S. A. Drobyshevich, “A Double Negation Operator in Logic <nobr>$N^*$</nobr>”, Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 2013, Volume 13, Issue 4,Pages <nobr>68

This article is cited in 5 papers

A Double Negation Operator in Logic $N^*$

S. A. Drobyshevich^ab

^a Novosibirsk State University
^b Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk

Abstract: An axiomatization of double Routley negation operator as a necessity operator in logic $N^*$ is obtained. Logic $N^{\sharp}$ describing the behavior of double Routley negation operator is introduced, its Kripke semantics is defined, completeness wrt to this semantics is proved as well as its finite approximation property and decidability. Constructive properties of logics $N^*$ and $N^{\sharp}$ are compared.

Keywords: modal logic, intuitionistic logic, Kripke semantics, Routley negation, necessity, constructive properties.

UDC: 510.643

Received: 14.01.2013