# Search results for: Mitio Takano

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

Studia Logica > 2016 > 104 > 5 > 917-929

Archive for Mathematical Logic > 2002 > 41 > 5 > 497-505

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...

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...

A sequential axiomatization is given for the 16-valued logic that has been proposed by Shramko-Wansing (J Philos Logic 34:121–153, 2005) as a candidate for the basic logic of logical bilattices.

Studia Logica > 2016 > 104 > 5 > 917-929

Sequent calculi for trilattice logics, including those that are determined by the truth entailment, the falsity entailment and their intersection, are given. This partly answers the problems in Shramko-Wansing (J Philos Logic 34:121–153, 2005).

Archive for Mathematical Logic > 2002 > 41 > 5 > 497-505

Abstract.Strong completeness of S. Titanis system for lattice valued logic is shown by means of Dedekind cuts.

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

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