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

100%

Yazaki D.

Bulletin of the Section of Logic

2019

tom 48

nr 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, Takano analyzed the relationships between the acceptable inference rules and semantical properties by constructing models. By using these relationships, he showed Kripke completeness and subformula property. However, his method is difficult to apply to inference rules for the sequent calculi for K4.3, KD4.3, and S4.3. Lookinglosely at Takano's proof, we nd that his method can be modied to construct nite models based on the sequent calculus for K4.3, if the calculus has (cut) and all the applications of the inference rules are acceptable. Similarly, we can apply our results to the calculi for KD4.3 and S4.3. This leads not only to Kripke completeness and subformula property, but also to finite model property of these logics simultaneously.

Nilpotent Minimum Logic NM and Pretabularity

88%

Yang E.

Bulletin of the Section of Logic

2020

tom 49

nr 1

This paper deals with pretabularity of fuzzy logics. For this, we first introduce two systems NMnfp and NM½, which are expansions of the fuzzy system NM (Nilpotent minimum logic), and examine the relationships between NMnfp and the another known extended system NM-. Next, we show that NMnfp and NM½ are pretabular, whereas NM is not. We also discuss their algebraic completeness.

Ograniczanie wyników

2 Bulletin of the Section of Logic

1 Yang E.

1 Yazaki D.

1 2020

1 2019

Wyniki wyszukiwania

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

Nilpotent Minimum Logic NM and Pretabularity