Many-valued propositional intuitionism
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The semantics for intuitionistic logic is based on “proof” rather than on “truth”. Since we frequently classify proofs in various ways, we are naturally motivated to consider many-valued theories of intuitionism. In this paper we provide a general syntactic and semantic theory for many-valued propositional intuitionism, where the values intuitively refer to types of proofs. Soundness and completeness results are presented, and it is shown that the many-valued theory is a conservative extension of the usual intuitionistic propositional calculus.
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