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On the relation of negations in Nelson algebras

Gomez Conrado, Marcos Miguel Andrés, San Martín Hernán Javier

Reports on Mathematical Logic

2021

Vol. 56

15--56

The aim of this paper is to investigate the relation between the strong and the “weak” or intuitionistic negation in Nelson algebras. To do this, we define the variety of Kleene algebras with intuitionistic negation and explore the Kalman’s construction for pseudocomplemented distributive lattices. We also study the centered algebras of this variety.

An Infinitary Sequent System for the Equational Theory of *-continuous Action Lattices

Palka E.

Fundamenta Informaticae

2007

Vol. 78, nr 2

295-309

We present an infinitary logic ACTw in the form of a Gentzen-style sequent system, which is equivalent to the equational theory of *-continuous action lattices [9]. We prove the cut-elimination theorem for ACTw and, as a consequence, a theorem on the elimination of negative occurrences of *. This shows that ACTw is P01, whence, by a result of Buszkowski [1], it is P01-complete.

On Finite Model Property of the Equational Theory of Kleene Algebras

Palka E.

Fundamenta Informaticae

2005

Vol. 68, nr 3

221-230

The finite model property of the equational fragment of the theory of Kleene algebras is a consequence of Kozen's [3] completeness theorem. We show that, conversely, this completeness theorem can be proved assuming the finite model property of this fragment.