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Contributions to the semantics of open logic programs. (English) Zbl 0868.68018
Institute for New Generation Computer Technology (ed.), 5th generation computer systems 1992. International conference, FGCS ’92. Japan 1992, Vol. 2. Amsterdam: IOS Press. 570-580 (1992).
Summary: The paper considers open logic programs originally introduced in (*) A. Bossi and M. Menegus [Una Semantica Composizionale per Programmi Logici Aperti. In P. Asirelli, editor, Proc. Sixth Italian Conference on Logic Programming, p. 95-109 (1991)] as a tool to build an OR-compositional semantics of logic programs. We extend the original semantic definitions in the framework of the general approach to the semantics of logic programs described in M. Gabbrielli; G. Levi [Automata, languages and programming, Proc. 18th Int. Colloq., Madrid/Spain 1991, Lect. Notes Comput. Sci. 510, 1-19 (1991; Zbl 0769.68013)]. We first define an OR-compositional operational semantics $${\mathcal O}_\Omega(P)$$ modeling computed answer substitutions. We consider next the semantic domain of $$\Omega$$-interpretations, which are sets of clauses with a suitable equivalence relation. The fixpoint semantics $${\mathcal F}_\Omega(P)$$ given in (*) is proved equivalent to the operational semantics, by using an intermediate unfolding semantics. From the model-theoretic viewpoint, an $$\Omega$$-interpretations is mapped onto a set of Herbrand interpretation, thus leading to a definition of $$\Omega$$-model based on the classical notion of truth. We show that under a suitable partial order, the glb of a set of $$\Omega$$-models of a program $$P$$ is an $$\Omega$$-model of $$P$$. Moreover, the glb of all the $$\Omega$$-models of $$P$$ is equal to the usual Herbrand model of $$P$$ while $${\mathcal F}_\Omega(P)$$ is a (non-minimal) $$\Omega$$-model.
For the entire collection see [Zbl 0853.00057].

##### MSC:
 68N17 Logic programming 68Q55 Semantics in the theory of computing