Logica Universalis 3 (1):59-94 (2009)

The goal of the paper is to develop a universal semantic approach to derivable rules of propositional multiple-conclusion sequent calculi with structural rules, which explicitly involve not only atomic formulas, treated as metavariables for formulas, but also formula set variables, upon the basis of the conception of model introduced in :27–37, 2001). One of the main results of the paper is that any regular sequent calculus with structural rules has such class of sequent models that a rule is derivable in the calculus iff it is sound with respect to each model of the semantics. We then show how semantics of admissible rules of such calculi can be found with using a method of free models. Next, our universal approach is applied to sequent calculi for many-valued logics with equality determinant. Finally, we exemplify this application by studying sequent calculi for some of such logics.
Keywords sequent calculus  structural rule  inference  derivable rule  admissible rule  distributive lattice  many-valued logic
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DOI 10.1007/s11787-009-0001-6
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References found in this work BETA

First-Order Logic.Raymond Merrill Smullyan - 1968 - Berlin, Germany: New York [Etc.]Springer-Verlag.
Proof Theory.Gaisi Takeuti - 1975 - Elsevier.
First-Order Logic.William Craig - 1975 - Journal of Symbolic Logic 40 (2):237-238.
Methoden zur Axiomatisierung beliebiger Aussagen- und Prädikatenkalküle.Karl Schröter - 1955 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 1 (4):241-251.

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