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 has left Baltimore
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
Proposal
● Hand built lexicon for function words
● Symbolic content word interpretations from
distributional semantics
● CCG for compositional semantics
Combining Distributional and
Logical Semantics
1
arrive in
reach
2
visit
leave
exit
depart
3
Combining Distributional and
Logical Semantics
1
arrive in
reach
2
visit
leave
exit
depart
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)
3
Combining Distributional and
Logical Semantics
Mike
NP
mike
reached
(S\NP)/NP
λyλxλe . rel2(x,y,e)
Baltimore
NP
baltimore
S\NP
λxλe . rel2(x, baltimore)
S
λe . rel2(mike, baltimore, e)
Combining Distributional and
Logical Semantics
Mike arrived in Baltimore
rel2(mike,
baltimore, e)
⇒ Mike reached Baltimore
rel2(mike,
baltimore, e)
Combining Distributional and
Logical Semantics
Mike
NP
mike
didn’t
(S\NP)/(S\NP)
λpλxλe. ¬p(x,e)
reach
(S\NP)/NP
λyλxλe . rel2(x,y,e)
Baltimore
NP
baltimore
S\NP
λxλe . rel2(x, baltimore)
S\NP
λxλe . ¬rel2(x, baltimore, e)
S
λe . ¬rel2(mike, baltimore, e)
Combining Distributional and
Logical Semantics
Mike didn’t arrive in Baltimore
¬rel2(mike,
baltimore)
Mike didn’t reach Baltimore
¬rel2(mike,
baltimore)
Combining Distributional and
Logical Semantics
Simple clustering is not enough
● Models words as either synonyms or
unrelated
● Many lexical semantic relations: temporal,
causal, hypernyms, etc.
Temporal Semantics
1
arrive in
reach
2
visit
leave
exit
depart
3
Temporal Semantics
in
iti
at
ed
by
1
arrive in
reach
2
visit
te
rm
in
at
ed
leave
exit
depart
by
3
Learn graph structures capturing relations between events
Similar to Scaria et al. (2013)
Temporal Semantics
visit
te
rm
in
at
in
iti
at
ed
by
1
arrive in
reach
2
ed
leave
exit
depart
arrive in ⊢ λxλyλe . rel2(x,y,e)
reach ⊢ λxλyλe . rel2(x,y,e)
leave
⊢ λxλyλe . rel3(x,y,e)
by
3
Temporal Semantics
in
iti
at
ed
by
1
arrive in
reach
visit
2
visit
te
rm
in
at
ed
leave
exit
depart
by
3
⊢ λxλyλe . rel1(x,y,e) ∧
∃e’[rel2(x,y,e’) ∧ before(e,e’)]
∃e’’[rel3(x,y,e’’) ∧ after(e,e’’)]
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’)]
Temporal Semantics
Mike
NP
mike
will
(S\NP)/(S\NP)
λpλxλe. p(x,e) ∧ after(r,e)
leave
(S\NP)/NP
λyλxλe . rel3(x,y,e)
Baltimore
NP
baltimore
S\NP
λxλe . rel3(x, baltimore)
S\NP
λxλe . rel3(x, baltimore, e) ∧ after(r,e)
S
λe . rel3(mike, baltimore, e) ∧ after(r,e)
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)]
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)]
⇒
Mike will leave Baltimore
∃e[rel3(mike, baltimore, e) ∧ after(r,e)]
Intensional Semantics
Mike set out for Baltimore
⇒ Mike tried to reach Baltimore
⇒ Mike headed to Baltimore
⇏ Mike reached Baltimore
Intensional Semantics
Mike failed to reach Baltimore
⇒ Mike tried to reach Baltimore
⇒ Mike headed to Baltimore
⇒ Mike didn’t reach Baltimore
Temporal Semantics
visit
in
iti
at
ed
by
1
arrive in
reach
2
te
rm
in
at
ed
leave
exit
depart
by
3
Intensional Semantics
1
in
iti
at
al
ed
go
set out for
head to
by
4
arrive in
reach
2
visit
te
rm
in
at
ed
leave
exit
depart
by
3
Intensional Semantics
1
in
iti
at
al
ed
go
set out for
head to
by
4
arrive in
reach
2
visit
te
rm
in
at
ed
leave
exit
depart
by
3
set out for ⊢ λxλyλe . rel4(x,y,e) ∧ ⋄∃e’[rel2(x,y,e’) ∧ goal(e,e’)]
Intensional Semantics
try
⊢ λpλxλe. ∃e’[goal(e, e’) ∧ ⋄ p(x, e’)]
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’’)]
Intensional Semantics
Mike set out for Baltimore
∃e[rel4(x,y,e) ∧ ⋄∃e’[rel2(mike, baltimore,e’) ∧ goal(e,e’)]
⇒
Mike tried to reach Baltimore
⋄∃e’[rel2(mike, baltimore, e’) ∧ goal(e,e’)]
Evaluation
Conclusions
● Many inferences rely on complex interaction
of formal and lexical semantics
● Recent work gives us the tools to
incorporate more linguistics into
computational semantics