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An algebraic framework for the definition of compositional semantics of normal logic programs. (English) Zbl 0933.68031
Summary: The aim of our work is the definition of compositional semantics for modular units over the class of normal logic programs. In this sense, we propose a declarative semantics for normal logic programs in terms of model classes that is monotonic in the sense that $$\text{Mod}(P\cup P')\subseteq \text{Mod}(P)$$, for any programs $$P$$ and $$P'$$, and we show that in the model class associated to every program there is a least model that can be seen as the semantics of the program, which may be built upwards as the least fix point of a continuous immediate consequence operator. In addition, it is proved that this least model is “typical” for the class of models of Clark-Kunen’s completion of the program. This means that our semantics is equivalent to Clark-Kunen’s completion. Moreover, following the approach defined in a previous paper, it is shown that our semantics constitutes a “specification frame” equipped with the adequate categorical constructions needed to define compositional and fully abstract (categorical) semantics for a number of program units. In particular, we provide a categorical semantics of arbitrary normal logic program fragments which is compositional and fully abstract with respect to the (standard) union.

##### MSC:
 68N17 Logic programming 68Q55 Semantics in the theory of computing
##### Keywords:
normal logic programs; categorical semantics
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