Extended multi-adjoint logic programming

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

“…Recently, extended multi-adjoint logic programs (EMALPs) were presented in [15] as an extension of multi-adjoint normal logic programs. In this setting, a special type of aggregator operator, called extended aggregator, is considered in the body of the rules and a new kind of rules, called constraints, have been included in the programs.…”

“…As shown in [15], extended aggregators can be used to simulate multiple negation operators or, in general, any kind of order-reversing behaviour for a propositional symbol. Additionally, the consideration of constraints enables a user to impose upper bounds to certain formulae.…”

“…This shed lights on the flexibility and the expressive power of the extended multi-adjoint logic programming framework. Besides presenting the syntax and the semantics of extended multi-adjoint logic programs, a procedure to translate an EMALP into a semantically equivalent MANLP was provided in [15].…”

“…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]. Besides presenting the syntax and the semantics of extended multi-adjoint logic programs, which is also based on stable models, a procedure to translate extended multi-adjoint logic programs into semantically equivalent multi-adjoint normal logic programs was provided in [15].…”

“…That ambition is achieved presenting a method which transforms a MANLP into a CFASP such that the stable models of the former coincide with the answer sets of the later, that is, both programs are semantically equivalent. As a result, the task initiated in [15] will be completed, giving rise to a procedure to translate an EMALP into a semantically equivalent CFASP.…”