Abstract
We claim that the well-known equivalence of declarative and procedural interpretations for Horn clauses (predicate logic or Prolog programs) has been unjustifiably used when discussing computation. The reason for this is that the Apt, van Emden and Kowalski theory is based on a 2-valued logic {true, false} whereas computation requires at least a 3-valued logic {true, false, "still computing"}. We introduce such logics and relate the results obtained to the traditional ones. This gives a characterization of under-defined clauses which naturally correspond to looping programs. Moreover, it further supports the view that strong correctness (including termination) should be considered, rather than weak correctness (eg 2-valued logic) together with a separate analysis of termination.
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References
Apt, K.R. and van Emden, M.H. "Contributions to the theory of logic programming" JACM, Vol. 29, No. 3, July 1982.
Clark, K.L. "Negation as failure" In "Logic and Data Bases", H. Gallaire and J. Minker (eds), 1978.
van Emden, M.H. and Kowalski, R.A. "The semantics of predicate logic as a programming language", JACM Vol. 23, No. 3, Oct. 1976.
Gordon, M.J., Milner, R. and Wadsworth, C.P. "Edinburgh LCF" Springer-Verlag "Lecture Notes in Computer Science", Vol. 78, 1979.
Jones, N.D. and Mycroft, A. "Stepwise development of operational and denotational semantics of Prolog" DIKU report, Copenhagen University 1983, also submitted to "Science of Computer Programming".
Kowalski, R.A. "Predicate logic as a programming language" In "Information processing 74", J. Rosenfeld (ed.), 1974.
Lassez, J.L. and Maher, M.J. "Optimal fixpoints of logic programs" To appear in TCS, also presented at FST, Bangalore 1983.
Lassez, J.L. and Maher, M.J. "Closures and fairness in the semantics of predicate logic" To appear in TCS, also internal report Melbourne University, Australia 1983.
Plotkin, G.D. "LCF considered as a programming language" TCS Vol. 5, 1976.
Plotkin, G.D. "A powerdomain construction", SIAM J. Comput., Vol. 5, 1976.
Robinson, J.A. "A machine-oriented logic based on the resolution principle", JACM Vol. 12, No. 1, Jan. 1965.
Robinson, J.A. and Sibert, E.E. "LOGLISP — an alternative to PROLOG" Technical Report 7-80, School of Comp. and Info. Sci., Syracuse University 1980.
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© 1984 Springer-Verlag Berlin Heidelberg
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Mycroft, A. (1984). Logic programs and many-valued logic. In: Fontet, M., Mehlhorn, K. (eds) STACS 84. STACS 1984. Lecture Notes in Computer Science, vol 166. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-12920-0_25
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DOI: https://doi.org/10.1007/3-540-12920-0_25
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