Lecture 20a Feature Based Grammars Topics Description Logic III Overview of MeaningReadings: Text Chapter 18 NLTK book Chapter 10 March 28, 2013 CSCE 771 Natural Language Processing

– 2 – CSCE 771 Spring 2013 Overview Last Time (Programming) Computational SemanticsToday Feature based grammarsReadings: Text NLTK Book: Chapters 9 and 10 Next Time: Computational Lexical Semantics

– 3 – CSCE 771 Spring 2013 Automated Reasoning Services Satisfiability: A concept C is satisfiable with respect to T if there exists a model I of T such that C I ≠ ∅. We also say that I is a model of C. Satisfiability: A concept C is satisfiable with respect to T if there exists a model I of T such that C I ≠ ∅. We also say that I is a model of C. Subsumption: A concept C 1 is subsumed by a concept C 2 with respect to T if CI ⊆ CI for every model I of T. We also write C 1 ⊑ T C 2 or T |= C 1 ⊑ C 2. Subsumption: A concept C 1 is subsumed by a concept C 2 with respect to T if CI ⊆ CI for every model I of T. We also write C 1 ⊑ T C 2 or T |= C 1 ⊑ C 2. Equivalence: Two concepts C 1 and C 2 are equivalent with respect to T if C 1 I = C 2 I for every model I of T. We also write C 1 ≡T C 2 or T |= C 1 ≡ C 2. Equivalence: Two concepts C 1 and C 2 are equivalent with respect to T if C 1 I = C 2 I for every model I of T. We also write C 1 ≡T C 2 or T |= C 1 ≡ C 2. Disjointness: Two concepts C 1 and C 2 are disjoint with respect to T if C 1 I ⊓ C 2 I = ∅ for every model I of T Disjointness: Two concepts C 1 and C 2 are disjoint with respect to T if C 1 I ⊓ C 2 I = ∅ for every model I of T Chuming Chen’s Dissertation 2008

– 4 – CSCE 771 Spring 2013 Abox Reasoning ABox consistency checking: An ABox A is consistent with respect to a TBox T if there exists an interpretation I that is a model of both T and A. Instance checking: An individual a is an instance of concept C with respect to T and A if aI ⊆ CI for every model of T and A. Instance checking: An individual a is an instance of concept C with respect to T and A if aI ⊆ CI for every model of T and A. Retrieval problem: Given an ABox A and a concept C, to find all individuals a such that A |= a : C. Retrieval problem: Given an ABox A and a concept C, to find all individuals a such that A |= a : C. Realization problem: Given an individual a and a set of concepts, find the most specific concepts C from the set such that A |= a : C. Note, the most specific concepts are those that are minimal with respect to the subsumption ordering ⊑. Realization problem: Given an individual a and a set of concepts, find the most specific concepts C from the set such that A |= a : C. Note, the most specific concepts are those that are minimal with respect to the subsumption ordering ⊑. Chuming Chen’s Dissertation 2008

– 5 – CSCE 771 Spring 2013 Figure 18.5 Quantifier Scope and Ambiguity Copyright ©2009 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved. Speech and Language Processing, Second Edition Daniel Jurafsky and James H. Martin Every Restaurant has a menu. Two possible meanings

– 6 – CSCE 771 Spring 2013 UnderSpecification Underspecification is supporting “ambiguous” meanings by leaving unspecified aspects unspecified So we need to be able to “Create underspecified representations that embody all possible readings without explicitly enumerating them”“Create underspecified representations that embody all possible readings without explicitly enumerating them” Extract the readings if necessaryExtract the readings if necessary Choose amongst those readingsChoose amongst those readings Haver(e,Restaurant) ^ had(e, Menu) “it should remain agonstic about the placement of qualifiers”

– 7 – CSCE 771 Spring 2013 Stores Cooper storage (1983) For meanings of nodes of parse tree we have been using predicate calculus (FOL) formulae In Cooper’s approach we replace the single formula with a “store” consisting of a list of quantified expressions gathered from below

– 8 – CSCE 771 Spring 2013 Figure 18.6 Semantic Stores for VP Copyright ©2009 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved. Speech and Language Processing, Second Edition Daniel Jurafsky and James H. Martin

– 9 – CSCE 771 Spring 2013 Hole Semantics Hole semantics (Bos 1996) λ - reductions replace λ- variables with “holes” Instead of using λ – reductions we just create labels (“holes”) Dominance constraints Plugging the holes

– 10 – CSCE 771 Spring 2013 Figure 18.7 Hole Semantic Repr. for Every Restaurant has a menu. Copyright ©2009 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved. Speech and Language Processing, Second Edition Daniel Jurafsky and James H. Martin

– 11 – CSCE 771 Spring 2013 Figure 18.8 Copyright ©2009 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved. Speech and Language Processing, Second Edition Daniel Jurafsky and James H. Martin

– 12 – CSCE 771 Spring 2013 Feature and Unification based approaches Feature structures associated with nodes of the parse tree and performing unifications

– 13 – CSCE 771 Spring 2013 Copyright ©2009 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved. Speech and Language Processing, Second Edition Daniel Jurafsky and James H. Martin Exists e Closing(e) ^ Closed(e, Rhumba)

– 14 – CSCE 771 Spring 2013 Figure 18.9 DAG for Semantic Features Copyright ©2009 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved. Speech and Language Processing, Second Edition Daniel Jurafsky and James H. Martin

– 15 – CSCE 771 Spring 2013 Copyright ©2009 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved. Speech and Language Processing, Second Edition Daniel Jurafsky and James H. Martin

– 16 – CSCE 771 Spring 2013 Copyright ©2009 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved. Speech and Language Processing, Second Edition Daniel Jurafsky and James H. Martin

– 17 – CSCE 771 Spring 2013 Figure Earley + Semantics Copyright ©2009 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved. Speech and Language Processing, Second Edition Daniel Jurafsky and James H. Martin

– 18 – CSCE 771 Spring 2013 Problem with SQL and Agents

– 19 – CSCE 771 Spring 2013 Consistency of Statements (5) a.Sylvania is to the north of Freedonia. b.Freedonia is a republic. (6) a.The capital of Freedonia has a population of 9,000. b.No city in Freedonia has a population of 9,000. (7) a.Sylvania is to the north of Freedonia. b.Freedonia is to the north of Sylvania. NLTK Book Chapter 10

– 20 – CSCE 771 Spring 2013 Models again “A model for a set W of sentences is a formal representation of a situation in which all the sentences in W are true.” NLTK Book Chapter 10

– 21 – CSCE 771 Spring 2013 Logic and the NLTK >>> nltk.boolean_ops() negation - conjunction & disjunction | implication -> equivalence equivalence >>> lp = nltk.LogicParser() >>> lp.parse('-(P & Q)') >>> lp.parse('P & Q') >>> lp.parse('P | (R -> Q)') Q))> Q))> >>> lp.parse('P -- P') --P)> --P)> NLTK Book Chapter 10

– 22 – CSCE 771 Spring 2013 Theorem Prover 9 >>> NotFnS = lp.parse('-north_of(f, s)') >>> SnF = lp.parse('north_of(s, f)') >>> R = lp.parse('all x. all y. (north_of(x, y) -> -north_of(y, x))') >>> prover = nltk.Prover9() >>> prover.prove(NotFnS, [SnF, R]) True >>> lp = nltk.LogicParser() >>> SnF = lp.parse('SnF') >>> NotFnS = lp.parse('-FnS') >>> R = lp.parse('SnF -> -FnS') >>> prover = nltk.Prover9() >>> prover.prove(NotFnS, [SnF, R]) True NLTK Book Chapter 10

– 23 – CSCE 771 Spring 2013 Models and Values >>> val = nltk.Valuation([('P', True), ('Q', True), ('R', False)]) >>> val['P'] True >>> dom = set([]) >>> g = nltk.Assignment(dom) >>> m = nltk.Model(dom, val) >>> print m.evaluate('(P & Q)', g) True >>> print m.evaluate('-(P & Q)', g) False >>> print m.evaluate('(P & R)', g) False NLTK Book Chapter 10

– 24 – CSCE 771 Spring 2013 First Order Logic and the NLTK >>> tlp = nltk.LogicParser(type_check=True) >>> parsed = tlp.parse('walk(angus)') >>> parsed.argument >>> parsed.argument.type e >>> parsed.function >>> parsed.function.type <e,?> NLTK Book Chapter 10

– 25 – CSCE 771 Spring 2013 Free Variables >>> lp = nltk.LogicParser() >>> lp.parse('dog(cyril)').free() set([]) >>> lp.parse('dog(x)').free() set([Variable('x')]) >>> lp.parse('own(angus, cyril)').free() set([]) >>> lp.parse('exists x.dog(x)').free() set([]) >>> lp.parse('((some x. walk(x)) -> sing(x))').free() set([Variable('x')]) >>> lp.parse('exists x.own(y, x)').free() set([Variable('y')]) NLTK Book Chapter 10

– 26 – CSCE 771 Spring 2013 >>> NotFnS = lp.parse('-north_of(f, s)') >>> SnF = lp.parse('north_of(s, f)') >>> R = lp.parse('all x. all y. (north_of(x, y) -> - north_of(y, x))') >>> prover = nltk.Prover9() >>> prover.prove(NotFnS, [SnF, R]) True >>> FnS = lp.parse('north_of(f, s)') >>> prover.prove(FnS, [SnF, R]) False NLTK Book Chapter 10

– 27 – CSCE 771 Spring 2013 >>> v = """... bertie => b... olive => o... cyril => c... boy => {b}... girl => {o}... dog => {c}... walk => {o, c}... see => {(b, o), (c, b), (o, c)}... """ >>> val = nltk.parse_valuation(v) >>> print val {'bertie': 'b', 'boy': set([('b',)]), 'boy': set([('b',)]), 'cyril': 'c', 'cyril': 'c', 'dog': set([('c',)]), 'dog': set([('c',)]), 'girl': set([('o',)]), 'girl': set([('o',)]), 'olive': 'o', 'olive': 'o', 'see': set([('o', 'c'), ('c', 'b'), ('b', 'o')]), 'see': set([('o', 'c'), ('c', 'b'), ('b', 'o')]), 'walk': set([('c',), ('o',)])} 'walk': set([('c',), ('o',)])} NLTK Book Chapter 10

– 28 – CSCE 771 Spring 2013 >>> fmla1 = lp.parse('girl(x) | boy(x)') >>> m.satisfiers(fmla1, 'x', g) set(['b', 'o']) >>> fmla2 = lp.parse('girl(x) -> walk(x)') >>> m.satisfiers(fmla2, 'x', g) set(['c', 'b', 'o']) >>> fmla3 = lp.parse('walk(x) -> girl(x)') >>> m.satisfiers(fmla3, 'x', g) set(['b', 'o']) NLTK Book Chapter 10

– 29 – CSCE 771 Spring 2013 Admire Relation >>> v2 = """... bruce => b... cyril => c... elspeth => e... julia => j... matthew => m... person => {b, e, j, m}... admire => {(j, b), (b, b), (m, e), (e, m), (c, a)}... """ >>> val2 = nltk.parse_valuation(v2) NLTK Book Chapter 10

– 30 – CSCE 771 Spring 2013 >>> dom2 = val2.domain >>> m2 = nltk.Model(dom2, val2) >>> g2 = nltk.Assignment(dom2) >>> fmla4 = lp.parse('(person(x) -> exists y.(person(y) & admire(x, y)))') >>> m2.satisfiers(fmla4, 'x', g2) set(['a', 'c', 'b', 'e', 'j', 'm']) >>> fmla5 = lp.parse('(person(y) & all x.(person(x) -> admire(x, y)))') >>> m2.satisfiers(fmla5, 'y', g2) set([]) NLTK Book Chapter 10

– 31 – CSCE 771 Spring 2013 Theorem9 prover arguments = [ ('(man(x) (not (not man(x))))', []), ('(not (man(x) & (not man(x))))', []), ('(man(x) | (not man(x)))', []), ('(man(x) & (not man(x)))', []), ('(man(x) -> man(x))', []), ('(not (man(x) & (not man(x))))', []), ('(man(x) | (not man(x)))', []), ('(man(x) -> man(x))', []), ('(man(x) man(x))', []), ('(not (man(x) (not man(x))))', []), ('mortal(Socrates)', ['all x.(man(x) -> mortal(x))', 'man(Socrates)']), ('((all x.(man(x) -> walks(x)) & man(Socrates)) -> some y.walks(y))', []),

– 32 – CSCE 771 Spring 2013 ('(all x.man(x) -> all x.man(x))', []), ('some x.all y.sees(x,y)', []), ('some e3.(walk(e3) & subj(e3, mary))', ['some e1.(see(e1) & subj(e1, john) & some e2.(pred(e1, e2) & walk(e2) & subj(e2, mary)))']), ('some x e1.(see(e1) & subj(e1, x) & some e2.(pred(e1, e2) & walk(e2) & subj(e2, mary)))', ['some e1.(see(e1) & subj(e1, john) & some e2.(pred(e1, e2) & walk(e2) & subj(e2, mary)))']) ]