PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
2019 | 48 | 4 |
Tytuł artykułu

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

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Rocznik
Tom
48
Numer
4
Opis fizyczny
Daty
wydano
2019-12-31
Twórcy
Bibliografia
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.ojs-doi-10_18778_0138-0680_48_4_01
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.