Some Additional Axioms for T-normal Logics. Defining K45, KB4, KD45 and S5 without Using Modal Rules

Abstract

The paper studies extensions of t-normal logics S0.5o and S0.5 obtained by means of some axioms of normal logics. We will prove determination theorems for these extensions by appropriate Kripke-style models. It will allow us to obtain the determinations of the logics K45, KB4 (= KB5), KD45 and S5 without using modal rules.

Keywords

• modal logic
• t-normal logics
• kripke-style semantics