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

Authors:
Ewa Palka
Affiliations:
Faculty of Mathematics and Computer Science, Adam Mickiewicz University of Poznań ul. Umultowska 87, 61-614 Poznań, Poland. E-mail: pewka@amu.edu.pl
Venue:
Fundamenta Informaticae
Year:
2007

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Abstract

We present an infinitary logic ACT_ω in the form of aGentzen-style sequent system, which is equivalent to the equationaltheory of *-continuous action lattices [9]. We prove thecut-elimination theorem for ACT_ω and, as a consequence, atheorem on the elimination of negative occurrences of *. This showsthat ACT_ω is Π^0_1, whence, by a result of Buszkowski[1], it is Π^0_1 complete.