Book ChapterDOI
Tree-Sequent Methods for Subintuitionistic Predicate Logics
Ryo Ishigaki,Kentaro Kikuchi +1 more
- pp 149-164
TLDR
After proving the completeness with respect to some classes of Kripke models, this paper introduces Hilbert-style axiom systems and proves their completeness through a translation from the tree-sequent calculi to give a solution to the problem posed by Restall.Abstract:
Subintuitionistic logics are a class of logics defined by using Kripke models with more general conditions than those for intuitionistic logic. In this paper we study predicate logics of this kind by the method of tree-sequent calculus (a special form of Labelled Deductive System). After proving the completeness with respect to some classes of Kripke models, we introduce Hilbert-style axiom systems and prove their completeness through a translation from the tree-sequent calculi. This gives a solution to the problem posed by Restall.read more
Citations
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Proceedings Article
Labelled tree sequents, Tree hypersequents and Nested (Deep) Sequents
Rajeev Goré,Revantha Ramanayake +1 more
TL;DR: It is shown that a subclass of labelled sequents called “labelled tree sequents” are notational variants of tree-hypersequents in the sense that a sequent of one type can be represented naturally as asequent of the other type, which can be extended to nested (deep) sequents using the relationship between tree- hypersequents and nested ( deep) sequent sequents, which is shown.
Journal Article
Speaking about transitive frames in propositional languages
TL;DR: A manageable model theory is developed for the induced consequence relation of the intuitionistic and classical modal languages interpreted in the standard way on transitive frames which reveals some unexpected phenomena.
Dissertation
On the relationship between hypersequent calculi and labelled sequent calculi for intermediate logics with geometric Kripke semantics
TL;DR: This thesis examines the relationship between hypersequent and some types of labelled sequent calculi for a subset of intermediate logics that have geometric Kripke semantics, which it is shown that hypersequents and simply labelled sequents for calculi in Int∗/Geo share the same models.
Journal ArticleDOI
Display calculi and other modal calculi: a comparison
TL;DR: This paper introduces and compares four different syntactic methods for generating sequent calculi for the main systems of modal logic and shows how the first three methods can all be translated in the fourth one.
Book ChapterDOI
Sequent Calculus in the Topos of Trees
Ranald Clouston,Rajeev Goré +1 more
TL;DR: A sound and cut-free complete sequent calculus for KM lin is given via a strategy that decomposes implication into its static and irreflexive components and yields decidability of the logic and the coNP-completeness of its validity problem.
References
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Book ChapterDOI
Chapter 13 – Labelled Deductive Systems
TL;DR: In this article, the authors introduce labelled deductive systems for deductive reasoning in a logical system, and present a translation of the Curry-Howard interpretation of the LDS formulation into a labeled analytic deduction.
Journal ArticleDOI
A propositional logic with explicit fixed points
TL;DR: In this paper, a propositional logic which is obtained by interpreting implication as formal provability is studied, which is also the logic of finite irreflexive Kripke Models.
Journal ArticleDOI
Basic Propositional Calculus I
Mohammad Ardeshir,Wim Ruitenburg +1 more
TL;DR: An axiomatization for Basic Propositional Calculus BPC is presented and a completeness theorem for the class of transitive Kripke structures is given and several refinements are presented, including a completion theorem for irreflexive trees.