Natural implicative expansions of variants of Kleene's strong 3-valued logic with Gödel-type and dual Gödel-type negation
Gemma Robles, José M. Méndez · Journal of Applied Non-Classical Logics · 2021
Let MK3I and MK3II be Kleene's strong 3-valued matrix with only one and two designated values, respectively. Next, let MK3G (resp., MK3dG) be defined exactly as MK3I (resp., MK3II), except that the characteristic Łukasiewicz-type negation of Kleene's strong 3-valued matrix is replaced by a ‘Gödel-type’ negation (resp., ‘dual Gödel-type’ negation). The aim of this paper is to axiomatize the logics determined by all natural implicative expansions of MK3G and MK3dG. The axiomatic formulations are defined by using a ‘two-valued’ Belnap-Dunn semantics.