http://hdl.handle.net/11089/56939 2026-04-06T19:28:58Z 2026-04-06T19:28:58Z Ichikura, Kaito http://hdl.handle.net/11089/56968 2025-12-13T02:23:58Z 2025-07-07T00:00:00Z

Continua of Logics Related to Intuitionistic and Minimal Logics Ichikura, Kaito We analyze the relationship between logics around intuitionistic logic and minimal logic. We characterize the intersection of minimal logic and co-minimal logic introduced by Vakarelov, and reformulate logics given in the previous studies by Vakarelov, Bezhanishvili, Colacito, de Jongh, Vargas, and Niki in a uniform language. We also compare the new logic with other known logics in terms of the cardinalities of logics between them. Specifically, we apply Wronski’s algebraic semantics, instead of neighborhood semantics used in the previous studies, to show the existence of continua of logics between known logics and the new logic. This result is an extension of the conventional results, and the proof is given in a simpler way.

2025-07-07T00:00:00Z Kamide, Norihiro Negri, Sara http://hdl.handle.net/11089/56967 2025-12-13T02:23:55Z 2025-11-27T00:00:00Z

Unified Sequent Calculi and Natural Deduction Systems for Until-free Linear-time Temporal Logics Kamide, Norihiro; Negri, Sara A unified Gentzen-style proof-theoretic framework for until-free propositional linear-time temporal logic and its intuitionistic variant is introduced. The framework unifies Gentzen-style single-succedent sequent calculi and natural deduction systems for both the classical and intuitionistic versions of these temporal logics. Theorems establishing the equivalence between the proposed sequent calculi and natural deduction systems are proved. Furthermore, the cut-elimination theorems for the proposed sequent calculi and the normalization theorems for the proposed natural deduction systems are established.

2025-11-27T00:00:00Z Kamide, Norihiro http://hdl.handle.net/11089/56965 2025-12-13T02:24:00Z 2025-07-02T00:00:00Z

Cut-elimination and Normalization Theorems for Connexive Logics over Wansing’s C Kamide, Norihiro Gentzen-style sequent calculi and Gentzen-style natural deduction systems are introduced for a family (C-family) of connexive logics over Wansing’s basic constructive connexive logic C. The C-family is derived from C by incorporating Peirce’s law, the law of excluded middle, and the generalized law of excluded middle. Natural deduction systems with general elimination rules are also introduced for the C-family. Theorems establishing the 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. Additionally, similar results are obtained for a family (N-family) of paraconsistent logics over Nelson’s constructive four-valued logic N4.

2025-07-02T00:00:00Z Sawasaki, Takahiro http://hdl.handle.net/11089/56966 2025-12-13T02:23:56Z 2025-09-18T00:00:00Z

Semantic Incompleteness of Liberman et al. (2020)’s Hilbert-style Systems for Term-modal Logics with Equality and Non-rigid Terms Sawasaki, Takahiro In this paper, we prove the semantic incompleteness of some expansions of the Hilbert-style system for the minimal normal term-modal logic with equality and non-rigid terms that were proposed in Liberman et al. (2020) “Dynamic Term-modal Logics for First-order Epistemic Planning.” Term-modal logic is a family of first-order modal logics having term-modal operators indexed with terms in the first-order language. While some first-order formula is valid over the corresponding class of frames in the involved Kripke semantics, it is not provable in those expansions. We show this fact by introducing a non-standard Kripke semantics which makes the meanings of constants and function symbols relative to the meanings of relation symbols combined with them. We also address an incorrect frame correspondence result given in Liberman et al. (2020).

2025-09-18T00:00:00Z