Coinductive Logic Programming with Negation

Regular corecursion in Prolog

“…To avoid this problem, one might define the complemented predicate not_member, which corresponds to a universally quantified property; unfortunately, this approach has the drawback that it requires coSLD negation [11].…”

Infinite Computation, Co-induction and Computational Logic

“…Co-SLDNF resolution further extends co-SLD resolution with negation as failure [15]. Essentially, it augments co-SLD with the negative coinductive hypothesis rule, which states that if a negated call not(p) is encountered during resolution, and another call to not(p) has been seen before in the same computation, then not(p) coinductively succeeds [20].…”

“…An attempt to place the same call in both tables will induce failure of the computation. The framework based on maintaining a pair of sets (corresponding to a partial interpretation of success set and failure set, resulting in a partial model [8]) provides a good basis for the operational semantics of co-SLDNF resolution [20].…”

Transformations of logic programs on infinite lists

“…There have been various proposals for extending logic programming languages to infinite structures (see, for instance, (Colmerauer 1982;Lloyd 1987;Min and Gupta 2010;Simon et al 2006)). In order to provide the semantics of infinite structures, these languages introduce new concepts, such as complete Herbrand interpretations, rational trees, and greatest models.…”

“…Also logic programming has been proposed as a formalism for specifying computations over infinite structures, such as infinite lists or infinite trees (see, for instance, (Colmerauer 1982;Lloyd 1987;Simon et al 2006;Min and Gupta 2010)). One advantage of using logic programming languages is that they are general purpose languages and, together with a model-theoretic semantics, they also have an operational semantics.…”