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Sequent Calculus and Equational Programming [PDF]
Electronic Proceedings in Theoretical Computer Science, 2015 Proof assistants and programming languages based on type theories usually come in two flavours: one is based on the standard natural deduction presentation of type theory and involves eliminators, while the other provides a syntax in equational style. We
Nicolas Guenot, Daniel Gustafsson
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A calculus of multiary sequent terms [PDF]
ACM Transactions on Computational Logic, 2011 Multiary sequent terms were originally introduced as a tool for proving termination of permutative conversions in cut-free sequent calculus. This work develops the language of multiary sequent terms into a term calculus for the computational (Curry ...
JOSÉ Espirito Santo, Luis Pinto
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The Sequent Calculus of Skew Monoidal Categories [PDF]
Electronic Notes in Theoretical Computer Science, 2018 Szlachányi's skew monoidal categories are a well-motivated variation of monoidal categories in which the unitors and associator are not required to be natural isomorphisms, but merely natural transformations in a particular direction.
Tarmo Uustalu +2 more
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Specialization of derivations in modal logic S5
Lietuvos Matematikos Rinkinys, 2023 Loop-check-free decidable specialization of sequent calculus for modal logic S5 is presented. Soundness and completness of this calculus is proved.
Aida Pliuškevičienė
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Cut-Free Gentzen Sequent Calculi for Tense Logics
Axioms, 2023 The cut-free single-succedent Gentzen sequent calculus GKt for the minimal tense logic Kt is introduced. This sequent calculus satisfies the displaying property.
Zhe Lin, Minghui Ma
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Relating Sequent Calculi for Bi-intuitionistic Propositional Logic [PDF]
Electronic Proceedings in Theoretical Computer Science, 2011 Bi-intuitionistic logic is the conservative extension of intuitionistic logic with a connective dual to implication. It is sometimes presented as a symmetric constructive subsystem of classical logic.
Luís Pinto, Tarmo Uustalu
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On noncommutative extensions of linear logic [PDF]
Logical Methods in Computer Science, 2019 Pomset logic introduced by Retor\'e is an extension of linear logic with a self-dual noncommutative connective. The logic is defined by means of proof-nets, rather than a sequent calculus.
Sergey Slavnov
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Sequent calculus for hybrid logic
Lietuvos Matematikos Rinkinys, 2023 There is not ...
Stanislovas Norgėla +1 more
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Logic of knowledge with infinitely many agents
Lietuvos Matematikos Rinkinys, 2023 Cut-free sequent calculus for logic of knowledge with infinitely many agents, based on multimodul S5n.
Regimantas Pliuškevičius
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The Sequent Calculus Trainer with Automated Reasoning - Helping Students to Find Proofs [PDF]
Electronic Proceedings in Theoretical Computer Science, 2018 The sequent calculus is a formalism for proving validity of statements formulated in First-Order Logic. It is routinely used in computer science modules on mathematical logic.
Arno Ehle +2 more
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