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1. Contraction-free calculi for modal logics S5 and KD45

Author

Julius Andrikonis and Regimantas Pliuškevičius

Subjects
modal logic, sequent calculus, termination, backtracking, contraction-free, Mathematics, QA1-939
Abstract

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 founded. These are index-style sequent calculi with some specific indexed axioms. The main new ideas in considered calculi are to use metavariables (along with natural numbers) as elements of indexes and to numerate by different natural number all the positive occurrences of modality 2.

Published
2011
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2. Dubliavimo eliminavimas modalumo logikoms S5 ir KD45

Author

Regimantas Pliuškevičius and Julius Andrikonis

Subjects
termination, contraction-free, Backtracking, lcsh:Mathematics, Modal logic, Sequent calculus, Natural number, lcsh:QA1-939, backtracking, sequent calculus, Modal, Contraction-free, Termination, Calculus, Sequent, Contraction (operator theory), Axiom, modal logic, Mathematics
Abstract

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 founded. These are index-style sequent calculi with some specific indexed axioms. The main new ideas in considered calculi are to use metavariables (along with natural numbers) as elements of indexes and to numerate by different natural number all the positive occurrences of modality 2.

Published
2011