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A formal framework for specifying sequent calculus proof systems
A General Proof System for Modalities in Concurrent Constraint Programming
TLDR
It is shown how a proper structure of the subexponential signature in SELL$^\Cap$ allows for the specification of concurrent systems with timed, spatial, and epistemic modalities, thus providing a proof-theoretic foundations for those calculi.
Lazy Strong Normalization
Modularisation of Sequent Calculi for Normal and Non-normal Modalities
TLDR
This work proposes local versions to ordinary sequent rules and obtains linear nested sequent calculi for a number of logics, including, to the authors' knowledge, the first nested sequents for a large class of simply dependent multimodal logics.
Using Linear Logic to Reason about Sequent Systems
Linear logic can be used as a meta-logic for the specification of some sequent calculus proof systems. We explore in this paper properties of such linear logic specifications. We show that
Proof Search in Nested Sequent Calculi
TLDR
A notion of focusing for nested sequent calculi for modal logics which brings down the complexity of proof search to that of the corresponding sequent Calculi is proposed, resulting in the first nested sequents for the considered non-normal modallogics.
LINEAR LOGIC AS A FRAMEWORK FOR SPECIFYING SEQUENT CALCULUS
In recent years, intuitionistic logic and type systems have been used in numerous computational systems as frameworks for the specification of natural deduction proof systems. As we shall illustrate
A Semantical View of Proof Systems
TLDR
A semantical characterisation of intuitionistic, normal and non-normal modal logics for all these systems are shown via a case-by-case translation between labelled nested to labelled sequent systems.
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