This article is cited in 6 papers

Mathematical logic, algebra and number theory

Finite model property for negative modalities

S. A. Drobyshevich, S. P. Odintsov

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk

Abstract: We prove that the logic $N^{Un}$ with negation as unnecessity operator and that its extension, a Heyting–Ockham logic $N^*$, have the finite model property and prove the analog of Dziobiak's theorem for extensions of these logics. Namely, we prove that an extension of $N^{Un}$ or $N^*$ is strongly complete wrt the class of finite frames iff it is tabular.

Keywords: Routley semantics, negation as modality, algebraic semantics, Heyting–Ockham algebra.

UDC: 510.64

MSC: 03B20,03B70

Received May 18, 2012, published January 3, 2013