Mitio Takano

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Strong completeness of S. Titani’s system for lattice valued logic is shown by means of Dedekind cuts. 1. Syntax of lattice valued logic The purpose of this note is to show strong completeness of the system L for lattice valued logic given in Titani [4], in which she formulates a lattice-valued set theory by introducing the logical implication which(More)
The sequent calculus GK5 (GK5D) for the modal propositional logic K5 (K5D) is presented, and it is shown that, every provable sequent Γ → Θ in GK5 (GK5D) has a GK5-proof (GK5D-proof) such that every formula occurring in it is either a subformula of some formulas in Γ, Θ, or the formula 2¬2B or ¬2B, where 2B occurs in the scope of some occurrence of 2 in(More)