Abstract
In the framework of extended logic programming we propose a criterion by which a negation operator can be said to express explicit falsity. We show that a certain system of constructive logic with strong negation, due to López-Escobar (1972) and Almukdad & Nelson (1984), fulfils this criterion, as do several recent systems of logic programming, including that of Gelfond & Lifschitz (1990). We use these facts to infer that, from a logical point of view, the programming systems in question can be viewed as subsystems of constructive logic.
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References
Akama, S, On the Proof Method for Constructive Falsity, Zeit. math. Logik & Grundlagen d. Math. 34 (1988), 385–392.
Almukdad, D & Nelson, D, Constructible Falsity and Inexact Predicates, J Symbolic Logic 49 (1984), 231–233.
Cellucci, C., Using Full First-Order Logic as a Programming Language, in Proc. Logic and Computer Sciences 1986, Rend. Sem. Mat. Univ. Pol. Torino, 1987.
Fitting, M, A Kripke-Kleene Semantics for Logic Programs, J Logic Programming 3 (1986), 75–88.
Gabbay, D & Sergot, M, Negation as Inconsistency, J Logic Programming 3 (1986), 1–35.
Gelfond, M & Lifschitz, V, The Stable Model Semantics for Logic Programming, in Kowalski, R & Bowen, K, (Eds), Proc. ICLP-88, MIT Press, 1988, 1070–1080.
Gelfond, M & Lifschitz, V, Logic Programs with Classical Negation, in Warren, D & Szeredi, P, (Eds), Proc. ICLP-90, MIT Press, 1990, 579–597.
Gurevich, Y, Intuitionistic Logic with Strong Negation, Studia Logica 36 (1977), 49–59.
Hallnäs, L & Schroeder-Heister, P, A Proof-Theoretic Approach to Logic Programming, J Logic and Computation 1(1990).
Kowalski, R & Sadri, F, Logic Programs with Exceptions, in Warren, D & Szeredi, P, (Eds.), Proc. ICLP-90, MIT Press, 1990.
Kutschera, F, Ein verallgemeinerter Widerlegungsbegriff für Gentzenkalküle, Arch. Math. Logik 12 (1969), 104–118.
Levesque, H, Making Believers out of Computers, Artificial Intelligence 30 (1986), 81–107.
López-Escobar, E G K, Refutability and Elementary Number Theory, Indag. Math. 34 (1972), 362–374.
Lu, J & Subrahmanian, V, Protected Completions of First-Order General Logic Programs, J Automated Reasoning 6 (1990), 147–172.
Miller, D, A Logical Analysis of Modules in Logic Programming, J Logic Programming 6 (1989), 79–108.
Nelson, D, Constructible Falsity, J Symbolic Logic 14 (1949), 16–26.
Nelson, D, Negation and Separation of Concepts in Constructive Systems, in Heyting, A (Ed), Constructivity in Mathematics, North-Holland, Amsterdam, 1959.
Pearce, D & Wagner, G, Reasoning with Negative Information, I: Strong Negation in Logic Programs, in Haaparanta, L, Kusch, M, & Niiniluoto, I, (eds.), Language, Knowledge, and Intentionality, (Acta Philosophica Fennica 49), Helsinki, 1990, 430–453.
Pearce, D & Wagner, G, Logic Programming with Strong Negation, in Schroeder-Heister, P, (Ed), Extensions of Logic Programming, Lecture Notes in AI, Vol. 475, Springer-Verlag, Berlin etc, 1991, 311–326.
Poole, D & Goebel, R, Gracefully Adding Negation and Disjunction to Prolog, Proc. ICLP-86, MIT Press, 1986.
Przymusinski, T, Perfect Model Semantics, in Kowalski, R, & Bowen, K, (Eds.), Proc. ICLP-88, MIT Press, 1988.
Reiter, R, A Logic for Default Reasoning, Artificial Intelligence 13 (1980), 81–132.
Sergot, M, Sadri, F, Kowalski, R, Kriwaczek, F, Hammond, P & Cory, H T, The British Nationality Act as a Logic Program, Communications of the ACM 29 (1986), 370–386.
Tan, Y-H, Standard Inference in Partial Logic, Technical Report, Free University Amsterdam, 1989.
Wagner, G, Logic Programming with Strong Negation and Inexact Predicates, Journal of Logic and Computation 1:6 (1991).
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Pearce, D. (1992). Reasoning with negative information, II: Hard negation, strong negation and logic programs. In: Pearce, D., Wansing, H. (eds) Nonclassical Logics and Information Processing. All-Berlin 1990. Lecture Notes in Computer Science, vol 619. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0031924
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DOI: https://doi.org/10.1007/BFb0031924
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