Declarative modeling of the operational behavior of logic languages

Coalgebraic Semantics for Parallel Derivation Strategies in Logic Programming

“…The least fixed point of T P is called the least Herbrand model of P and duly satisfies model-theoretic properties that justify that expression [19]. A non-ground alternative to the ground fixed point semantics has been given in [9]; and further developed in terms of categorical logic [2,6].…”

“…SLD-resolution is sound and complete with respect to the least fixed point semantics. The classical theorems of soundness and completeness of this operational semantics [19,9] show that every atom in the set computed by the least fixed point of T P has a finite SLD-refutation, and vice versa. …”

Complementing logic program semantics

“…s-semantics, denoted by S, has been introduced in [12] in order to provide a fully abstract description of computed answer substitutions of logic programs. Recall that ϑ is a computed answer substitution for a goal G and a program P iff G ϑ −→ * P Λ. Clark's semantics, denoted by C, has been introduced in [2].…”

“…Recall that ϑ is a computed answer substitution for a goal G and a program P iff G ϑ −→ * P Λ. Clark's semantics, denoted by C, has been introduced in [2]. In [12], it was proved that C is fully abstract with respect to the "more abstract" notion of correct answer substitution. Recall that ϑ is a correct answer substitution for a goal G and a program P iff Gϑ−→ * P Λ.…”

“…Our approach gives rise to a hierarchy of declarative semantics for logic programs where semantics, and the corresponding observable properties, can be manipulated algebraically by complementation and reduced product. After some results in Section 4 on complementation and reduced product in denotational semantics, we show in Sections 5-7 the interaction between well known semantics, like the s-semantics for computed answers of [12], Clark's semantics for correct answers ( [2,12]), least Herbrand model semantics for successful computations ( [10]), and the semantics for call patterns in [16]. Logic programming provides here a clean and simple interpretation for the operators of our framework.…”