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Cut-elimination for the modal Grzegorczyk logic via non-well-founded proofs
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A sequent calculus is presented for the modal Grzegorczyk logic Grz allowing non-well-founded proofs and the cut-elimination theorem is obtained by constructing a continuous cut-Elimination mapping acting on these proofs.Abstract:
We present a sequent calculus for the modal Grzegorczyk logic Grz allowing non-well-founded proofs and obtain the cut-elimination theorem for it by constructing a continuous cut-elimination mapping acting on these proofs.read more
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The Lambek calculus with iteration: two variants
TL;DR: In this paper, the Lambek calculus is extended using a unary connective, positive Kleene iteration, which corresponds to a variant of action logic that corresponds to general residuated Kleene algebras, not necessarily *-continuous.
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The Lambek Calculus with Iteration: Two Variants
TL;DR: It is shown that, in contrast with the case without division operations (considered by Kozen), the first system is strictly stronger than the second one and is not recursively enumerable and cannot be described by a calculus with finite derivations.
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Non-well-founded proofs for the grzegorczyk modal logic
TL;DR: In this article, a sequent calculus for the Grzegorczyk modal logic allowing cyclic and other non-well-founded proofs is presented, and a continuous cut-elimination mapping acting on these proofs is constructed.
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Cut Elimination for the Weak Modal Grzegorczyk Logic via Non-well-Founded Proofs
TL;DR: In this paper, a sequent calculus for the modal Grzegorczyk logic is presented, allowing non-well-founded proofs and obtaining the cut-elimination theorem for it by constructing a continuous cut elimination mapping acting on these proofs.
References
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Book ChapterDOI
Tableau Methods for Modal and Temporal Logics
TL;DR: This chapter gives a systematic and unified introduction to tableau methods for automating deduction in modal and temporal logics and focuses on the propositional fragments restricted to a two-valued (classical) basis.
Journal ArticleDOI
On Modal Systems Having Arithmetical Interpretations
TL;DR: It is shown that cut-elimination fails for QGL (the extension of GL to a language with quantifiers), and it is further shown that, despite this failure, QGL still has some of GL' s interesting properties (e.g., the disjunction property).
Journal ArticleDOI
A fixed point theorem in non-Archimedean vector spaces
C. Petalas,T. Vidalis +1 more
TL;DR: In this paper, it was shown that every contractive mapping on a spherically complete non-Archimedean normed space has a unique fixed point, which is the same as the fixed point for any non-architectural mapping.
Journal Article
A unifying approach to recursive and Co-recursive definitions
TL;DR: In this article, a general approach for systematically defining fixed points for a broad class of well given recursive definitions is proposed, which unifies the ones based on well-founded order and complete metrics and contractive functions, allowing for mixed recursive/corecursive definitions.