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Abstract: Due to the usual incompleteness of information representation, any approach to assign a semantics to logic programs has to rely on a default assumption on the missing information. The stable model semantics, that has become the dominating approach to give semantics to logic programs, relies on the Closed World Assumption (CWA), which asserts that by default the truth of an atom is false. There is a second well-known assumption, called Open World Assumption (OWA), which asserts that the truth of the atoms is supposed to be unknown by default. However, the CWA, the OWA and the combination of them are extremal, though important, assumptions over a large variety of possible assumptions on the truth of the atoms, whenever the truth is taken from an arbitrary truth space. The topic of this paper is to allow any assignment (i.e. interpretation), over a truth space, to be a default assumption. Our main result is that our extension is conservative in the sense that under the “everywhere false” default assumption (CWA) the usual stable model semantics is captured. Due to the generality and the purely algebraic nature of our approach, it abstracts from the particular formalism of choice and the results may be applied in other contexts as well. [Copyright &y& Elsevier]

Although the usual goal of sharing analysis is to detect which pairs of variables share, the standard choice for sharing analysis is a domain that characterizes set-sharing. In this paper, we question, apparently for the first time, whether this domain is over-complex for pair-sharing analysis. We show that the answer is yes. By defining an equivalence relation over the set-sharing domain we obtain a simpler domain, reducing the complexity of the abstract unification procedure. We present experimental results showing that, in practice, our domain compares favorably with the set-sharing one over a wide range of benchmark and real programs. [Copyright &y& Elsevier]

In (Gerla and Sessa, Fuzzy Logic and Soft Computing, Kluwer, Norwell, 1999, pp. 19–31) a methodology that allows to manage uncertain and imprecise information in the frame of the declarative paradigm of Logic Programming has been proposed. With this aim, a Similarity relation R between function and predicate symbols in the language of a logic program is considered. Approximate inferences are then possible since similarity relation allows us to manage alternative instances of entities that can be considered “equal” with a given degree. The declarative semantics of the proposed transformation technique of logic programs is analyzed. The notion of fuzzy least Herbrand model is also introduced. In this paper the corresponding operational semantics is provided by introducing a modified version of SLD resolution. This top-down refutation procedure overcomes failure situations in the unification process by using the similarity relation. A generalized notion of most general unifier provides a numeric value which gives a measure of the exploited approximation. In this way, the SLD resolution is enhanced since it is possible both to handle uncertain or imprecise information, and to compute approximate answer substitutions, with an associated approximation-degree, when failures of the exact inference process occur. It can lead to the implementation of a more general PROLOG interpreter, without detracting from the elegance of the language. [Copyright &y& Elsevier]