Abstract
Logic programming with strong negation (LPS) was proposed by Pearce and Wagner (1991) to handle both explicit and implicit negative information in knowledge representation in AI. We describe tableau calculi for LPS and establish the completeness. The proposed tableau calculi can deal with a wider class of programs in LPS. We also discuss possible refinements of the tableau calculi to improve efficiency.
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Akama, S. (1987): Resolution in constructivism, Logique et Analyse 120, 385–399.
Akama, S. (1988a): On the proof method for constructive falsity, Zeitschrift für mathematische Logik und Grundlagen der Mathematik 34, 385–392.
Akama, S. (1988b): Constructive predicate logic with strong negation and model theory, Notre Dame Journal of Formal Logic 29, 18–27.
Akama, S. (1989): Constructive Falsity: Foundations and Their Applications to Computer Science, Ph.D. dissertation, Department of Administration Engineering, Keio University, Yokohama, Japan.
Akama, S. (1990): Subformula semantics for strong negation systems, The Journal of Philosophical Logic 19, 217–226.
Akama, S. (1995): Three-valued constructive logic and logic programs, Proc. of the IEEE 25th International Symposium on Multiple-Valued Logic, 276–281, Bloomington, USA, May.
Akama, S. (1996): Curry's paradox in contractionless constructive logic, The Journal of Philosophical Logic 25, 135–150.
Alferes, J. J. and Pereira, L. M. (1996): Reasoning with Logic Programming, LNAI 1111, Springer, Berlin.
Almukdad, A. and Nelson, D. (1984): Constructible falsity and inexact predicates, The Journal of Symbolic Logic 49, 8–37, 231–233.
Clark, K. L. (1978): Negation as failure, H. Gallaire and J. Minker (eds.), Logic and Databases, 293–322, Plenum Press, New York.
Fitting, M. (1969): Intuitionistic Logic, Model Theory and Forcing, North-Holland, Amsterdam.
Gelfond, M. and Lifschitz, V. (1990): Logic programs with classical negation, D. H. D. Warren and P. Szeredi (eds.), Proc. of ICLP'90, 579–597, MIT Press, Cambridge, Mass.
Hähnle, R. (1993): Automated Deduction in Multiple-Valued Logics, Oxford University Press, Oxford.
Kowalski, R. and Sadri, F. (1990): Logic programs with exceptions, D. H. D. Warren and P. Szeredi (eds.), Proc. of ICLP'90, 598–613, MIT Press, Cambridge, Mass.
Miglioli, P., Moscato, U. and Ornaghi, M. (1994): An improved refutation system for intuitionistic predicate logic, Journal of Automated Reasoning 13, 361–373.
Nelson, D. (1949): Constructible falsity, The Journal of Symbolic Logic 14, 16–26.
Pearce, D. (1992): Default logic and constructive logic, Proc. of ECAI'92, 309–313.
Pearce, D. (1993): Answer sets and constructive logic Part II: Extended logic programs and related nonmonotonic formalisms, L. M. Pereira and A. Nerode (eds.), Logic Programming and Non-Monotonic Reasoning, Proc. of the 2nd International Workshop, 457–475, MIT Press, Cambridge, Mass.
Pearce, D. and Wagner, G. (1990): Reasoning with negative information I: Strong negation in logic programs, Acta Philosophica Fennica 49, 430–453.
Pearce, D. and Wagner, G. (1991): Logic programming with strong negation, P. Schroeder-Heister (ed.), Extensions in Logic Programming, 311–326, Springer, Berlin.
Rautenberg, W. (1979): Klassische and Nichtklassische Aussagenlogik, Vieweg, Wiesbaden.
Schöenfeld, W. (1985): PROLOG extensions based on tableau calculus, Proc. of IJCAI'85, 730–732.
Smullyan, R. (1968): First-Order Logic, Springer, Berlin.
Thomason, R. H. (1969): A semantical study of constructible falsity, Zeitschrift für mathematische Logik und Grundlagen der Mathematik 15, 247–257.
Wagner, G. (1991): Logic programming with strong negation and inexact predicates, Journal of Logic and Computation 1, 835–859.
Wagner, G. (1992): Vivid Logic: Knoweldge-Based Reasoning with Two Kinds of Negation, Ph.D. dissertation, Freien Universität Berlin.
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Akama, S. (1997). Tableaux for logic programming with strong negation. In: Galmiche, D. (eds) Automated Reasoning with Analytic Tableaux and Related Methods. TABLEAUX 1997. Lecture Notes in Computer Science, vol 1227. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0027403
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DOI: https://doi.org/10.1007/BFb0027403
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