Abstract
A Rasiowa-Sikorski system is a sequence-type formalization of logics based on building decomposition trees of formulae labelled with sequences of formulae. Proofs are nite decomposition trees with leaves having “fundamental“, valid labels. The system is dual to the tableau system. The author gives examples of applying the R-S formalism to various C.S and A.I. logic, including a logic for reasoning about relative similarity, a three-valued software specication logic with McCarthy's connectives, and a logic for nondeterministic specications. As a new result, an R-S system for many-sorted rst order logic with possibly empty carriers of some sorts is developed.
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References
Beth E.W. (tiThe Foundations of Mathematics North-Holland, 1959
Bialasik M. Konikowska B. Reasoning with rst-order nondeterministic speci-cations, to appear in Acta Informatica
Bialasik M. Konikowska B. A logic for non-deterministic specications, to appear in: E. Orlowska, ed., Logic at work: essays dedicated to the memory of H. Rasiowa, Kluwer, Holland
Cohn A.G. A many sorted logic with possibly empty sorts, in Proceedings CADE-11, LNAI 607, pp 633–647 1992.
Gabbay D. Labelled deductive systems, Oxford University Press, Oxford 1991.
Hussmann H. Nondeterministic algebraic specications and non-confluent term rewriting, Journal of Logic Programming 12, 1992, pp. 237–255.
Konikowska B. A logic for reasoning about similarity, E. Orlowska, ed., Incomplete information: Rough Set Analysis, Physica-Verlag, New York 1997.
Konikowska B. A logic for reasoning about relative similarity, in: H. Rasiowa, E. Orlowska, ed., Special Issue of Studia Logica, Reasoning with incomplete information, No 1, 1997, pp. 185–22
Konikowska B. Two over three: a two-valued logic for software specication and validation over a three-valued predicate calculus, Journal for Applied Nonclassical Logic, Vol. 3(1), 1993, pp. 39–71.
Ohlbach H.J. Weidenbach C. A resolution calculus with dynamic sort structures and partial functions, in Proceedings ECAI, ed. L.C. Aiello, Pitman, London 1990.
Orlowska E. Relational proof systems for modal logics. In: H. Wansing (ed) Proof Theory of Modal Logics. Kluwer, Dordrecht, 55–77, 1996.
Rasiowa H. Sikorski R. The mathematics of metamathematics, Warsaw, PWN 1963
Walicki M. Meldal S., A complete calculus for multialgebraic and functional semantics of nondeterminism, ACM TOPLAS, 17(2), 1995.
Weidenbach C. Unication in sort theories and its applications, Annals of Mathematics and Articial Intelligence, vol. 18, pp. 261–293, 1996.
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Konikowska, B. (1999). Rasiowa-Sikorski Deduction Systems: A Handy Tool for Computer Science Logics. In: Fiadeiro, J.L. (eds) Recent Trends in Algebraic Development Techniques. Lecture Notes in Computer Science, vol 1589. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48483-3_13
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DOI: https://doi.org/10.1007/3-540-48483-3_13
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