Combining Axiom Injection and Knowledge Base Completion for Efficient Natural Language Inference Masashi Yoshikawa, Koji Mineshima, Hiroshi Noji, Daisuke Bekki Nara Institute of Science and Technology Ochanomizu University Artificial Intelligence Research Center, AIST AAAI-33 2019/1/31
- lexical, logical, syntactic phenomena, etc. - Question answering, reading comprehension, etc. Recognizing Textual Entailment Premise(s) Hypothesis a.k.a. Natural Language Inference P1 : Clients at the demonstration were all H : Smith was impressed by the impressed by the system’s performance. system’s performance. P2 : Smith was a client at the demonstration. {entailment, contradiction, unknown} • A testbed to evaluate if a machine can reason as we do • Elemental technology for improving other NLP tasks � 2
Approaches to RTE Rocktäschel et al., 2016 ( B ) Attention ( C ) Word-by-word Attention h 1 h 2 h 3 h 4 h 5 h 6 h 7 h 8 h 9 • Machine learning (Rocktäschel et al., 2016, etc.) ( A ) Conditional c 1 c 2 c 3 c 4 c 5 c 6 c 7 c 8 c 9 Encoding • e.g. Neural Networks x 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 A wedding party taking pictures :: Someone got married Premise Hypothesis � 3
Approaches to RTE Rocktäschel et al., 2016 Mineshima et al., 2015 ( B ) Attention ( C ) Word-by-word Attention h 1 h 2 h 3 h 4 h 5 h 6 h 7 h 8 h 9 • Machine learning (Rocktäschel et al., 2016, etc.) ( A ) Conditional c 1 c 2 c 3 c 4 c 5 c 6 c 7 c 8 c 9 Encoding • e.g. Neural Networks x 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 A wedding party taking pictures :: Someone got married Premise Hypothesis • Logic (Mineshima et al., 2015, Abzianidze 2017, etc) Premise (P) T: A man hikes. H: A man walks. & Hypothesis (H) • Traditional pipeline systems S S Syntactic Parsing NP NP • Theorem prover (e.g. Coq) Semantic Parsing NP/N N S\NP NP/N N S\NP A man hikes A man walks Theorem Proving { yes, no, unknown } � 3
Approaches to RTE Rocktäschel et al., 2016 Mineshima et al., 2015 ( B ) Attention ( C ) Word-by-word Attention h 1 h 2 h 3 h 4 h 5 h 6 h 7 h 8 h 9 • Machine learning (Rocktäschel et al., 2016, etc.) ( A ) Conditional c 1 c 2 c 3 c 4 c 5 c 6 c 7 c 8 c 9 Encoding • e.g. Neural Networks x 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 A wedding party taking pictures :: Someone got married Premise Hypothesis • Logic (Mineshima et al., 2015, Abzianidze 2017, etc) Premise (P) T: A man hikes. H: A man walks. & Hypothesis (H) • Traditional pipeline systems S S Syntactic Parsing NP NP • Theorem prover (e.g. Coq) Semantic Parsing NP/N N S\NP NP/N N S\NP A man hikes A man walks Theorem Proving • Ours : logic-based, extended by ML! (Hybrid) { yes, no, unknown } � 3
ccg2lambda (Mineshima et al., 2015) Coq go walk hike theorem prover P: A man hikes. H: A man walks. Premise (P) P: A man hikes. H: A man walks. Premise (P) & Hypothesis (H) S & Hypothesis (H) S S S NP NP Syntactic Parsing NP NP Syntactic Parsing NP/N N S\NP NP/N N S\NP NP/N N S\NP NP/N N S\NP CCG Derivations A man walks A man hikes CCG Derivations A man walks A man hikes Semantic Parsing Semantic Parsing Logical Formulas Logical Formulas Theorem Proving Coq < Theorem t1: Theorem Proving (exists x : Entity, man x /\ (exists e : Event, hike e /\ subj e x)) -> exists x : Entity, man x /\ (exists e : Event, walk e /\ subj e x). Coq < Proof. ccg2lambda. Qed. result: unknown { yes, no, unknown } result: unknown { yes, no, unknown } hypernym Search on KBs Search on KBs New Axioms hypernym New Axioms � 4 Theorem Proving Coq < Axiom ax1: forall x: Event, hike e -> walk e. Theorem Proving { yes, no, unknown } result: yes { yes, no, unknown } result: yes
ccg2lambda (Mineshima et al., 2015) Coq - 83.6 % accuracy in SICK go hike prover theorem walk P: A man hikes. H: A man walks. Premise (P) P: A man hikes. H: A man walks. Premise (P) & Hypothesis (H) S & Hypothesis (H) S S S NP NP Syntactic Parsing NP NP Syntactic Parsing NP/N N S\NP NP/N N S\NP NP/N N S\NP NP/N N S\NP CCG Derivations A man walks A man hikes CCG Derivations A man walks A man hikes Semantic Parsing Semantic Parsing Logical Formulas Logical Formulas Theorem Proving Coq < Theorem t1: Theorem Proving (exists x : Entity, man x /\ (exists e : Event, hike e /\ subj e x)) -> exists x : Entity, man x /\ (exists e : Event, walk e /\ subj e x). Coq < Proof. ccg2lambda. Qed. result: unknown { yes, no, unknown } result: unknown { yes, no, unknown } 👎 Unsupervised hypernym Search on KBs Search on KBs 👎 Captures linguistic phenomena New Axioms hypernym New Axioms � 4 Theorem Proving Coq < Axiom ax1: forall x: Event, hike e -> walk e. Theorem Proving { yes, no, unknown } result: yes { yes, no, unknown } result: yes
ccg2lambda (Mineshima et al., 2015) Coq the search space of theorem proving! - Use WordNet as axioms blows up e.g. How to handle external knowledge? - 83.6 % accuracy in SICK walk hike prover theorem go P: A man hikes. H: A man walks. Premise (P) P: A man hikes. H: A man walks. Premise (P) & Hypothesis (H) S & Hypothesis (H) S S S NP NP Syntactic Parsing NP NP Syntactic Parsing NP/N N S\NP NP/N N S\NP NP/N N S\NP NP/N N S\NP CCG Derivations A man walks A man hikes CCG Derivations A man walks A man hikes Semantic Parsing Semantic Parsing Logical Formulas Logical Formulas Theorem Proving Coq < Theorem t1: Theorem Proving (exists x : Entity, man x /\ (exists e : Event, hike e /\ subj e x)) -> exists x : Entity, man x /\ (exists e : Event, walk e /\ subj e x). Coq < Proof. ccg2lambda. Qed. result: unknown { yes, no, unknown } result: unknown { yes, no, unknown } 🤕 👎 Unsupervised hypernym Search on KBs ∀ x . hike ( x ) → walk ( x ) Search on KBs 👎 Captures linguistic phenomena New Axioms hypernym New Axioms � 4 Theorem Proving Coq < Axiom ax1: forall x: Event, hike e -> walk e. Theorem Proving { yes, no, unknown } result: yes { yes, no, unknown } result: yes
" Abduction " Mechanism (Martínez-Gómez et al., 2017) Coq go walk hike theorem prover P: A man hikes. H: A man walks. Premise (P) P: A man hikes. H: A man walks. Premise (P) & Hypothesis (H) S & Hypothesis (H) S S S NP NP Syntactic Parsing NP NP Syntactic Parsing NP/N N S\NP NP/N N S\NP NP/N N S\NP NP/N N S\NP CCG Derivations A man walks A man hikes CCG Derivations A man walks A man hikes Semantic Parsing Semantic Parsing Logical Formulas Logical Formulas Theorem Proving Coq < Theorem t1: Theorem Proving (exists x : Entity, man x /\ (exists e : Event, hike e /\ subj e x)) -> exists x : Entity, man x /\ (exists e : Event, walk e /\ subj e x). Coq < Proof. ccg2lambda. Qed. result: unknown { yes, no, unknown } result: unknown { yes, no, unknown } hypernym Search on KBs Search on KBs New Axioms hypernym New Axioms � 5 Theorem Proving Coq < Axiom ax1: forall x: Event, hike e -> walk e. Theorem Proving { yes, no, unknown } result: yes { yes, no, unknown } result: yes
P: A man hikes. H: A man walks. Premise (P) P: A man hikes. H: A man walks. Premise (P) & Hypothesis (H) S & Hypothesis (H) S S S NP NP Syntactic Parsing NP NP Syntactic Parsing NP/N N S\NP NP/N N S\NP NP/N N S\NP NP/N N S\NP CCG Derivations A man walks A man hikes CCG Derivations A man walks A man hikes Semantic Parsing Semantic Parsing " Abduction " Mechanism (Martínez-Gómez et al., 2017) More steps when the 1st theorem proving is unsuccessful 1. Search KBs (e.g. WordNet) for useful lexical relations go walk hike prover Coq theorem prover theorem Coq 2. Rerun Coq with additional axioms Logical Formulas Logical Formulas Theorem Proving Coq < Theorem t1: Theorem Proving (exists x : Entity, man x /\ (exists e : Event, hike e /\ subj e x)) -> exists x : Entity, man x /\ (exists e : Event, walk e /\ subj e x). Coq < Proof. ccg2lambda. Qed. result: unknown { yes, no, unknown } result: unknown { yes, no, unknown } hypernym Search on KBs Search on KBs New Axioms hypernym New Axioms Theorem Proving Coq < Axiom ax1: forall x: Event, hike e -> walk e. Theorem Proving Coq < Theorem t1: (exists x : Entity, man x /\ (exists e : Event, hike e /\ subj e x)) -> exists x : Entity, man x /\ (exists e : Event, walk e /\ subj e x). Coq < Proof. ccg2lambda. Qed. { yes, no, unknown } result: yes { yes, no, unknown } result: yes � 5
" Abduction " Mechanism (Martínez-Gómez et al., 2017) • Promising approach to handling external knowledge within a logic-based system � 6
" Abduction " Mechanism (Martínez-Gómez et al., 2017) • Promising approach to handling external knowledge within a logic-based system • (However,) Practical issues : • We want to add more knowledge to increase the coverage of reasoning • We want the KBs to be compact for efficient inference & memory usage � 6
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