd('$x'), Not(Even('$x')))))) + formulas.append(Forall('$x', Implies(Even('$x'), Exists('$y', Odd(Successor('$x', '$y')))))) + formulas.append(Forall('$x', Implies(Odd('$x'), Exists('$y', Even(Successor('$x', '$y')))))) + formulas.append(Forall('$x', Implies(Exists('$y', Successor('$x', '$y')), Larger('$y', '$x')))) + formulas.append(Forall('$x', Forall('$y', Forall('$z', Implies(And(Larger('$x', '$y'), Larger('$y', '$z')), Larger('$x', '$z')))))) + + query = Forall('$x', Exists('$y', And(Even('$y'), Larger('$y', '$x')))) + return formulas, query \ No newline at end of file diff --git a/hw2/knights/__pycache__/logic.cpython-312.pyc 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zn-6vr;-_>j*!@916oPylDdJue6m_IQ=ubLkUpvV6{Sx}{sMw!er9NhI>wkfDjFPr9x7m)rvF>>1YP$r1=Z?TX)9eDeQuS4pVgff`iW@E yDg{5Qotx-k8c*S9K=< literal 0 HcmV?d00001 diff --git a/hw2/knights/logic.py b/hw2/knights/logic.py new file mode 100644 index 0000000..627bec3 --- /dev/null +++ b/hw2/knights/logic.py @@ -0,0 +1,260 @@ +class Sentence: + + def evaluate(self, model): + """Evaluates the logical sentence.""" + raise Exception("nothing to evaluate") + + def formula(self): + """Returns string formula representing logical sentence.""" + return "" + + def symbols(self): + """Returns a set of all symbols in the logical sentence.""" + return set() + + @classmethod + def validate(cls, sentence): + if not isinstance(sentence, Sentence): + raise TypeError("must be a logical sentence") + + @classmethod + def parenthesize(cls, s): + """Parenthesizes an expression if not already parenthesized.""" + def balanced(s): + """Checks if a string has balanced parentheses.""" + count = 0 + for c in s: + if c == "(": + count += 1 + elif c == ")": + if count <= 0: + return False + count -= 1 + return count == 0 + if not len(s) or s.isalpha() or ( + s[0] == "(" and s[-1] == ")" and balanced(s[1:-1]) + ): + return s + else: + return f"({s})" + + +class Symbol(Sentence): + + def __init__(self, name): + self.name = name + + def __eq__(self, other): + return isinstance(other, Symbol) and self.name == other.name + + def __hash__(self): + return hash(("symbol", self.name)) + + def __repr__(self): + return self.name + + def evaluate(self, model): + try: + return bool(model[self.name]) + except KeyError: + raise Exception(f"variable {self.name} not in model") + + def formula(self): + return self.name + + def symbols(self): + return {self.name} + + +class Not(Sentence): + def __init__(self, operand): + Sentence.validate(operand) + self.operand = operand + + def __eq__(self, other): + return isinstance(other, Not) and self.operand == other.operand + + def __hash__(self): + return hash(("not", hash(self.operand))) + + def __repr__(self): + return f"Not({self.operand})" + + def evaluate(self, model): + return not self.operand.evaluate(model) + + def formula(self): + return "¬" + Sentence.parenthesize(self.operand.formula()) + + def symbols(self): + return self.operand.symbols() + + +class And(Sentence): + def __init__(self, *conjuncts): + for conjunct in conjuncts: + Sentence.validate(conjunct) + self.conjuncts = list(conjuncts) + + def __eq__(self, other): + return isinstance(other, And) and self.conjuncts == other.conjuncts + + def __hash__(self): + return hash( + ("and", tuple(hash(conjunct) for conjunct in self.conjuncts)) + ) + + def __repr__(self): + conjunctions = ", ".join( + [str(conjunct) for conjunct in self.conjuncts] + ) + return f"And({conjunctions})" + + def add(self, conjunct): + Sentence.validate(conjunct) + self.conjuncts.append(conjunct) + + def evaluate(self, model): + return all(conjunct.evaluate(model) for conjunct in self.conjuncts) + + def formula(self): + if len(self.conjuncts) == 1: + return self.conjuncts[0].formula() + return " ∧ ".join([Sentence.parenthesize(conjunct.formula()) + for conjunct in self.conjuncts]) + + def symbols(self): + return set.union(*[conjunct.symbols() for conjunct in self.conjuncts]) + + +class Or(Sentence): + def __init__(self, *disjuncts): + for disjunct in disjuncts: + Sentence.validate(disjunct) + self.disjuncts = list(disjuncts) + + def __eq__(self, other): + return isinstance(other, Or) and self.disjuncts == other.disjuncts + + def __hash__(self): + return hash( + ("or", tuple(hash(disjunct) for disjunct in self.disjuncts)) + ) + + def __repr__(self): + disjuncts = ", ".join([str(disjunct) for disjunct in self.disjuncts]) + return f"Or({disjuncts})" + + def evaluate(self, model): + return any(disjunct.evaluate(model) for disjunct in self.disjuncts) + + def formula(self): + if len(self.disjuncts) == 1: + return self.disjuncts[0].formula() + return " ∨ ".join([Sentence.parenthesize(disjunct.formula()) + for disjunct in self.disjuncts]) + + def symbols(self): + return set.union(*[disjunct.symbols() for disjunct in self.disjuncts]) + + +class Implication(Sentence): + def __init__(self, antecedent, consequent): + Sentence.validate(antecedent) + Sentence.validate(consequent) + self.antecedent = antecedent + self.consequent = consequent + + def __eq__(self, other): + return (isinstance(other, Implication) + and self.antecedent == other.antecedent + and self.consequent == other.consequent) + + def __hash__(self): + return hash(("implies", hash(self.antecedent), hash(self.consequent))) + + def __repr__(self): + return f"Implication({self.antecedent}, {self.consequent})" + + def evaluate(self, model): + return ((not self.antecedent.evaluate(model)) + or self.consequent.evaluate(model)) + + def formula(self): + antecedent = Sentence.parenthesize(self.antecedent.formula()) + consequent = Sentence.parenthesize(self.consequent.formula()) + return f"{antecedent} => {consequent}" + + def symbols(self): + return set.union(self.antecedent.symbols(), self.consequent.symbols()) + + +class Biconditional(Sentence): + def __init__(self, left, right): + Sentence.validate(left) + Sentence.validate(right) + self.left = left + self.right = right + + def __eq__(self, other): + return (isinstance(other, Biconditional) + and self.left == other.left + and self.right == other.right) + + def __hash__(self): + return hash(("biconditional", hash(self.left), hash(self.right))) + + def __repr__(self): + return f"Biconditional({self.left}, {self.right})" + + def evaluate(self, model): + return ((self.left.evaluate(model) + and self.right.evaluate(model)) + or (not self.left.evaluate(model) + and not self.right.evaluate(model))) + + def formula(self): + left = Sentence.parenthesize(str(self.left)) + right = Sentence.parenthesize(str(self.right)) + return f"{left} <=> {right}" + + def symbols(self): + return set.union(self.left.symbols(), self.right.symbols()) + + +def model_check(knowledge, query): + """Checks if knowledge base entails query.""" + + def check_all(knowledge, query, symbols, model): + """Checks if knowledge base entails query, given a particular model.""" + + # If model has an assignment for each symbol + if not symbols: + + # If knowledge base is true in model, then query must also be true + if knowledge.evaluate(model): + return query.evaluate(model) + return True + else: + + # Choose one of the remaining unused symbols + remaining = symbols.copy() + p = remaining.pop() + + # Create a model where the symbol is true + model_true = model.copy() + model_true[p] = True + + # Create a model where the symbol is false + model_false = model.copy() + model_false[p] = False + + # Ensure entailment holds in both models + return (check_all(knowledge, query, remaining, model_true) and + check_all(knowledge, query, remaining, model_false)) + + # Get all symbols in both knowledge and query + symbols = set.union(knowledge.symbols(), query.symbols()) + + # Check that knowledge entails query + return check_all(knowledge, query, symbols, dict()) \ No newline at end of file diff --git a/hw2/knights/puzzle.py b/hw2/knights/puzzle.py new file mode 100644 index 0000000..a72eced --- /dev/null +++ b/hw2/knights/puzzle.py @@ -0,0 +1,82 @@ +from logic import * + +AKnight = Symbol("A is a Knight") +AKnave = Symbol("A is a Knave") + +BKnight = Symbol("B is a Knight") +BKnave = Symbol("B is a Knave") + +CKnight = Symbol("C is a Knight") +CKnave = Symbol("C is a Knave") + +# Puzzle 0 +# A says "I am both a knight and a knave." +knowledge0 = And( + Or(AKnight, AKnave), # A is either a knight or a knave + Not(And(AKnight, AKnave)), # A cannot be both a knight and a knave + Biconditional(AKnight, And(AKnight, AKnave)) # If A is a knight, then the statement is true; if A is a knave, the statement is false +) + +# Puzzle 1 +# A says "We are both knaves." +# B says nothing. +knowledge1 = And( + Or(AKnight, AKnave), # A is either a knight or a knave + Or(BKnight, BKnave), # B is either a knight or a knave + Not(And(AKnight, AKnave)), # A cannot be both a knight and a knave + Not(And(BKnight, BKnave)), # B cannot be both a knight and a knave + Biconditional(AKnight, And(AKnave, BKnave)), # If A is a knight, then the statement is true; if A is a knave, the statement is false + Biconditional(AKnave, Not(And(AKnave, BKnave))) # If A is a knave, then the opposite of the statement is true +) + +# Puzzle 2 +# A says "We are the same kind." +# B says "We are of different kinds." +knowledge2 = And( + Or(AKnight, AKnave), # A is either a knight or a knave + Or(BKnight, BKnave), # B is either a knight or a knave + Not(And(AKnight, AKnave)), # A cannot be both a knight and a knave + Not(And(BKnight, BKnave)), # B cannot be both a knight and a knave + Biconditional(AKnight, Or(And(AKnight, BKnight), And(AKnave, BKnave))), # If A is a knight, then A's statement is true; if A is a knave, then A's statement is false + Biconditional(BKnight, Or(And(AKnight, BKnave), And(AKnave, BKnight))) # If B is a knight, then B's statement is true; if B is a knave, then B's statement is false +) + +# Puzzle 3 +# A says either "I am a knight." or "I am a knave.", but you don't know which. +# B says "A said 'I am a knave'." +# B says "C is a knave." +# C says "A is a knight." +knowledge3 = And( + Or(AKnight, AKnave), + Or(BKnight, BKnave), + Or(CKnight, CKnave), + Biconditional(AKnight, Not(AKnave)), + Biconditional(BKnight, Not(BKnave)), + Biconditional(CKnight, Not(CKnave)), + Implication(BKnight, Not(AKnave)), + Implication(BKnave, And(AKnight, CKnight)), + Implication(AKnight, CKnight), + Implication(AKnight, Not(BKnight)) +) + + +def main(): + symbols = [AKnight, AKnave, BKnight, BKnave, CKnight, CKnave] + puzzles = [ + ("Puzzle 0", knowledge0), + ("Puzzle 1", knowledge1), + ("Puzzle 2", knowledge2), + ("Puzzle 3", knowledge3) + ] + for puzzle, knowledge in puzzles: + print(puzzle) + if len(knowledge.conjuncts) == 0: + print(" Not yet implemented.") + else: + for symbol in symbols: + if model_check(knowledge, symbol): + print(f" {symbol}") + + +if __name__ == "__main__": + main() diff --git a/main.aux b/main.aux index cacda7b..afe5557 100644 --- a/main.aux +++ b/main.aux @@ -10,4 +10,8 @@ \@writefile{toc}{\contentsline {subsection}{\numberline {1.1}Grid City}{7}{}\protected@file@percent } \@writefile{toc}{\contentsline {subsection}{\numberline {1.2}Six Degrees}{8}{}\protected@file@percent } \@writefile{toc}{\contentsline {subsection}{\numberline {1.3}Tic Tac Toe}{8}{}\protected@file@percent } -\gdef \@abspage@last{9} +\@writefile{toc}{\contentsline {section}{\numberline {2}Homework 2}{8}{}\protected@file@percent } +\@writefile{toc}{\contentsline {subsection}{\numberline {2.1}Cake}{8}{}\protected@file@percent } +\@writefile{toc}{\contentsline {subsection}{\numberline {2.2}Knights and Knaves}{10}{}\protected@file@percent } +\@writefile{toc}{\contentsline {subsection}{\numberline {2.3}Odds and Evens}{10}{}\protected@file@percent } +\gdef \@abspage@last{11} diff --git a/main.fdb_latexmk b/main.fdb_latexmk index 36f9914..2339b38 100644 --- a/main.fdb_latexmk +++ b/main.fdb_latexmk @@ -1,8 +1,8 @@ # Fdb version 4 -["pdflatex"] 1709000449.89094 "c:/Users/uzair/OneDrive/Documents/CSC 665/main.tex" "main.pdf" "main" 1709000450.74539 0 - "C:/Users/uzair/AppData/Local/MiKTeX/fonts/map/pdftex/pdftex.map" 1707457733 80909 eab91d9745dd2edfd62a31d53cd5fe15 "" - "C:/Users/uzair/AppData/Local/MiKTeX/fonts/pk/ljfour/jknappen/ec/dpi600/tcrm1000.pk" 1707288887 11548 1854d2b3451e3d517cccd4e0b4daead1 "" - "C:/Users/uzair/AppData/Local/MiKTeX/miktex/data/le/pdftex/pdflatex.fmt" 1707288883 24210786 eea8c83a2618bf979528f763e32e98c9 "" +["pdflatex"] 1710976757.77869 "c:/Users/uzair/OneDrive/Documents/Programming/classes/spring-2024/CSC_665_Homework/main.tex" "main.pdf" "main" 1710976758.61168 0 + 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maximize the cake they receive. + \begin{enumerate} + \item 1/2 + \item 1/2 + \item 1/2 + \end{enumerate} + \item [b. ] Alice still trying to maximize, Bob now playing collaboratively and helping Alice. + \begin{enumerate} + \item 2/3 + \item 1/2 + \item 2/3 + \end{enumerate} + \item [c. ] Random play. + \begin{enumerate} + \item Node 2 or 3 + \item Doesn't matter because of constant utility + \item Node 3 + \end{enumerate} + \item [d. ] Alpha Beta pruning + \begin{enumerate} + \item Leaf notes with utility 1/3, 1/3, 1/3, 1/3 on left, and right leaf node with utility 1/6 + \end{enumerate} + \item [e. ] Alpha Beta pruning with tree elements swapped. + \begin{enumerate} + \item No nodes are pruned + \end{enumerate} + \end{itemize} + + \begin{itemize} + \item [2. ] Logical Formulas + \begin{itemize} + \item [a. ] $(P \land \neg Q) \lor (\neg P \land Q)$ + \item [b. ] $(\exists x \text{Course}(x) \land \text{Enrolled}(A, x) \land \text{Enrolled}(B,x))$ + \item [c. ] $(\forall x \text{Course}(x) \land \text{Enrolled}(A, x) \rightarrow \text{Enrolled}(B,x))$ + \item [d. ] $\forall x \forall y (\text{Enrolled}(x,y) \land \text{Course}(y) \rightarrow \text{Student}(x))$ + \item [e. ] $\forall x (\text{Course}(x) \rightarrow \exists y (\text{Student}(y) \land \text{Enrolled}(y,x)))$ + \end{itemize} + \end{itemize} + + \subsection{Knights and Knaves} + See attached puzzle.py file + + \subsection{Odds and Evens} + See attached submission.py file + + \end{document} \ No newline at end of file