Journal ArticleDOI
Proof Theory for Modal Logic
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The axiomatic presentation of modal systems and the standard formulations of natural deduction and sequent calculus for modal logic are reviewed, together with the difficulties that emerge with these approaches.Abstract:
The axiomatic presentation of modal systems and the standard formulations of natural deduction and sequent calculus for modal logic are reviewed, together with the difficulties that emerge with these approaches. Generalizations of standard proof systems are then presented. These include, among others, display calculi, hypersequents, and labelled systems, with the latter surveyed from a closer perspective.read more
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Book
Neighborhood Semantics for Modal Logic
TL;DR: The focus is on the basics of neighborhood semantics with only pointers to literature relating to the more advanced topics.
Journal ArticleDOI
Proof analysis in intermediate logics
Roy Dyckhoff,Sara Negri +1 more
TL;DR: Using labelled formulae, a cut-free sequent calculus for intuitionistic propositional logic is presented, together with an easy cut-admissibility proof; both extend to cover all intermediate logics characterised by frames satisfying conditions expressible by one or more geometric implications.
Journal ArticleDOI
Proofs and Countermodels in Non-Classical Logics
TL;DR: A method is presented that makes it possible to establish completeness in a direct way: for any given sequent either a proof in the given logical system or a countermodel in the corresponding frame class is found.
Proceedings Article
A cut-free gentzen formulation of the modal logic S5
TL;DR: A new sequent system for S5 is given which is a straightforward and technically simple extension of Gentzen’s original sequent System for classical logic which satisfies cut-elimination as well as the subformula property.
Journal ArticleDOI
Uniform interpolation and sequent calculi in modal logic
TL;DR: The results imply that for modal logics K4 and S4, which are known not to have uniform interpolation, certain sequent calculi cannot exist.
References
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Book
An Introduction to Modal Logic
Max J. Cresswell,G. E. Hughes +1 more
TL;DR: This long-awaited book replaces Hughes and Cresswell's two classic studies of modal logic with all the new developments that have taken place since 1968 in both modal propositional logic and modal predicate logic, without sacrificing clarity of exposition and approachability.
Journal ArticleDOI
Semantical analysis of modal logic i. normal propositional calculi
TL;DR: In this article, a semantical analysis of modal logic ii and non-normal modal propositional calculi is presented, and the tableaux that leads to a decision procedure for the propositional calculus is considered.