## Works by Katsumi Sasaki

13 found
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1. A Sequent Systems without Improper Derivations.Katsumi Sasaki - 2022 - Bulletin of the Section of Logic 51 (1):91-108.
In the natural deduction system for classical propositional logic given by G. Gentzen, there are some inference rules with assumptions discharged by the rule. D. Prawitz calls such inference rules improper, and others proper. Improper inference rules are more complicated and are often harder to understand than the proper ones. In the present paper, we distinguish between proper and improper derivations by using sequent systems. Specifically, we introduce a sequent system $$\vdash_{\bf Sc}$$ for classical propositional logic with only structural rules, (...)

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2. The simple substitution property of the intermediate propositional logics.Katsumi Sasaki - 1989 - Bulletin of the Section of Logic 18 (3):94-99.

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3. The simple substitution property of gödel's intermediate propositional logics sn's.Katsumi Sasaki - 1990 - 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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4. An $$\omega$$-Rule for the Logic of Provability and Its Models.Katsumi Sasaki & Yoshihito Tanaka - forthcoming - Studia Logica:1-18.
In this paper, we discuss semantical properties of the logic $$\textbf{GL}$$ of provability. The logic $$\textbf{GL}$$ is a normal modal logic which is axiomatized by the the Löb formula $$\Box (\Box p\supset p)\supset \Box p$$, but it is known that $$\textbf{GL}$$ can also be axiomatized by an axiom $$\Box p\supset \Box \Box p$$ and an $$\omega$$ -rule $$(\Diamond ^{*})$$ which takes countably many premises $$\phi \supset \Diamond ^{n}\top$$ $$(n\in \omega )$$ and returns a conclusion \(\phi \supset (...)

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5. Finite Logics and the simple substitution property.Tsutomu Hosoi & Katsumi Sasaki - 1990 - Bulletin of the Section of Logic 19 (3):74-78.

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6. A cut-free Gentzen formulation of basic propositional calculus.Kentaro Kikuchi & Katsumi Sasaki - 2003 - 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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7. A Classification of Improper Inference Rules.Katsumi Sasaki - 2022 - Bulletin of the Section of Logic 51 (2):243-266.
In the natural deduction system for classical propositional logic given by G. Gentzen, there are some inference rules with assumptions discharged by the rule. D. Prawitz calls such inference rules improper as opposed to proper ones. Improper inference rules are more complicated than proper ones and more difficult to understand. In 2022, we provided a sequent system based solely on the application of proper rules. In the present paper, on the basis of our system from 2022, we classify improper inference (...)

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8. A cut-free sequent system for the smallest interpretability logic.Katsumi Sasaki - 2002 - 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. More precisely, there exists a function f on the formulas of the language of T such that T + B C implies T + A f.The interpretability logics were considered (...)

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9. A sequent system of the logic r− for Rosser sentences2.Katsumi Sasaki & Shigeo Ohama - 2004 - Bulletin of the Section of Logic 33 (1):11-21.

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10. Formulas in modal logic s4.Katsumi Sasaki - 2010 - 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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11. On sequent systems for bimodal provability logics MOS and prl1.Katsumi Sasaki - 2002 - Bulletin of the Section of Logic 31 (2):91-101.

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12. Transitivity of finite models constructed from normal forms for a modal logic containing k4.Katsumi Sasaki - 2012 - Bulletin of the Section of Logic 41 (1/2):75-88.