Non-normal modal logics and conditional logics: Semantic analysis and proof theory

Chen, Jinsheng; Greco, Giuseppe; Palmigiano, Alessandra; Tzimoulis, Apostolos

doi:10.1016/j.ic.2021.104756

Cited by 5 publications

References 54 publications

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CoNP Complexity for Combinations of Non-normal Modal Logics

Dalmonte,

Mazzullo

2023

Lecture Notes in Computer Science

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We study the complexity of the validity/derivability problem for combinations of non-normal modal logics in the form of logic fusions, possibly extended with simple interaction axioms. We first present cut-free sequent calculi for these logic combinations. Then, we introduce hypersequent calculi with invertible rules, and show that they allow for a coNP proof search procedure. In the last part of the paper, we consider the case of combinations of logics sharing a universal modality. Using the hypersequent calculi, we show that these logics remain coNP-complete, and also provide an equivalent axiomatisation for them.

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CoNP Complexity for Combinations of Non-normal Modal Logics

Dalmonte,

Mazzullo

2023

Lecture Notes in Computer Science

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On the Finite Model Property of Non-normal Modal Logics

Peng,

Wang

2023

Lecture Notes in Computer Science

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Linear Logic Properly Displayed

Greco¹,

Palmigiano²

2023

ACM Trans. Comput. Logic

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We introduce proper display calculi for intuitionistic, bi-intuitionistic and classical linear logics with exponentials, which are sound, complete, conservative, and enjoy cut elimination and subformula property. Based on the same design, we introduce a variant of Lambek calculus with exponentials, aimed at capturing the controlled application of exchange and associativity. Properness (i.e. closure under uniform substitution of all parametric parts in rules) is the main technical novelty of the present proposal, allowing both for the smoothest proof of cut elimination, and for the development of an overarching and modular treatment for a vast class of axiomatic extensions and expansions of intuitionistic, bi-intuitionistic and classical linear logics with exponentials. Our proposal builds on an algebraic and order-theoretic analysis of linear logic, and applies the guidelines of the multi-type methodology in the design of display calculi. Keywords : Linear logic, substructural logics, algebraic proof theory, sequent calculi, cut elimination, display calculi, multi-type calculi, proof calculi for categorial grammar. 2010 Math. Subj. Class. CCS, Theory of computation, Logic, Proof theory.

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Non-normal modal logics and conditional logics: Semantic analysis and proof theory

Cited by 5 publications

References 54 publications

CoNP Complexity for Combinations of Non-normal Modal Logics

CoNP Complexity for Combinations of Non-normal Modal Logics

On the Finite Model Property of Non-normal Modal Logics

Linear Logic Properly Displayed

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