Abstract
This paper investigates a three-valued logic L3, that has been introduced in the study of natural language semantics. A complete proof system based on a three-valued analogon of negative resolution is presented. A subclass of L3 corresponding to Horn clauses in two-valued logic is defined. Its model theoretic properties are studied and it is shown to admit a PROLOG-style proof procedure.
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References
J. Barwise and J. Perry. 1983 Situations and Attitudes. Bradford Books, Cambridge, Mass.
S.Blamey. Partial logic. In: (Gabbay and Guenthner 1986), p.1–70.
U.Blau. Die dreiwertige Logik der Sprache. Walter de Gruyter.
J.M. Dunn and G. Epstein (eds.). 1977 Modern Uses of Multiple-Valued Logic. D.Reidel Publish. Co., Dordrecht.
H.-D. Ebbinghaus. 1969 Über eine Prädikatenlogik mit partiell definierten Prädikaten und Funktionen. Archiv für mathematische Logik 12, p.39–53.
J.E.Fenstad, P.-K.Halvorsen, T.Langholm and J.van Benthem. Equations, Schemata and Situations: A framework for linguistic semantics. CSLI Report No. 29. Center For The Study Of Language And Information, Stanford, CA 94305.
D. Gabbay and F. Guenthner (eds.). Handbook of Philosophical Logic, Vol.III: Alternatives in Classical Logic. D. Reidel Publishing Co., Dordrecht.
T.Langholm. Characterizations of persistent formulas in a three-valued logic. University of Oslo, Sweden.
J.A.Makowski. Why Horn formulas matter in computer science: initial structures and generic examples. Techn.Report No.329, Technion, Haifa.
S.McCall (ed.). Polish Logic 1920–1939. Oxford.
C.G. Morgan. 1973 A Resolution Procedure For A Class Of Many-valued Logics. Journal of Symbolic Logic vol. 39, 199–200 (abstract).
N. Rescher. 1969 Many-Valued Logic. McGraw Hill Book Co., New York.
J.B. Rosser and A.R. Turquette. 1952 Many-Valued Logics. North-Holland Publishing Co., Amsterdam.
J. Slupecki. 1936 Der volle dreiwertige Aussagenkalkül. Comptes rendues des s&eaccr.ance de la Soci&eaccr.t&eaccr. des Science de Lettres de Varsovie, Classe III, vol. 29, 9–11. English translation in (McCall) 335–337.
A.Urquhart. Many-valued logic. In: (Gabbay and Guenthner 1986), p.71–116.
H.Volger. On Theories which Admit Initial Structures. FNS-Bericht 85-1. Universität Tübingen, Forschungsstelle für natürlich-sprachige Systeme.
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© 1986 Springer-Verlag Berlin Heidelberg
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Schmitt, P.H. (1986). Computational aspects of three-valued logic. In: Siekmann, J.H. (eds) 8th International Conference on Automated Deduction. CADE 1986. Lecture Notes in Computer Science, vol 230. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-16780-3_90
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DOI: https://doi.org/10.1007/3-540-16780-3_90
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