A Strong Logic Programming View for Static Embedded Implications

• Authors: R. Arruabarrena;P. Lucio;Marisa Navarro
• Venue: FoSSaCS '99 Proceedings of the Second International Conference on Foundations of Software Science and Computation Structure, Held as Part of the European Joint Conferences on the Theory and Practice of Software, ETAPS'99
• Year: 1999

A strong (L) logic programming language ([14, 15]) is given by two subclasses of formulas (programs and goals) of the underlying logic L, provided that: firstly, any program P (viewed as a L-theory) has a canonical model MP which is initial in the category of all its L-models; secondly, the L-satisfaction of a goal G in MP is equivalent to the L-derivability of G from P, and finally, there exists an effective (computable) proof-subcalculus of the L-calculus which works out for derivation of goals from programs. In this sense, Horn clauses constitute a strong (first-order) logic programming language. Following the methodology suggested in [15] for designing logic programming languages, an extension of Horn clauses should be made by extending its underlying first-order logic to a richer logic which supports a strong axiomatization of the extended logic programming language. A well-known approach for extending Horn clauses with embedded implications is the static scope programming language presented in [8]. In this paper we show that such language can be seen as a strong FO⊃ logic programming language, where FO⊃ is a very natural extension of first-order logic with intuitionistic implication. That is, we present a new characterization of the language in [8] which shows that Horn clauses extended with embedded implications, viewed as FO⊃-theories, preserves all the attractive mathematical and computational properties that Horn clauses satisfy as first-order-theories.