Syntax and semantics of multi-adjoint normal logic programming

Relating Multi-Adjoint Normal Logic Programs to Core Fuzzy Answer Set Programs from a Semantical Approach

“…Multi-adjoint normal logic programming was presented in [14] as a general non-monotonic logic programming framework, which is characterized by the use of different adjoint pairs and a negation operator. Its syntax is defined from a multi-adjoint lattice with negation.…”

“…Since its introduction, multi-adjoint logic programming has broadly been studied in order to, for example, improve the computation of the least model with either an efficient unfolding process [4,5] or with the computation of reductants [6,7]; consider propositional symbols of different sorts and termination theorems [8,9]; analyze incoherence and contradiction measures [10,11]; and extend it to a first order logic [12,13]. Later, multi-adjoint normal logic programming (MANLP) was presented as an extension of multi-adjoint logic programming, where the use of a negation operator is allowed in the body of the rules [14]. A complete study on the syntax and semantics of multi-adjoint normal logic programs, containing important results about the existence and the unicity of stable models, was carried out in [14].…”

“…Later, multi-adjoint normal logic programming (MANLP) was presented as an extension of multi-adjoint logic programming, where the use of a negation operator is allowed in the body of the rules [14]. A complete study on the syntax and semantics of multi-adjoint normal logic programs, containing important results about the existence and the unicity of stable models, was carried out in [14]. Recently, extended multi-adjoint logic programming (EMALP) has been proposed with the purpose of increasing the versatility and the expressive power of the multi-adjoint approach, by means of the inclusion of different negation operators in the body of the rules and the consideration of constraint rules [15].…”

“…For this purpose, a method for translating an arbitrary CFASP into a semantically equivalent MANLP has been shown. Among others, this method entails the possibility of using current theorems in MALP and MANLP in CFASP, such as the existence theorem for stable models given in the multi-adjoint framework [14], to provide a sufficient condition for the existence of answer sets.…”

Abductive reasoning in normal residuated logic programming via bipolar max-product fuzzy relation equations

“…On the other hand, fuzzy logic programming is another promising research area whose goal is introducing fuzzy logic methods in logic programming in order to have the possibility to handle partial truth, imprecision and uncertainty. The inclusion of a negation operator in these logic programs allows to simulate the non-monotonic behavior of human reasoning and provides the fuzzy logic programming with more flexibility [3,4,6,22,23]. Different semantics have been developed for logic programs with negation such as the well-founded semantics [29], the stable models semantics [15] and the answer sets semantics [14].…”