We prove the decidability of Dummet's Logic LC by simultaneously constructing either a counter-model or a derivation. This proof describes an algorithm which has a sequent as input and returns either a derivation or a linear counter-model. The search tree of this algorithm is linearly bounded by the number of connectives of the input. 1 Introduction to be writen 2 Preliminaries We use P , Q; : : : to denote atoms, A, B; : : : to denote formulae, and , to denote multisets of formulae. Dummet's Logic LC is intuitionistic propositional logic together with the axioms (A B) _ (B A). We use a sequent calculus to describe the search, but by a rule 1 ) 1 : : : n ) n ) we mean a function which computes a derivation (in an arbitrary but xed calculus) of the conclusion, given derivations of all premises. Thus admissibilty has the following meaning. 2.1. Denition. A rule is admissible if, for each instance, we can compute a derivation of the conclusion, given derivations of all p..
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