SLIDE 1
Monotonic Inference for Underspecified Episodic Logic
Mandar Juvekar University of Rochester Natural Logic Meets Machine Learning 17 July 2020
Gene Louis Kim UR Lenhart K. Schubert UR
Monotonic Inference for Underspecified Episodic Logic Mandar - - PowerPoint PPT Presentation
Monotonic Inference for Underspecified Episodic Logic Mandar - - PowerPoint PPT Presentation
Monotonic Inference for Underspecified Episodic Logic Mandar Juvekar University of Rochester Natural Logic Meets Machine Learning 17 July 2020 Gene Louis Kim Lenhart K. Schubert UR UR Snchez Valencia Lambek Derivations Tableau-style
SLIDE 2
SLIDE 3
“abelard sees a carp” “every carp is a fish” “abelard sees a fish”
Lambek Derivations Tableau-style proofs
(|Abelard| (see.v (a.d carp.n)))
Sánchez Valencia ULF
Replace Lambek derivations and sentences with ULFs
(|Abelard| (see.v (a.d fish.n)))
SLIDE 4
Episodic Logic (EL)
An extended FOL that closely matches the form and expressivity of natural language.
Unscoped Logical Form (ULF)
An underspecified form of EL. Specifies semantic type structure while leaving scope, anaphora, and word sense unresolved.
SLIDE 5
(|Adam| ((past place.v) |John| (under.p (k arrest.n)))) “Adam placed John under arrest.”
SLIDE 6
Typical EL Inference Unscoped episodic logical forms are fully resolved before inference
SLIDE 7
Premises Interpret Infer Conclude
SLIDE 8
Key Observation ULF provides the structural foundation for monotonic inference
SLIDE 9
(|Ali| (do.aux-s not (know.v (that (i.pro (work.v (adv-a (with.p (a.d dog.n))))))))) “Ali does not know that I work with a dog”
SLIDE 10
(|Ali| (do.aux-s not (know.v (that (i.pro (work.v (adv-a (with.p (a.d dog.n))))))))) “Ali does not know that I work with a dog”
Preserved Word Order
SLIDE 11
(|Ali| (do.aux-s not (know.v (that (i.pro (work.v (adv-a (with.p (a.d dog.n))))))))) “Ali does not know that I work with a dog”
Grammatical Structure
SLIDE 12
(|Ali| (do.aux-s not (know.v (that (i.pro (work.v (adv-a (with.p (a.d dog.n))))))))) “Ali does not know that I work with a dog”
Semantic Types
e ⟨e,⟨e,t’⟩⟩ ⟨t’,e⟩ ⟨t’,t’⟩ e ⟨e,⟨e,t’⟩⟩ ⟨⟨e,t’⟩,e⟩ ⟨e,⟨e,t’⟩⟩ ⟨⟨e,t’⟩,e⟩ ⟨e,t’⟩ ⟨t’,t’⟩
SLIDE 13
“Some man holds no apple”
Some: (+,+) No: (-,-)
We need semantic argument structure
SLIDE 14
((Some man) (holds (no apple)))
“Some man holds no apple”
Some: (+,+) No: (-,-)
Some man touches no apple Some man holds no apple
We need semantic argument structure
Grammatical
SLIDE 15
((Some man) (holds (no apple))) (Some x: (x man) (no y: (y apple) (x holds y)))
“Some man holds no apple”
Some: (+,+) No: (-,-)
Some man touches no apple Some man holds no apple Some man clenches no apple
We need semantic argument structure
Grammatical Semantic
SLIDE 16
Proposal Directly use ULFs as the basis for inference
SLIDE 17
Scope Marking
Sánchez Valencia
Label
SLIDE 18
Scope Marking
Sánchez Valencia
Label
ULF
SLIDE 19
Polarity Marking
Sánchez Valencia
SLIDE 20
Polarity Marking
Sánchez Valencia ULF
SLIDE 21
Inference Rules
SLIDE 22
Inference Rules
SLIDE 23
Inference Rules
SLIDE 24
Inference Rules
SLIDE 25
Inference Rules
SLIDE 26
Inference Rules
SLIDE 27
Generalized Inference
Rule Instantiation (EL)
“Every carp is a fish” “Abelard sees a carp”
SLIDE 28
Generalized Inference
Rule Instantiation (EL) 1. Select logical fragments with opposing polarities
“Every carp is a fish” “Abelard sees a carp”
SLIDE 29
Generalized Inference
Rule Instantiation (EL) 1. Select logical fragments with opposing polarities 2. Matchably bind the two fragments (fail if unable)
“Every carp is a fish” “Abelard sees a carp”
(x → y)
SLIDE 30
Generalized Inference
Rule Instantiation (EL) 1. Select logical fragments with opposing polarities 2. Matchably bind the two fragments (fail if unable) 3. Convert the formula with the negative polarity fragment
(y carp.n) → T
“Every carp is a fish” “Abelard sees a carp”
(x → y)
SLIDE 31
Generalized Inference
Rule Instantiation (EL) 1. Select logical fragments with opposing polarities 2. Matchably bind the two fragments (fail if unable) 3. Convert the formula with the negative polarity fragment
“Every carp is a fish” “Abelard sees a carp”
(y carp.n) → T
=
(x → y)
SLIDE 32
Generalized Inference
Rule Instantiation (EL) 1. Select logical fragments with opposing polarities 2. Matchably bind the two fragments (fail if unable) 3. Convert the formula with the negative polarity fragment
SLIDE 33
Generalized Inference
Rule Instantiation (EL) 1. Select logical fragments with opposing polarities 2. Matchably bind the two fragments (fail if unable) 3. Convert the formula with the negative polarity fragment 4. Substitute converted formula for other match
“Abelard sees a fish”
SLIDE 34
Generalized Inference
Rule Instantiation (EL) 1. Select logical fragments with opposing polarities 2. Matchably bind the two fragments (fail if unable) 3. Convert the formula with the negative polarity fragment 4. Substitute converted formula for other match
“Abelard sees a fish”
MAJ: MIN:
SLIDE 35
Generalized Inference
Rule Instantiation (EL)
generalizes
ULF Monotonic Inference
SLIDE 36
Benefits
- Reduce sources of parsing error
- Dynamically choose scoping
assumptions
- Retain a record of assumptions and
inferences
- Simple interface to surface form
SLIDE 37
Integration with ML
- ULF was designed for ease of ML-based parsing.
Parser under review with similar performance to initial AMR parsers
- ML-assisted ambiguity resolution (e.g. scopes,
word sense, polarity)
- Retain semantic type and polarity coherence for
interpretable inferences.
SLIDE 38