arXiv subjects
Publications and source records attributed to Norihiro Kamide.
A unified Gentzen-style framework for until-free propositional linear-time temporal logic is introduced. The proposed framework, based on infinitary rules and rules for primitive negation, can handle uniformly both a single-succedent sequent calculus and a natural deduction system. Furthermore, an equivalence between these systems, alongside with proofs of cut-elimination and normalization theorems, is established.
Gentzen-style sequent calculi and Gentzen-style natural deduction systems are introduced for a family (C-family) of connexive logics over Wansing's basic connexive logic C. The C-family is derived from C by incorporating the Peirce law, the law of excluded middle, and the generalized law of excluded middle. Theorems establishing equivalence between the proposed sequent calculi and natural deduction systems are demonstrated. Cut-elimination and normalization theorems are established for the proposed sequent calculi and natural deduction systems, respectively.
Two Gentzen-style twist sequent calculi for the normal modal logic S4 are introduced and investigated. The proposed calculi, which do not employ the standard logical inference rules for the negation connective, are characterized by several twist logical inference rules for negated logical connectives. Using these calculi, short proofs can be generated for provable negated modal formulas that contain numerous negation connectives. The cut-elimination theorems for the calculi are proved, and the subformula properties for the calculi are also obtained. Additionally, Gentzen-style twist (hyper)sequent calculi for other normal modal logics including S5 are considered.