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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.