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New Modification of the Subformula Property for a Modal Logic

Mitio Takano

Bulletin of the Section of Logic > 2020 > 49 > 3 > 255-268

A modified subformula property for the modal logic KD with the additionalaxiom □ ◊(A ∨ B) ⊃ □ ◊ A ∨ □ ◊B is shown. A new modification of the notion of subformula is proposed for this purpose. This modification forms a natural extension of our former one on which modified subformula property for the modal logics K5, K5D and S4.2 has been shown ([2] and [4]). The finite model property as well as decidability...

article

Semantical Proof of Subformula Property for the Modal Logics K4.3, KD4.3, and S4.3

Daishi Yazaki

Bulletin of the Section of Logic > 2019 > 48 > 4

The main purpose of this paper is to give alternative proofs of syntactical and semantical properties, i.e. the subformula property and the nite model property, of the sequent calculi for the modal logics K4.3, KD4.3, and S4.3. The application of the inference rules is said to be acceptable, if all the formulas in the upper sequents are subformula of the formulas in lower sequent. For some modal logics,...

article

A Modified Subformula Property for the Modal Logic S4.2

Mitio Takano

Bulletin of the Section of Logic > 2019 > 48 > 1

The modal logic S4.2 is S4 with the additional axiom ◊□A ⊃ □◊A. In this article, the sequent calculus GS4.2 for this logic is presented, and by imposing an appropriate restriction on the application of the cut-rule, it is shown that, every GS4.2-provable sequent S has a GS4.2-proof such that every formula occurring in it is either a subformula of some formula in S, or the formula □¬□B or ¬□B, where...

article

A semantical analysis of cut-free calculi for modal logics

M. Takano

Reports on Mathematical Logic > 2018 > Vol. 53 > 43--65

We analyze semantically the logical inference rules in cut-free sequent calculi for the modal logics which are obtained from the least normal logic K by adding axioms from T, 4, 5, D and B. This implies Kripke completeness, as well as the cutelimination property or the subformula property of the calculi. By slightly modifying the arguments, the finite model property of the logics also follows.

article

Terminating Calculi for Propositional Dummett Logic with Subformula Property

Guido Fiorino

Journal of Automated Reasoning > 2014 > 52 > 1 > 67-97

In this paper we present two terminating tableau calculi for propositional Dummett logic obeying the subformula property. The ideas of our calculi rely on the linearly ordered Kripke semantics of Dummett logic. The first calculus works on two semantical levels: the present and the next possible world. The second calculus employs the semantical levels of known or not known at the present state of knowledge,...

article

Contraction-Free Linear Depth Sequent Calculi for Intuitionistic Propositional Logic with the Subformula Property and Minimal Depth Counter-Models

Mauro Ferrari, Camillo Fiorentini, Guido Fiorino

Journal of Automated Reasoning > 2013 > 51 > 2 > 129-149

In this paper we present LSJ, a contraction-free sequent calculus for Intuitionistic propositional logic whose proofs are linearly bounded in the length of the formula to be proved and satisfy the subformula property. We also introduce a sequent calculus RJ for intuitionistic unprovability with the same properties of LSJ. We show that from a refutation of RJ of a sequent σ we can extract a Kripke...

article

A Modified Subformula Property for the Modal Logic S4.2

Wydawnictwo Uniwersytetu Łódzkiego, Mitio Takano, Niigata Niigata University, takano@emeritus.niigata-u.ac.jp

Bulletin of the Section of Logic > Bulletin of the Section of Logic 48/1 (2019)

The modal logic S4.2 is S4 with the additional axiom ◊□A ⊃ □◊A. In this article, the sequent calculus GS4.2 for this logic is presented, and by imposing an appropriate restriction on the application of the cut-rule, it is shown that, every GS4.2-provable sequent S has a GS4.2-proof such that every formula occurring in it is either a subformula of some formula in S, or the formula □¬□B or ¬□B, where...

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Search results

New Modification of the Subformula Property for a Modal Logic

Semantical Proof of Subformula Property for the Modal Logics K4.3, KD4.3, and S4.3

A Modified Subformula Property for the Modal Logic S4.2

A semantical analysis of cut-free calculi for modal logics

Terminating Calculi for Propositional Dummett Logic with Subformula Property

Contraction-Free Linear Depth Sequent Calculi for Intuitionistic Propositional Logic with the Subformula Property and Minimal Depth Counter-Models

A Modified Subformula Property for the Modal Logic S4.2

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INFONA - science communication portal

Search results

New Modification of the Subformula Property for a Modal Logic

Semantical Proof of Subformula Property for the Modal Logics K4.3, KD4.3, and S4.3

A Modified Subformula Property for the Modal Logic S4.2

A semantical analysis of cut-free calculi for modal logics

Terminating Calculi for Propositional Dummett Logic with Subformula Property

Contraction-Free Linear Depth Sequent Calculi for Intuitionistic Propositional Logic with the Subformula Property and Minimal Depth Counter-Models

A Modified Subformula Property for the Modal Logic S4.2

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