Results 21 to 30 of about 25,817 (283)
Tools and techniques for formalising structural proof theory [PDF]
, 2010 Whilst results from Structural Proof Theory can be couched in many formalisms, it is the sequent calculus which is the most amenable of the formalisms to metamathematical treatment.
Chapman, Peter
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Cut free sequent calculus for logic S5n(ED)
Lietuvos Matematikos Rinkinys, 2010 Hilbert style, Gentzen style sequent and Kanger style sequent calculi for logic S5n(ED) are considered in this paper. Gentzen style sequent calculus is constructed and its equivalence with Hilbert style system is proved, getting soundness and ...
Haroldas Giedra
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Contraction-free calculi for modal logics S5 and KD45
Lietuvos Matematikos Rinkinys, 2011 It is known that termination and backtracking are among the most important problems in constructing derivations in non-classical logics. In this paper contractionfree and backtracking-free sequent calculi for modal logics S5 and KD45 are presented and ...
Julius Andrikonis +1 more
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LNL polycategories and doctrines of linear logic [PDF]
Logical Methods in Computer Science, 2023 We define and study LNL polycategories, which abstract the judgmental structure of classical linear logic with exponentials. Many existing structures can be represented as LNL polycategories, including LNL adjunctions, linear exponential comonads, LNL ...
Michael Shulman
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Sequent calculi for induction and infinite descent [PDF]
Journal of Logic and Computation, 2010 The authors develop and compare proof-theoretic foundations for proof by induction and proof by infinite descent in the context of a first-order logic \(\text{FOL}_{\text{ID}}\) containing inductively defined predicates. These two styles of reasoning are formalized as the corresponding sequent calculi. It is shown that the proof system \(\text{LKID}\),
Brotherston, James, Simpson, Alexander
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Two complete finitary sequent calculi for reflexive common knowledge
Lietuvos Matematikos Rinkinys, 2013 This paper discusses the use of complete sequent calculi for reflexive common knowledge logic. Description of language and complete infinitary calculus for RCL is presented.
Aurimas Paulius Girčys +1 more
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Admissibility, compatibility, and deducibility in first-order sequent logics [PDF]
Computer Science Journal of Moldova, 2015 The paper is about the notions of admissibility and compatibility and their significance for deducibility in different sequent logics including first-order classical and intuitionistic ones both without and with equality and, possibly, with modal rules.
Alexander Lyaletski
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Two-sided Sequent Calculi for FDE-like Four-valued Logics [PDF]
, 2023 We present a method that generates two-sided sequent calculi for four-valued logics like first degree entailment (FDE). (We say that a logic is FDE-like if it has finitely many operators of finite arity, including negation, and if all of its operators ...
Kooi, Barteld +2 more
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Finite sequent calculi for PLTL
Lietuvos Matematikos Rinkinys, 2015 Two sequent calculi for temporal logic of knowledge are presented: one containing invariant-like rule and the other containing looping axioms. Its proved that the calculi are equivalent, sound and complete.
Romas Alonderis +2 more
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Generic Modal Cut Elimination Applied to Conditional Logics [PDF]
Logical Methods in Computer Science, 2011 We develop a general criterion for cut elimination in sequent calculi for propositional modal logics, which rests on absorption of cut, contraction, weakening and inversion by the purely modal part of the rule system. Our criterion applies also to a wide
Dirk Pattinson, Lutz Schröder
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