Soft Subexponentials and Multiplexing

Kanovich, Max I.; Kuznetsov, Stepan L.; Nigam, Vivek; Scedrov, Andre

doi:10.1007/978-3-030-51074-9_29

Cited by 8 publications

(7 citation statements)

References 21 publications

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“…The latest iteration of compositional distributional analysis of discourse uses the Lambek calculus with soft subexponentials, SLLM [12], which is Lambek calculus with two modalities, ! and ∇, allowing !-formulas to be copied and ∇-formulas to be permuted.…”

Section: Discourse In Discocatmentioning

confidence: 99%

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DisCoCat for Donkey Sentences

McPheat

Wang

2023

Electron. Proc. Theor. Comput. Sci.

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We demonstrate how to parse Geach's Donkey sentences in a compositional distributional model of meaning. We build on previous work on the DisCoCat (Distributional Compositional Categorical) framework, including extensions that model discourse, determiners, and relative pronouns. We present a type-logical syntax for parsing donkey sentences, for which we define both relational and vector space semantics.

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Section: Discourse In Discocatmentioning

confidence: 99%

“…This calculus has a decidable derivation problem once one fixes a global bound on the number of copies in the ! L rule, we call it k. The authors also prove a cut-elimination theorem for SLLM [12].…”

Section: Discourse In Discocatmentioning

confidence: 99%

DisCoCat for Donkey Sentences

McPheat

Wang

2023

Electron. Proc. Theor. Comput. Sci.

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“…SLLM is a cut-free logic with a decidable fragment and a directed proof system. We recall its definition from [10] in table 1. The decidable fragment is found when one chooses a global bound (k 0 ) on the number of formulas you may contract using the multiplexing rule (denoted by !…”

Section: Sllm Lambek Calculus With Soft Subexponentialsmentioning

confidence: 99%

“…The calculus we depended on for this work, !L * , however, was proven undecidable in the same paper it was introduced which has posed a challenge for all the work we have done on top of it. Thankfully, the creators of !L * have since defined a new logic with a similar expressive power but with a decidable fragment, referred to by SLLM [10]. In SLLM permutation and contraction (now called 'multiplexing') are separated into two different modalities, whose logical rules are inspired by Light and Soft linear logic [4,14].…”

Section: Introductionmentioning

confidence: 99%

Vector Space Semantics for Lambek Calculus with Soft Subexponentials

McPheat¹,

Wazni²,

Sadrzadeh³

2021

Preprint

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We develop a vector space semantics for Lambek Calculus with Soft Subexponentials, apply the calculus to construct compositional vector interpretations for parasitic gap noun phrases and discourse units with anaphora and ellipsis, and experiment with the constructions in a distributional sentence similarity task. As opposed to previous work, which used Lambek Calculus with a Relevant Modality the calculus used in this paper uses a bounded version of the modality and is decidable. The vector space semantics of this new modality allows us to meaningfully define contraction as projection and provide a linear theory behind what we could previously only achieve via nonlinear maps.

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“…The conjunctive Kleene star behaves similar to the exponential modality ! (or, more precisely, to the soft subexponential as in [5]). However, the conjunctive Kleene star has a different motivation and its axiomatization involves, in particular, the omega rule (see Section 5).…”

Section: Introductionmentioning

confidence: 99%

From Double Pushout Grammars to Hypergraph Lambek Grammars With and Without Exponential Modality

Pshenitsyn

2023

Electron. Proc. Theor. Comput. Sci.

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We study how to relate well-known hypergraph grammars based on the double pushout (DPO) approach and grammars over the hypergraph Lambek calculus HL (called HL-grammars). It turns out that DPO rules can be naturally encoded by types of HL using methods similar to those used by Kanazawa for multiplicative-exponential linear logic. In order to generalize his reasonings we extend the hypergraph Lambek calculus by adding the exponential modality, which results in a new calculus HMEL 0 ; then we prove that any DPO grammar can be converted into an equivalent HMEL 0grammar. We also define the conjunctive Kleene star, which behaves similarly to this exponential modality, and establish a similar result. If we add neither the exponential modality nor the conjunctive Kleene star to HL, then we can still use the same encoding and show that any DPO grammar with a linear restriction on the length of derivations can be converted into an equivalent HL-grammar.

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Soft Subexponentials and Multiplexing

Cited by 8 publications

References 21 publications

DisCoCat for Donkey Sentences

DisCoCat for Donkey Sentences

Vector Space Semantics for Lambek Calculus with Soft Subexponentials

From Double Pushout Grammars to Hypergraph Lambek Grammars With and Without Exponential Modality

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