Computational Semantics: Events NL to FOL: Loose ends Misc syn. - PowerPoint PPT Presentation

Computational Mapping NL to FOL: Negation Semantics: Events Scott Farrar CLMA, University of Washington far- rar@u.washington.edu Negative markers are mapped to formulas with the negation NL to FOL: Loose symbol. ends Fred is not a gentleman. Misc syn. categories VPs, Verbs Problems with verbs Event semantics Semantic roles FrameNet 7/35

Computational Mapping NL to FOL: Negation Semantics: Events Scott Farrar CLMA, University of Washington far- rar@u.washington.edu Negative markers are mapped to formulas with the negation NL to FOL: Loose symbol. ends Fred is not a gentleman. Misc syn. categories VPs, Verbs ¬ gentleman ( FRED ) Problems with verbs Event semantics Semantic roles FrameNet 7/35

Computational Mapping NL to FOL: Negation Semantics: Events Scott Farrar CLMA, University of Washington far- rar@u.washington.edu Negative markers are mapped to formulas with the negation NL to FOL: Loose symbol. ends Fred is not a gentleman. Misc syn. categories VPs, Verbs ¬ gentleman ( FRED ) Problems with verbs Event semantics Semantic roles FrameNet Fred is neither gentle nor a man. 7/35

Computational Mapping NL to FOL: Negation Semantics: Events Scott Farrar CLMA, University of Washington far- rar@u.washington.edu Negative markers are mapped to formulas with the negation NL to FOL: Loose symbol. ends Fred is not a gentleman. Misc syn. categories VPs, Verbs ¬ gentleman ( FRED ) Problems with verbs Event semantics Semantic roles FrameNet Fred is neither gentle nor a man. ¬ ( gentle ( FRED ) ∨ man ( FRED )) 7/35

Computational Mapping NL to FOL: Negation Semantics: Events Scott Farrar CLMA, University of Washington far- rar@u.washington.edu Negative markers are mapped to formulas with the negation NL to FOL: Loose symbol. ends Fred is not a gentleman. Misc syn. categories VPs, Verbs ¬ gentleman ( FRED ) Problems with verbs Event semantics Semantic roles FrameNet Fred is neither gentle nor a man. ¬ ( gentle ( FRED ) ∨ man ( FRED )) which (by De Morgan’s Laws) is logically equivalent to: 7/35

Computational Mapping NL to FOL: Negation Semantics: Events Scott Farrar CLMA, University of Washington far- rar@u.washington.edu Negative markers are mapped to formulas with the negation NL to FOL: Loose symbol. ends Fred is not a gentleman. Misc syn. categories VPs, Verbs ¬ gentleman ( FRED ) Problems with verbs Event semantics Semantic roles FrameNet Fred is neither gentle nor a man. ¬ ( gentle ( FRED ) ∨ man ( FRED )) which (by De Morgan’s Laws) is logically equivalent to: ¬ gentle ( FRED ) ∧ ¬ man ( FRED ) 7/35

Computational Mapping NL to FOL: Negation Semantics: Events Scott Farrar CLMA, University of Washington far- rar@u.washington.edu Negative markers are mapped to formulas with the negation NL to FOL: Loose symbol. ends Fred is not a gentleman. Misc syn. categories VPs, Verbs ¬ gentleman ( FRED ) Problems with verbs Event semantics Semantic roles FrameNet Fred is neither gentle nor a man. ¬ ( gentle ( FRED ) ∨ man ( FRED )) which (by De Morgan’s Laws) is logically equivalent to: ¬ gentle ( FRED ) ∧ ¬ man ( FRED ) Ubuntu is not Kubuntu. 7/35

Computational Mapping NL to FOL: Negation Semantics: Events Scott Farrar CLMA, University of Washington far- rar@u.washington.edu Negative markers are mapped to formulas with the negation NL to FOL: Loose symbol. ends Fred is not a gentleman. Misc syn. categories VPs, Verbs ¬ gentleman ( FRED ) Problems with verbs Event semantics Semantic roles FrameNet Fred is neither gentle nor a man. ¬ ( gentle ( FRED ) ∨ man ( FRED )) which (by De Morgan’s Laws) is logically equivalent to: ¬ gentle ( FRED ) ∧ ¬ man ( FRED ) Ubuntu is not Kubuntu. ¬ ( UBUNTU = KUBUNTU ) 7/35

Computational Mapping NL to FOL: Identity Semantics: Events Scott Farrar CLMA, University of Washington far- Copulas (certain occurrences of be ) are mapped to identity: rar@u.washington.edu NL to FOL: Loose ends Misc syn. categories VPs, Verbs Problems with verbs Event semantics Semantic roles FrameNet 8/35

Computational Mapping NL to FOL: Identity Semantics: Events Scott Farrar CLMA, University of Washington far- Copulas (certain occurrences of be ) are mapped to identity: rar@u.washington.edu Jane is Ms. Jones , JANE = JONES 321 NL to FOL: Loose ends Misc syn. categories VPs, Verbs Problems with verbs Event semantics Semantic roles FrameNet 8/35

Computational Mapping NL to FOL: Identity Semantics: Events Scott Farrar CLMA, University of Washington far- Copulas (certain occurrences of be ) are mapped to identity: rar@u.washington.edu Jane is Ms. Jones , JANE = JONES 321 NL to FOL: Loose ends Misc syn. categories Definition VPs, Verbs Problems with verbs The = operator (actually a binary predicate) shows Event semantics indentity , or when two individuals are one in the same. Semantic roles FrameNet 8/35

Computational Mapping NL to FOL: Identity Semantics: Events Scott Farrar CLMA, University of Washington far- Copulas (certain occurrences of be ) are mapped to identity: rar@u.washington.edu Jane is Ms. Jones , JANE = JONES 321 NL to FOL: Loose ends Misc syn. categories Definition VPs, Verbs Problems with verbs The = operator (actually a binary predicate) shows Event semantics indentity , or when two individuals are one in the same. Semantic roles FrameNet Everyone who is not Pavel is owed money by Pavel. 8/35

Computational Mapping NL to FOL: Identity Semantics: Events Scott Farrar CLMA, University of Washington far- Copulas (certain occurrences of be ) are mapped to identity: rar@u.washington.edu Jane is Ms. Jones , JANE = JONES 321 NL to FOL: Loose ends Misc syn. categories Definition VPs, Verbs Problems with verbs The = operator (actually a binary predicate) shows Event semantics indentity , or when two individuals are one in the same. Semantic roles FrameNet Everyone who is not Pavel is owed money by Pavel. ∀ x ( x � = PAVEL → OwesMoney ( PAVEL , x )) 8/35

Computational Mapping NL to FOL: Identity Semantics: Events Scott Farrar CLMA, University of Washington far- Copulas (certain occurrences of be ) are mapped to identity: rar@u.washington.edu Jane is Ms. Jones , JANE = JONES 321 NL to FOL: Loose ends Misc syn. categories Definition VPs, Verbs Problems with verbs The = operator (actually a binary predicate) shows Event semantics indentity , or when two individuals are one in the same. Semantic roles FrameNet Everyone who is not Pavel is owed money by Pavel. ∀ x ( x � = PAVEL → OwesMoney ( PAVEL , x )) What’s wrong with this formula? female ( x ) ∧ teacher ( x ) ∧ single ( x ) = oldmaid ( x ) ??? 8/35

Computational Mapping NL to FOL: Identity Semantics: Events Scott Farrar CLMA, University of Washington far- Copulas (certain occurrences of be ) are mapped to identity: rar@u.washington.edu Jane is Ms. Jones , JANE = JONES 321 NL to FOL: Loose ends Misc syn. categories Definition VPs, Verbs Problems with verbs The = operator (actually a binary predicate) shows Event semantics indentity , or when two individuals are one in the same. Semantic roles FrameNet Everyone who is not Pavel is owed money by Pavel. ∀ x ( x � = PAVEL → OwesMoney ( PAVEL , x )) What’s wrong with this formula? female ( x ) ∧ teacher ( x ) ∧ single ( x ) = oldmaid ( x ) ??? Identity only holds between terms (variables and constants), not formulas. 8/35

Computational Mapping NL to FOL: Biconditional implication Semantics: Events Scott Farrar CLMA, University of Washington far- rar@u.washington.edu NL to FOL: Loose ends To represent definitional statements, such as: Misc syn. categories A female, unmarried teacher is an old maid. VPs, Verbs Problems with verbs Use the biconditional , ↔ : Event semantics Semantic roles FrameNet 9/35

Computational Mapping NL to FOL: Biconditional implication Semantics: Events Scott Farrar CLMA, University of Washington far- rar@u.washington.edu NL to FOL: Loose ends To represent definitional statements, such as: Misc syn. categories A female, unmarried teacher is an old maid. VPs, Verbs Problems with verbs Use the biconditional , ↔ : Event semantics Semantic roles FrameNet ∀ x ( female ( x ) ∧ teacher ( x ) ∧ single ( x ) ↔ oldmaid ( x )) 9/35

Computational Mapping NL to FOL: Biconditional implication Semantics: Events Scott Farrar CLMA, University of Washington far- rar@u.washington.edu NL to FOL: Loose ends To represent definitional statements, such as: Misc syn. categories A female, unmarried teacher is an old maid. VPs, Verbs Problems with verbs Use the biconditional , ↔ : Event semantics Semantic roles FrameNet ∀ x ( female ( x ) ∧ teacher ( x ) ∧ single ( x ) ↔ oldmaid ( x )) A person who races horses is a jockey. 9/35

Computational Mapping NL to FOL: Biconditional implication Semantics: Events Scott Farrar CLMA, University of Washington far- rar@u.washington.edu NL to FOL: Loose ends To represent definitional statements, such as: Misc syn. categories A female, unmarried teacher is an old maid. VPs, Verbs Problems with verbs Use the biconditional , ↔ : Event semantics Semantic roles FrameNet ∀ x ( female ( x ) ∧ teacher ( x ) ∧ single ( x ) ↔ oldmaid ( x )) A person who races horses is a jockey. ∀ x ∀ y ( person ( x ) ∧ race ( x , y ) ∧ horse ( y ) ↔ jockey ( x )) 9/35

Computational Mapping NL to FOL: Definite determiners Semantics: Events Scott Farrar What about definite determiners, what function do they CLMA, University of Washington far- serve? rar@u.washington.edu NL to FOL: Loose ends Misc syn. categories VPs, Verbs Problems with verbs Event semantics Semantic roles FrameNet 10/35

Computational Mapping NL to FOL: Definite determiners Semantics: Events Scott Farrar What about definite determiners, what function do they CLMA, University of Washington far- serve? They pick out a single individual from the discourse rar@u.washington.edu context. NL to FOL: Loose ends Misc syn. categories That collection agency called. VPs, Verbs Problems with verbs (a specific individual of type collection agency) Event semantics The woman said you owe money. Semantic roles FrameNet (a specific individual of type woman) The amount is five thousand dollars. (a specific individual of type amount) 10/35

Computational Mapping NL to FOL: Definite determiners Semantics: Events Scott Farrar What about definite determiners, what function do they CLMA, University of Washington far- serve? They pick out a single individual from the discourse rar@u.washington.edu context. NL to FOL: Loose ends Misc syn. categories That collection agency called. VPs, Verbs Problems with verbs (a specific individual of type collection agency) Event semantics The woman said you owe money. Semantic roles FrameNet (a specific individual of type woman) The amount is five thousand dollars. (a specific individual of type amount) Similar examples: 10/35

Computational Mapping NL to FOL: Definite determiners Semantics: Events Scott Farrar What about definite determiners, what function do they CLMA, University of Washington far- serve? They pick out a single individual from the discourse rar@u.washington.edu context. NL to FOL: Loose ends Misc syn. categories That collection agency called. VPs, Verbs Problems with verbs (a specific individual of type collection agency) Event semantics The woman said you owe money. Semantic roles FrameNet (a specific individual of type woman) The amount is five thousand dollars. (a specific individual of type amount) Similar examples: my father the woman’s right hand Waldo’s image 10/35

Computational Definite descriptions Semantics: Events Scott Farrar CLMA, University of Washington far- rar@u.washington.edu Definition NL to FOL: Loose A definite description is any NP that picks out a single ends Misc syn. categories individual by means of a unique description. Definite VPs, Verbs Problems with verbs descriptions are distinct from proper names. Event semantics Semantic roles FrameNet 11/35

Computational Definite descriptions Semantics: Events Scott Farrar CLMA, University of Washington far- rar@u.washington.edu Definition NL to FOL: Loose A definite description is any NP that picks out a single ends Misc syn. categories individual by means of a unique description. Definite VPs, Verbs Problems with verbs descriptions are distinct from proper names. Event semantics Semantic roles FrameNet To incorporate definite descriptions into FOL, for example, in the car is red , we can add a special uniqueness quantifier: 11/35

Computational Definite descriptions Semantics: Events Scott Farrar CLMA, University of Washington far- rar@u.washington.edu Definition NL to FOL: Loose A definite description is any NP that picks out a single ends Misc syn. categories individual by means of a unique description. Definite VPs, Verbs Problems with verbs descriptions are distinct from proper names. Event semantics Semantic roles FrameNet To incorporate definite descriptions into FOL, for example, in the car is red , we can add a special uniqueness quantifier: ∃ ! x ( car ( x ) ∧ red ( x )) Paraphrase: There is one and only one x such that x is a car and x is red. 11/35

Computational Another solution Semantics: Events Scott Farrar CLMA, University of Washington far- rar@u.washington.edu Use existential quantification with the identity operator: NL to FOL: Loose ends Misc syn. categories VPs, Verbs Problems with verbs Event semantics Semantic roles FrameNet 12/35

Computational Another solution Semantics: Events Scott Farrar CLMA, University of Washington far- rar@u.washington.edu Use existential quantification with the identity operator: NL to FOL: Loose ∃ x [ car ( x ) ∧ ¬∃ y ( car ( y ) ∧ x � = y )] ends Misc syn. categories VPs, Verbs Problems with verbs Event semantics Semantic roles FrameNet 12/35

Computational Another solution Semantics: Events Scott Farrar CLMA, University of Washington far- rar@u.washington.edu Use existential quantification with the identity operator: NL to FOL: Loose ∃ x [ car ( x ) ∧ ¬∃ y ( car ( y ) ∧ x � = y )] ends There is something x which is a car, there is no such thing y Misc syn. categories VPs, Verbs such that y is a car and for which x is not y . Problems with verbs Event semantics Semantic roles FrameNet 12/35

Computational Another solution Semantics: Events Scott Farrar CLMA, University of Washington far- rar@u.washington.edu Use existential quantification with the identity operator: NL to FOL: Loose ∃ x [ car ( x ) ∧ ¬∃ y ( car ( y ) ∧ x � = y )] ends There is something x which is a car, there is no such thing y Misc syn. categories VPs, Verbs such that y is a car and for which x is not y . Problems with verbs Event semantics Semantic roles FrameNet The car is red. ∃ x [ car ( x ) ∧ ¬∃ y ( car ( y ) ∧ x � = y ) ∧ red ( x )] The formula makes three claims: 12/35

Computational Another solution Semantics: Events Scott Farrar CLMA, University of Washington far- rar@u.washington.edu Use existential quantification with the identity operator: NL to FOL: Loose ∃ x [ car ( x ) ∧ ¬∃ y ( car ( y ) ∧ x � = y )] ends There is something x which is a car, there is no such thing y Misc syn. categories VPs, Verbs such that y is a car and for which x is not y . Problems with verbs Event semantics Semantic roles FrameNet The car is red. ∃ x [ car ( x ) ∧ ¬∃ y ( car ( y ) ∧ x � = y ) ∧ red ( x )] The formula makes three claims: 1 There is a car. (an existence claim) 2 At most one thing is a car. (a uniqueness claim) 3 This car is red. (a claim of predication) 12/35

Computational Mapping NL to FOL: prepositions Semantics: Events Scott Farrar CLMA, University of Washington far- rar@u.washington.edu What do (most) prepositions refer to? NL to FOL: Loose ends Misc syn. categories VPs, Verbs Problems with verbs Event semantics Semantic roles FrameNet 13/35

Computational Mapping NL to FOL: prepositions Semantics: Events Scott Farrar CLMA, University of Washington far- rar@u.washington.edu What do (most) prepositions refer to? ... some relation NL to FOL: Loose ends Misc syn. categories VPs, Verbs Problems with verbs Event semantics Semantic roles FrameNet 13/35

Computational Mapping NL to FOL: prepositions Semantics: Events Scott Farrar CLMA, University of Washington far- rar@u.washington.edu What do (most) prepositions refer to? ... some relation NL to FOL: Loose ends Misc syn. categories VPs, Verbs Spatial prepositions, for instance, can be easily mapped onto Problems with verbs Event semantics binary predicates: Semantic roles FrameNet Joe is in Seattle, in ( JOE , SEATTLE ) 13/35

Computational Mapping NL to FOL: prepositions Semantics: Events Scott Farrar CLMA, University of Washington far- rar@u.washington.edu What do (most) prepositions refer to? ... some relation NL to FOL: Loose ends Misc syn. categories VPs, Verbs Spatial prepositions, for instance, can be easily mapped onto Problems with verbs Event semantics binary predicates: Semantic roles FrameNet Joe is in Seattle, in ( JOE , SEATTLE ) We could then utilize some spatial calculus to reason about the locations of various objects: ∀ x ∀ y ( in ( x , y ) → near ( x , y )), ∀ x ∀ y ( on ( x , y ) ↔ contact ( x , y ) ... ) 13/35

Computational NL to FOL: various calculi Semantics: Events Scott Farrar Definition CLMA, University of Washington far- rar@u.washington.edu A calculus is a theory of some domain usually expressed in a formal logic (e.g., FOL). Some commonly used calculi in NL to FOL: Loose ends used to study NL semantics: Misc syn. categories VPs, Verbs Problems with verbs spatial calculus: a theory of spatial objects/relations. Event semantics Semantic roles FrameNet temporal calculus: a theory of time points and durations. (cf. NL tense) agency calculus: a theory of agents and causation. (cf. NL voice) event calculus: a theory of events and participants. (cf. NL aspect) Such calculi are part of the ontology of the underlying domain. 14/35

NL to FOL: Summary II Syn Cat NL example FOL Cat example not, no, dis-, ¬ fish(x) negation logical negation un- various is, is the same identity JOHN = as, equals SMITH various is, is defined logical biconditional ↔ as, equals prepositions in, near, be- binary predicates in ( x , y ), side near ( a , b ), beside ( m , n ) definites the house, my constant HOUSE 2, dog DOG 13 or ∃ x ( house ( x ) ∧ ¬∃ y ( house ( y ) ∧ x � = y ))

Computational Mapping NL to FOL: Verbs Semantics: Events Scott Farrar CLMA, University of Washington far- rar@u.washington.edu In most logic textbooks and some NL semantics works, the main verb is mapped to an n -ary predicate in FOL. Verb NL to FOL: Loose ends valence is transferred to the level of semantic representation. Misc syn. categories VPs, Verbs Problems with verbs Event semantics Semantic roles FrameNet 16/35

Computational Mapping NL to FOL: Verbs Semantics: Events Scott Farrar CLMA, University of Washington far- rar@u.washington.edu In most logic textbooks and some NL semantics works, the main verb is mapped to an n -ary predicate in FOL. Verb NL to FOL: Loose ends valence is transferred to the level of semantic representation. Misc syn. categories VPs, Verbs Problems with verbs Event semantics Intransitives can be represented as unary predicates. Semantic roles FrameNet swim ( x ) 16/35

Computational Mapping NL to FOL: Verbs Semantics: Events Scott Farrar CLMA, University of Washington far- rar@u.washington.edu In most logic textbooks and some NL semantics works, the main verb is mapped to an n -ary predicate in FOL. Verb NL to FOL: Loose ends valence is transferred to the level of semantic representation. Misc syn. categories VPs, Verbs Problems with verbs Event semantics Intransitives can be represented as unary predicates. Semantic roles FrameNet swim ( x ) Transitives can be represented as binary predicates. steal ( x , y ) 16/35

Computational Mapping NL to FOL: Verbs Semantics: Events Scott Farrar CLMA, University of Washington far- rar@u.washington.edu In most logic textbooks and some NL semantics works, the main verb is mapped to an n -ary predicate in FOL. Verb NL to FOL: Loose ends valence is transferred to the level of semantic representation. Misc syn. categories VPs, Verbs Problems with verbs Event semantics Intransitives can be represented as unary predicates. Semantic roles FrameNet swim ( x ) Transitives can be represented as binary predicates. steal ( x , y ) Ditransitives can be represented as ternary predicates. give ( x , y , z ) 16/35

Computational Mapping NL to FOL: Verbs Semantics: Events Scott Farrar CLMA, University of Washington far- rar@u.washington.edu In most logic textbooks and some NL semantics works, the main verb is mapped to an n -ary predicate in FOL. Verb NL to FOL: Loose ends valence is transferred to the level of semantic representation. Misc syn. categories VPs, Verbs Problems with verbs Event semantics Intransitives can be represented as unary predicates. Semantic roles FrameNet swim ( x ) Transitives can be represented as binary predicates. steal ( x , y ) Ditransitives can be represented as ternary predicates. give ( x , y , z ) But there are a few problems. 16/35

Computational Problem I: valence and arity Semantics: Events Scott Farrar CLMA, University of Washington far- rar@u.washington.edu Consider this sentence: NL to FOL: Loose Sue bought the Honda. ends Misc syn. categories VPs, Verbs buy ( SUE , HONDA 321) Problems with verbs Event semantics Semantic roles FrameNet 17/35

Computational Problem I: valence and arity Semantics: Events Scott Farrar CLMA, University of Washington far- rar@u.washington.edu Consider this sentence: NL to FOL: Loose Sue bought the Honda. ends Misc syn. categories VPs, Verbs buy ( SUE , HONDA 321) Problems with verbs Event semantics Semantic roles FrameNet Sue bought the Honda in Oregon. buy ( SUE , HONDA 321 , OREGON ) 17/35

Computational Problem I: valence and arity Semantics: Events Scott Farrar CLMA, University of Washington far- rar@u.washington.edu Consider this sentence: NL to FOL: Loose Sue bought the Honda. ends Misc syn. categories VPs, Verbs buy ( SUE , HONDA 321) Problems with verbs Event semantics Semantic roles FrameNet Sue bought the Honda in Oregon. buy ( SUE , HONDA 321 , OREGON ) Sue bought the car in Oregon for Sam. buy ( SUE , HONDA 321 , OREGON , SAM ) 17/35

Computational Problem I: valence and arity Semantics: Events Scott Farrar CLMA, University of Washington far- rar@u.washington.edu NL to FOL: Loose ends Misc syn. categories Sue bought the Honda in Oregon for Sam with a loan... VPs, Verbs Problems with verbs Event semantics Semantic roles For a given verb, we would need a way to arbitrarily increase FrameNet the predicate arity at the level of semantic representation. So, how to capture the common meaning among buy ( x , y ), buy ( x , y , z ), etc.? 18/35

Davidon’s famous example This was used in the original argument against allowing arbitrary arity of predicates: John buttered the toast. Butter ( JOHN , TOAST ) John buttered the toast at midnight. Butter ( JOHN , TOAST , MIDNIGHT ) John buttered the toast at midnight with a knife. Butter ( JOHN , TOAST , MIDNIGHT , KNIFE ) John buttered the toast at midnight with a knife before he went to bed. Butter ( JOHN , TOAST , MIDNIGHT , KNIFE , ... )

Computational Problem 2: Tense Semantics: Events Scott Farrar CLMA, University of Washington far- rar@u.washington.edu NL to FOL: Loose What do the tenses mean? ends Misc syn. categories VPs, Verbs Problems with verbs Event semantics Semantic roles FrameNet 20/35

Computational Problem 2: Tense Semantics: Events Scott Farrar CLMA, University of Washington far- rar@u.washington.edu NL to FOL: Loose What do the tenses mean? ends Misc syn. categories VPs, Verbs Problems with verbs Sue bought a car. Event semantics Semantic roles FrameNet The act of buying occurred before the time of speech. 20/35

Computational Problem 2: Tense Semantics: Events Scott Farrar CLMA, University of Washington far- rar@u.washington.edu NL to FOL: Loose What do the tenses mean? ends Misc syn. categories VPs, Verbs Problems with verbs Sue bought a car. Event semantics Sue is buying a car. (present progressive) Semantic roles FrameNet The act of buying occurred before the time of speech. The act of buying is occurring at the time of speech. 20/35

Computational Problem 2: Tense Semantics: Events Scott Farrar CLMA, University of Washington far- rar@u.washington.edu NL to FOL: Loose What do the tenses mean? ends Misc syn. categories VPs, Verbs Problems with verbs Sue bought a car. Event semantics Sue is buying a car. (present progressive) Semantic roles FrameNet Sue will buy a car. The act of buying occurred before the time of speech. The act of buying is occurring at the time of speech. The act of buying will occur after the time of speech. 20/35

Computational Problem 2: Tense Semantics: Events Scott Farrar Any reasonable account of the semantics of a tense system CLMA, University of Washington far- requires explicit reference to temporal relations : before, rar@u.washington.edu after, during, etc. The states and processes referred to by NL to FOL: Loose verbs are the arguments of such relations. ends Misc syn. categories VPs, Verbs Problems with verbs Event semantics Semantic roles FrameNet 21/35

Computational Problem 2: Tense Semantics: Events Scott Farrar Any reasonable account of the semantics of a tense system CLMA, University of Washington far- requires explicit reference to temporal relations : before, rar@u.washington.edu after, during, etc. The states and processes referred to by NL to FOL: Loose verbs are the arguments of such relations. ends Misc syn. categories VPs, Verbs Problems with verbs PAST TENSE: before ( x , T 1 ), where x is the state or process Event semantics referred to by the verb, and T 1 is the speech time. Semantic roles FrameNet 21/35

Computational Problem 2: Tense Semantics: Events Scott Farrar Any reasonable account of the semantics of a tense system CLMA, University of Washington far- requires explicit reference to temporal relations : before, rar@u.washington.edu after, during, etc. The states and processes referred to by NL to FOL: Loose verbs are the arguments of such relations. ends Misc syn. categories VPs, Verbs Problems with verbs PAST TENSE: before ( x , T 1 ), where x is the state or process Event semantics referred to by the verb, and T 1 is the speech time. Semantic roles FrameNet Predicates such as buy ( x ), teach ( x , y ), bite ( x , y ) are then arguments of temporal predications. before ( buy ( SUE , CAR 1) , T 1 ) 21/35

Computational Problem 2: Tense Semantics: Events Scott Farrar Any reasonable account of the semantics of a tense system CLMA, University of Washington far- requires explicit reference to temporal relations : before, rar@u.washington.edu after, during, etc. The states and processes referred to by NL to FOL: Loose verbs are the arguments of such relations. ends Misc syn. categories VPs, Verbs Problems with verbs PAST TENSE: before ( x , T 1 ), where x is the state or process Event semantics referred to by the verb, and T 1 is the speech time. Semantic roles FrameNet Predicates such as buy ( x ), teach ( x , y ), bite ( x , y ) are then arguments of temporal predications. before ( buy ( SUE , CAR 1) , T 1 ) The above formula is incompatible with our logical machinery! A sentence cannot be the argument of a predicate. 21/35

Computational First- verses second-order logic Semantics: Events Scott Farrar CLMA, University Definition of Washington far- rar@u.washington.edu A second-order logic is one in which predicates can be NL to FOL: Loose arguments of other predicates. A second-order logic allows ends quantification over subsets and relations, that is, over all Misc syn. categories VPs, Verbs predicates: Problems with verbs Event semantics Semantic roles ∀ buy ∀ x ( x ∈ buy ∨ x / ∈ buy ) FrameNet 22/35

Computational First- verses second-order logic Semantics: Events Scott Farrar CLMA, University Definition of Washington far- rar@u.washington.edu A second-order logic is one in which predicates can be NL to FOL: Loose arguments of other predicates. A second-order logic allows ends quantification over subsets and relations, that is, over all Misc syn. categories VPs, Verbs predicates: Problems with verbs Event semantics Semantic roles ∀ buy ∀ x ( x ∈ buy ∨ x / ∈ buy ) FrameNet By using a first-order logic, performance issues are already a problem. For example, FOL is undecidable which means that it is not possible to write a theorem prover which, when given an arbitrary formula as input, is guaranteed to halt in finitely many steps and correctly classify the input as consistent or not. For a second-order system, the problem is even worse. 22/35

Computational Today’s lecture Semantics: Events Scott Farrar CLMA, University of Washington far- rar@u.washington.edu NL to FOL: Loose ends NL to FOL: Loose ends 1 Misc syn. categories Misc syn. categories VPs, Verbs Problems with verbs VPs, Verbs Event semantics Problems with verbs Semantic roles FrameNet Event semantics 2 Semantic roles FrameNet 23/35

Computational Event semantics Semantics: Events Scott Farrar CLMA, University of Washington far- rar@u.washington.edu One way to get around the need for second-order logic is to NL to FOL: Loose reify as events those entities referred to by verbs, and model ends those events as unary predicates: Misc syn. categories VPs, Verbs BuyingEvent ( x ), VotingEvent ( y ), BowlingEvent ( z ) Problems with verbs Event semantics Semantic roles FrameNet 24/35

Computational Event semantics Semantics: Events Scott Farrar CLMA, University of Washington far- rar@u.washington.edu One way to get around the need for second-order logic is to NL to FOL: Loose reify as events those entities referred to by verbs, and model ends those events as unary predicates: Misc syn. categories VPs, Verbs BuyingEvent ( x ), VotingEvent ( y ), BowlingEvent ( z ) Problems with verbs Event semantics Semantic roles FrameNet Definition Event semantics is an approach to modeling states and processes where the event is referred to directly such that individual events can be referred to in the universe of discourse. The study of the structure of events in linguistics was initiated by philosophers, cf. the work of Donald Davidson (d. 2003). 24/35

Computational Event semantics Semantics: Events Scott Farrar CLMA, University of Washington far- rar@u.washington.edu NL to FOL: Loose ends Furthermore, quantifiers can have scope over event variables, Misc syn. categories VPs, Verbs as in: Problems with verbs Event semantics Semantic roles FrameNet 25/35

Computational Event semantics Semantics: Events Scott Farrar CLMA, University of Washington far- rar@u.washington.edu NL to FOL: Loose ends Furthermore, quantifiers can have scope over event variables, Misc syn. categories VPs, Verbs as in: Problems with verbs Event semantics ∀ e BuyingEvent ( e ) Semantic roles FrameNet 25/35

Computational Event semantics Semantics: Events Scott Farrar CLMA, University of Washington far- rar@u.washington.edu NL to FOL: Loose ends Furthermore, quantifiers can have scope over event variables, Misc syn. categories VPs, Verbs as in: Problems with verbs Event semantics ∀ e BuyingEvent ( e ) Semantic roles FrameNet ∃ x SellingEvent ( x ) 25/35

Computational Event semantics Semantics: Events Scott Farrar CLMA, University of Washington far- rar@u.washington.edu NL to FOL: Loose ends Furthermore, quantifiers can have scope over event variables, Misc syn. categories VPs, Verbs as in: Problems with verbs Event semantics ∀ e BuyingEvent ( e ) Semantic roles FrameNet ∃ x SellingEvent ( x ) But how are the NL subjects and objects (constants) then related to the event? 25/35

Computational Semantic roles Semantics: Events Scott Farrar Definition CLMA, University of Washington far- A semantic role is a relation holding between an event and rar@u.washington.edu the individual that participates in that event. Roles are NL to FOL: Loose modeled as binary predicates. Role types are based on an ends Misc syn. categories individual’s participation in an event. Common types of VPs, Verbs Problems with verbs semantic roles, in relation to some event e : Event semantics Semantic roles FrameNet 26/35

Computational Semantic roles Semantics: Events Scott Farrar Definition CLMA, University of Washington far- A semantic role is a relation holding between an event and rar@u.washington.edu the individual that participates in that event. Roles are NL to FOL: Loose modeled as binary predicates. Role types are based on an ends Misc syn. categories individual’s participation in an event. Common types of VPs, Verbs Problems with verbs semantic roles, in relation to some event e : Event semantics Semantic roles FrameNet agent : the individual that provides the energy for or causes e 26/35

Computational Semantic roles Semantics: Events Scott Farrar Definition CLMA, University of Washington far- A semantic role is a relation holding between an event and rar@u.washington.edu the individual that participates in that event. Roles are NL to FOL: Loose modeled as binary predicates. Role types are based on an ends Misc syn. categories individual’s participation in an event. Common types of VPs, Verbs Problems with verbs semantic roles, in relation to some event e : Event semantics Semantic roles FrameNet agent : the individual that provides the energy for or causes e patient : the individual affected or changed by e 26/35

Computational Semantic roles Semantics: Events Scott Farrar Definition CLMA, University of Washington far- A semantic role is a relation holding between an event and rar@u.washington.edu the individual that participates in that event. Roles are NL to FOL: Loose modeled as binary predicates. Role types are based on an ends Misc syn. categories individual’s participation in an event. Common types of VPs, Verbs Problems with verbs semantic roles, in relation to some event e : Event semantics Semantic roles FrameNet agent : the individual that provides the energy for or causes e patient : the individual affected or changed by e experiencer : the (cognizant) individual that perceives e 26/35

Computational Semantic roles Semantics: Events Scott Farrar Definition CLMA, University of Washington far- A semantic role is a relation holding between an event and rar@u.washington.edu the individual that participates in that event. Roles are NL to FOL: Loose modeled as binary predicates. Role types are based on an ends Misc syn. categories individual’s participation in an event. Common types of VPs, Verbs Problems with verbs semantic roles, in relation to some event e : Event semantics Semantic roles FrameNet agent : the individual that provides the energy for or causes e patient : the individual affected or changed by e experiencer : the (cognizant) individual that perceives e theme : the entity that is transferred (buy/sell), moved in space, etc. by e 26/35

Computational Semantic roles Semantics: Events Scott Farrar Definition CLMA, University of Washington far- A semantic role is a relation holding between an event and rar@u.washington.edu the individual that participates in that event. Roles are NL to FOL: Loose modeled as binary predicates. Role types are based on an ends Misc syn. categories individual’s participation in an event. Common types of VPs, Verbs Problems with verbs semantic roles, in relation to some event e : Event semantics Semantic roles FrameNet agent : the individual that provides the energy for or causes e patient : the individual affected or changed by e experiencer : the (cognizant) individual that perceives e theme : the entity that is transferred (buy/sell), moved in space, etc. by e instrument : the individual acting as the means by which e was carried out 26/35

Computational Semantic roles Semantics: Events Scott Farrar Definition CLMA, University of Washington far- A semantic role is a relation holding between an event and rar@u.washington.edu the individual that participates in that event. Roles are NL to FOL: Loose modeled as binary predicates. Role types are based on an ends Misc syn. categories individual’s participation in an event. Common types of VPs, Verbs Problems with verbs semantic roles, in relation to some event e : Event semantics Semantic roles FrameNet agent : the individual that provides the energy for or causes e patient : the individual affected or changed by e experiencer : the (cognizant) individual that perceives e theme : the entity that is transferred (buy/sell), moved in space, etc. by e instrument : the individual acting as the means by which e was carried out beneficiary : the individual that gains from e 26/35

Computational Semantic roles Semantics: Events Scott Farrar Definition CLMA, University of Washington far- A semantic role is a relation holding between an event and rar@u.washington.edu the individual that participates in that event. Roles are NL to FOL: Loose modeled as binary predicates. Role types are based on an ends Misc syn. categories individual’s participation in an event. Common types of VPs, Verbs Problems with verbs semantic roles, in relation to some event e : Event semantics Semantic roles FrameNet agent : the individual that provides the energy for or causes e patient : the individual affected or changed by e experiencer : the (cognizant) individual that perceives e theme : the entity that is transferred (buy/sell), moved in space, etc. by e instrument : the individual acting as the means by which e was carried out beneficiary : the individual that gains from e location , source , goal , path : spatial individuals in relation to e 26/35

Mapping NL to FOL: VPs John buttered the toast. ButteringEvent ( E 1 ) ∧ agent ( E 1 , JOHN ) ∧ patient ( E 1 , TOAST 1)

Mapping NL to FOL: VPs John buttered the toast. ButteringEvent ( E 1 ) ∧ agent ( E 1 , JOHN ) ∧ patient ( E 1 , TOAST 1) John buttered the toast at midnight. ButteringEvent ( E 2 ) ∧ agent ( E 2 , JOHN ) ∧ patient ( E 2 , TOAST 1) ∧ time ( E 2 , MIDNIGHT )

Mapping NL to FOL: VPs John buttered the toast. ButteringEvent ( E 1 ) ∧ agent ( E 1 , JOHN ) ∧ patient ( E 1 , TOAST 1) John buttered the toast at midnight. ButteringEvent ( E 2 ) ∧ agent ( E 2 , JOHN ) ∧ patient ( E 2 , TOAST 1) ∧ time ( E 2 , MIDNIGHT ) John buttered the toast at midnight with a knife. ButteringEvent ( E 3 ) ∧ agent ( E 3 , JOHN ) ∧ patient ( E 3 , TOAST 1) ∧ time ( E 3 , MIDNIGHT ) ∧ instrument ( E 3 , k ) ∧ knife ( k )

Computational Semantic role axioms Semantics: Events Scott Farrar CLMA, University of Washington far- rar@u.washington.edu NL to FOL: Loose ends axiom Misc syn. categories VPs, Verbs All events take place in space: Problems with verbs ∀ e ∃ x ( Event ( e ) → location ( e , x )) Event semantics Semantic roles FrameNet 28/35

Computational Semantic role axioms Semantics: Events Scott Farrar CLMA, University of Washington far- rar@u.washington.edu NL to FOL: Loose ends axiom Misc syn. categories VPs, Verbs All events take place in space: Problems with verbs ∀ e ∃ x ( Event ( e ) → location ( e , x )) Event semantics Semantic roles FrameNet axiom If some individual is an agent of a cognition event (think, know, consider), then the individual is human. ∀ e ∀ a ( CognitionEvent ( e ) ∧ agent ( e , a ) → human ( a )) 28/35