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Warianty tytułu
Języki publikacji
Abstrakty
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.
Słowa kluczowe
Wydawca
Czasopismo
Rocznik
Tom
Strony
295--309
Opis fizyczny
bibliogr. 10 poz.
Twórcy
autor
- Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Umultowska 87, 61-614 Poznań, Poland, pewka@amu.edu.pl
Bibliografia
- [1] Buszkowski, W.: On Action Logic, manuscript, to appear in: Journal of Logic and Computation, www.staff.amu.edu.pl/ buszko/actlog2.pdf
- [2] Jipsen, P.: From Semirings to Residuated Kleene Algebras, Studia Logica, 76, 2004, 291-303.
- [3] Kozen, D.: On Kleene algebras and closed semirings, in: Proc. MFCS 1990, Lecture Notes in Comp. Science 452, 1990, 26-47.
- [4] Kozen, D.: A completeness theorem for Kleene algebras and the algebra of regular events, Information and Computation 110:2, 1994, 366-390.
- [5] Kozen, D.: On Action Algebras, manuscript, in: Logic and the Flow of Information Amsterdam, 1991.
- [6] Lambek, J.: The mathematics of sentence structure, The American Mathematical Monthly 65, 1958, 154-170.
- [7] Ono, H.: Semantics for Substructural Logics, in: Substructural Logics, (Schroeder-Heister, P., Došen, K., eds.), Clarendon Press, Oxford, 1993, 259-291.
- [8] Palka, E.: On Finite Model Property of the Equational Theory of Kleene Algebras, Fundamenta Informaticae 68.3, 2005, 221-230.
- [9] Pratt V.: Action Logic and Pure Induction, in: Logics in AI. Proc. of JELIA'90, Lecture Notes in Artif. Inteligence 478, 1991, 97-120.
- [10] Redko, V.N.: On defining relations for the algebra of regular events, Ukrain. Mat. Z. 16, 1964, 120-126. In Russian.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BUS5-0010-0031