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Combining Formal and Distributional Models of Temporal and - - PowerPoint PPT Presentation
Combining Formal and Distributional Models of Temporal and - - PowerPoint PPT Presentation
Combining Formal and Distributional Models of Temporal and Intensional Semantics Mike Lewis and Mark Steedman Inference with Temporal Senantics Mike is visiting Baltimore Mike has arrived in Baltimore Mike will leave Baltimore Mike
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Inference with Temporal Senantics
Mike is visiting Baltimore ⇒ Mike has arrived in Baltimore ⇒ Mike will leave Baltimore ⇏ Mike has left Baltimore Temporal information can be expressed by both function words and content words
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Proposal
- Hand built lexicon for function words
- Symbolic content word interpretations from
distributional semantics
- CCG for compositional semantics
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1 2 3
leave exit depart visit arrive in reach
Combining Distributional and Logical Semantics
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visit ⊢ λxλyλe . rel1(x,y,e) arrive in ⊢ λxλyλe . rel2(x,y,e) reach ⊢ λxλyλe . rel2(x,y,e) leave ⊢ λxλyλe . rel3(x,y,e) 1 2 3
leave exit depart visit arrive in reach
Combining Distributional and Logical Semantics
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Mike NP mike reached (S\NP)/NP λyλxλe . rel2(x,y,e) Baltimore NP baltimore S λe . rel2(mike, baltimore, e) S\NP λxλe . rel2(x, baltimore)
Combining Distributional and Logical Semantics
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Mike arrived in Baltimore
rel2(mike, baltimore, e)
Mike reached Baltimore
rel2(mike, baltimore, e)
Combining Distributional and Logical Semantics
⇒
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Mike NP mike reach (S\NP)/NP λyλxλe . rel2(x,y,e) Baltimore NP baltimore S\NP λxλe . ¬rel2(x, baltimore, e) S λe . ¬rel2(mike, baltimore, e) didn’t (S\NP)/(S\NP) λpλxλe. ¬p(x,e) S\NP λxλe . rel2(x, baltimore)
Combining Distributional and Logical Semantics
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Mike didn’t arrive in Baltimore
¬rel2(mike, baltimore)
Mike didn’t reach Baltimore
¬rel2(mike, baltimore)
Combining Distributional and Logical Semantics
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Simple clustering is not enough
- Models words as either synonyms or
unrelated
- Many lexical semantic relations: temporal,
causal, hypernyms, etc.
Combining Distributional and Logical Semantics
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Temporal Semantics
1 2 3
leave exit depart visit arrive in reach
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Temporal Semantics
Learn graph structures capturing relations between events Similar to Scaria et al. (2013)
terminated by i n i t i a t e d b y
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leave exit depart visit arrive in reach
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Temporal Semantics
arrive in ⊢ λxλyλe . rel2(x,y,e) reach ⊢ λxλyλe . rel2(x,y,e) leave ⊢ λxλyλe . rel3(x,y,e)
terminated by i n i t i a t e d b y
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leave exit depart visit arrive in reach
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Temporal Semantics
visit ⊢ λxλyλe . rel1(x,y,e) ∧ ∃e’[rel2(x,y,e’) ∧ before(e,e’)] ∃e’’[rel3(x,y,e’’) ∧ after(e,e’’)]
terminated by i n i t i a t e d b y
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leave exit depart visit arrive in reach
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Temporal Semantics
Hand-build lexical entries for auxiliary verbs, using same temporal relations: has ⊢ λpλxλe . before(r, e) ∧ p(x, e) will ⊢ λpλxλe . after(r, e) ∧ p(x, e) is ⊢ λpλxλe . during(r, e) ∧ p(x, e) used ⊢ λpλxλe . before(r, e) ∧ p(x, e) ∧ ¬∃e’[during(r, e) ∧ p(x, e’)]
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Temporal Semantics
Mike NP mike leave (S\NP)/NP λyλxλe . rel3(x,y,e) Baltimore NP baltimore S\NP λxλe . rel3(x, baltimore, e) ∧ after(r,e) S λe . rel3(mike, baltimore, e) ∧ after(r,e) will (S\NP)/(S\NP) λpλxλe. p(x,e) ∧ after(r,e) S\NP λxλe . rel3(x, baltimore)
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Temporal Semantics
Mike is visiting Baltimore
∃e[rel1(mike, baltimore, e) ∧ during(r,e)] ∧ ∃e’[rel2(mike, baltimore, e’) ∧ before(e,e’)] ∧ ∧ ∃e’’[rel3(mike, baltimore, e) ∧ after(e’’,e)]
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Temporal Semantics
Mike is visiting Baltimore Mike will leave Baltimore
∃e[rel3(mike, baltimore, e) ∧ after(r,e)] ∃e[rel1(mike, baltimore, e) ∧ during(r,e)] ∧ ∃e’[rel2(mike, baltimore, e’) ∧ before(e,e’)] ∧ ∧ ∃e’’[rel3(mike, baltimore, e) ∧ after(e’’,e)]
⇒
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Intensional Semantics
Mike set out for Baltimore ⇒ Mike tried to reach Baltimore ⇒ Mike headed to Baltimore ⇏ Mike reached Baltimore
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Intensional Semantics
Mike failed to reach Baltimore ⇒ Mike tried to reach Baltimore ⇒ Mike headed to Baltimore ⇒ Mike didn’t reach Baltimore
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Temporal Semantics
1
2 3
i n i t i a t e d b y terminated by leave exit depart visit arrive in reach
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Intensional Semantics
4
g
- a
l
set out for head to
terminated by i n i t i a t e d b y
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leave exit depart visit arrive in reach
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Intensional Semantics
set out for ⊢ λxλyλe . rel4(x,y,e) ∧ ⋄∃e’[rel2(x,y,e’) ∧ goal(e,e’)] 4
g
- a
l
set out for head to
terminated by i n i t i a t e d b y
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leave exit depart visit arrive in reach
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Intensional Semantics
try ⊢ λpλxλe. ∃e’[goal(e, e’) ∧ ⋄ p(x, e’)]
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Intensional Semantics
try ⊢ λpλxλe. ∃e’[goal(e, e’) ∧ ⋄ p(x, e’)] fail ⊢ λpλxλe. ∃e’[goal(e, e’) ∧ ⋄ p(x,e’)] ∧ ¬∃e’’[goal(e, e’’) ∧ p(x, e’’)]
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Intensional Semantics
Mike set out for Baltimore Mike tried to reach Baltimore
⋄∃e’[rel2(mike, baltimore, e’) ∧ goal(e,e’)] ∃e[rel4(x,y,e) ∧ ⋄∃e’[rel2(mike, baltimore,e’) ∧ goal(e,e’)]
⇒
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Evaluation
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Conclusions
- Many inferences rely on complex interaction
- f formal and lexical semantics
- Recent work gives us the tools to