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  1. Katsumi Sasaki (2012). Transitivity of Finite Models Constructed From Normal Forms for a Modal Logic Containing K4. Bulletin of the Section of Logic 41 (1/2):75-88.
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  2. Katsumi Sasaki (2010). Formulas in Modal Logic S4. Review of Symbolic Logic 3 (4):600-627.
    Here, we provide a detailed description of the mutual relation of formulas with finite propositional variables p1, …, pm in modal logic S4. Our description contains more information on S4 than those given in Shehtman (1978) and Moss (2007); however, Shehtman (1978) also treated Grzegorczyk logic and Moss (2007) treated many other normal modal logics. Specifically, we construct normal forms, which behave like the principal conjunctive normal forms in the classical propositional logic. The results include finite and effective methods to (...)
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  3. Katsumi Sasaki & Shigeo Ohama (2004). A Sequent System of the Logic R− for Rosser Sentences2. Bulletin of the Section of Logic 33 (1):11-21.
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  4. Kentaro Kikuchi & Katsumi Sasaki (2003). A Cut-Free Gentzen Formulation of Basic Propositional Calculus. Journal of Logic, Language and Information 12 (2):213-225.
    We introduce a Gentzen style formulation of Basic Propositional Calculus(BPC), the logic that is interpreted in Kripke models similarly tointuitionistic logic except that the accessibility relation of eachmodel is not necessarily reflexive. The formulation is presented as adual-context style system, in which the left hand side of a sequent isdivided into two parts. Giving an interpretation of the sequents inKripke models, we show the soundness and completeness of the system withrespect to the class of Kripke models. The cut-elimination theorem isproved (...)
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  5. Katsumi Sasaki (2002). A Cut-Free Sequent System for the Smallest Interpretability Logic. Studia Logica 70 (3):353-372.
    The idea of interpretability logics arose in Visser [Vis90]. He introduced the logics as extensions of the provability logic GLwith a binary modality . The arithmetic realization of A B in a theory T will be that T plus the realization of B is interpretable in T plus the realization of A (T + A interprets T + B). More precisely, there exists a function f (the relative interpretation) on the formulas of the language of T such that T + (...)
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  6. Katsumi Sasaki (2002). On Sequent Systems for Bimodal Provability Logics MOS and Prl1. Bulletin of the Section of Logic 31 (2):91-101.
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  7. Katsumi Sasaki (1993). The Simple Substitution Property of the Intermediate Propositional Logics on Finite Slices. Studia Logica 52 (1):41 - 62.
    The simple substitution property provides a systematic and easy method for proving a theorem by an axiomatic way. The notion of the property was introduced in Hosoi [4] but without a definite name and he showed three examples of the axioms with the property. Later, the property was given it's name as above in Sasaki [7].Our main result here is that the necessary and sufficient condition for a logicL on a finite slice to have the simple substitution property is thatL (...)
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  8. Tsutomu Hosoi & Katsumi Sasaki (1990). Finite Logics and the Simple Substitution Property. Bulletin of the Section of Logic 19 (3):74-78.
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  9. Katsumi Sasaki (1990). The Simple Substitution Property of Gödel's Intermediate Propositional Logics Sn's. Studia Logica 49 (4):471 - 481.
    The simple substitution property provides a systematic and easy method for proving a theorem from the additional axioms of intermediate prepositional logics. There have been known only four intermediate logics that have the additional axioms with the property. In this paper, we reformulate the many valued logics S' n defined in Gödel [3] and prove the simple substitution property for them. In our former paper [9], we proved that the sets of axioms composed of one prepositional variable do not have (...)
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  10. Katsumi Sasaki (1989). The Simple Substitution Property of the Intermediate Propositional Logics. Bulletin of the Section of Logic 18 (3):94-99.
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