A family of genuine and non-algebraisable C-systems. Issue 1 (2nd January 2021) - Osorio, Mauricio; Figallo-Orellano, Aldo; Pérez-Gaspar, Miguel
ABSTRACT: In 2016, Béziau introduced the notion of genuine paraconsistent logic as logic that does not verify the principle of non-contradiction; as an important example, he presented the genuine paraconsistent logic S P 3 A in terms of three connectives, , and . In this paper, we show that S P 3 A is an axiomatic extension of C 1 through the introduction of a non-primitive deductive implication. Furthermore, we prove that S P 3 A is an algebraisable logic with Blok-Pigozzi's method. From the proof that C 1 is non-algebraisable logic, we are able to see that C ω is not algebraisable logic and studying the borders of algebrisabilty, we can give an enumerable family of new genuine, paraconsistent and non-algebraisable logics, extensions of C ω . Finally, we introduced n -valued ( n < ω ) and infinite-valued C ω logic and show that they are genuine and non-algebraisable paraconsistent ones; in addition, we present semantics for this extensions of C ω by means of Fidel's structures.