Translations and similarity-based logic programming

Abstract

In order to provide approximate reasoning capabilities, in Gerla G, Sessa MI (1999) Chen G, Ying M, Cai K-Y (Eds) Fuzzy Logic and Soft computing, 19±31, Kluwer Academic Publishers, Boston an extension of Logic Programming has been proposed. Logic programs on function-free languages are considered, and approximate and imprecise information are represented by introducing a similarity relation R in the set of predicate names and object names of the language. The inference system exploits the classical resolution rule of the Logic Programming paradigm. Moreover, the notion of fuzzy least Herbrand model is also provided. In this paper, by introducing the general notion of structural translation of languages, we generalize these results to the case of logic programs with function symbols. Some properties of the similarity relations are also proven.

Applications of Classification Based on Similarities and Dissimilarities

“…In this paper, by using some examples, we have shown how our ideas and propositions posed in [12] and in [13] can be applied to the real world problems. Lots of work has to be done in the future to answer the open questions that have been posed in the above mentioned papers.…”

Similarities between powersets of terms

“…The re exivity of E T follows easily by structural induction and the re exivity of E . Using symmetry of E we obtain Note that the deÿnition of similarity on TX adopted in this paper di ers from the one adopted in [25] in that the latter requires additionally that E T (x 1 ; x 2 ) = 0 if x 1 = x 2 .…”

A Transformation-based implementation for CLP with qualification and proximity

“…As implementation technique for SQLP, Caballero et al (2008) proposed a semantically correct program transformation into QLP, whose goal-solving procedure has been described above. Other related works on transformation-based implementations of SLP languages include Sessa (2001) and Medina et al (2004). More recently, the SLP approach has been generalized to work with proximity relations in the sense of Dubois and Prade (1980) represented by mappings S : S × S → [0, 1] that satisfy reflexivity and symmetry axioms but do not always satisfy transitivity.…”