On the Declarative Semantics of Multi-Adjoint Logic Programs

Beyond multi-adjoint logic programming

“…We formally introduce now the semantic notions of Herbrand interpretation and Herbrand model, or directly, interpretation and model for short, for a MALP program P, in a similar way to [21,41]. I is extended in a natural way to the set of ground formulae of the language.…”

“…In order to interpret a non-ground formula A (closed, and universally quantified in the case of the MALP language), it suffices to take I(A) = inf{I(Aξ) : Aξ is a ground instance of A}. In [21] we have defined, for the first time in the literature related with MALP, a declarative semantics based on model theory for describing the least fuzzy Herbrand model of a MALP program (other adaptations for alternative fuzzy frameworks can be found in [51,55,59]). This construction reproduces, in our fuzzy context, the classic construction of least Herbrand model of pure logic programming [2,27].…”

“…On the other hand, in [21] we have obtained, for the first time in the literature related with MALP, the semantic notion of least fuzzy model conceived as the infimum of a set of interpretations. This concept, which reproduces the classical conception of least model of pure logic programming, is equivalent to the fix-point semantics and, also, to the procedural semantics conceived as the set of fuzzy computed answers.…”

“…Focusing on this setting, in [1,17,18,21,[43][44][45] we describe some fundamental and practical issues regarding the design of declarative languages, programming environments and real-world applications with a fuzzy taste 1 developed in our research group during the last years. In essence, our research on MALP follows the fruitful path initiated by Lee [26], where the classical inference mechanism of selective linear definite clause resolution (SLD-resolution) used in LP, has been replaced by a fuzzy variant able to handle partial truth and uncertainty in a comfortable way.…”

Fuzzy Logic, Soft Computing, and Applications

“…In this respect, theoretical studies on areas such as extensions of fuzzy sets (type-2 fuzzy sets, L-fuzzy sets, interval-valued fuzzy sets, fuzzy rough sets) or aggregation operators (fuzzy measures, linguistic aggregators, inter-valued aggregators) are specially useful. Some specific application domains of preferences modelling are the following: data-base theory, classification and data mining, information retrieval, non-monotonic reasoning, recommendation systems, etc [23].…”