Towards a Systematic Account of Different Semantics for Logic Programs

In [Hitzler and Wendt 2002, 2005], a new methodology has been proposed which allows to derive uniform characterizations of different declarative semantics for logic programs with negation. One result from this work is that the well-founded semantics can formally be understood as a stratified version of the Fitting (or Kripke-Kleene) semantics. The constructions leading to this result, however, show a certain asymmetry which is not readily understood. We will study this situation here with the result that we will obtain a coherent picture of relations between different semantics for normal logic programs.Comment: 20 page

On the Equivalence between Logic Programming Semantics and Argumentation Semantics

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Transforming acyclic programs

An unfold/fold transformation system is a source-to-source rewriting methodology devised to improve the efficiency of a program. Any such transformation should preserve the main properties of the initial program: among them, termination. In the field of logic programming, the class of acyclic programs plays an important role in this respect, since it is closely related to the one of terminating programs. The two classes coincide when negation is not allowed in the bodies of the clauses. We prove that the Unfold/Fold transformation system defined by Tamaki and Sato preserves the acyclicity of the initial program. From this result, it follows that when the transformation is applied to an acyclic program, then the finite failure set for definite programs is preserved; in the case of normal programs, all major declarative and operational semantics are preserved as well. These results cannot be extended to the class of left-terminating programs without modifying the definition of the transformation

On the equivalence between logic programming semantics and argumentation semantics

This work has been supported by the National Research Fund, Luxembourg (LAAMI project), by the Engineering and Physical Sciences Research Council (EPSRC, UK), grant Ref. EP/J012084/1 (SAsSy project), by CNPq (Universal 2012 – Proc. 473110/2012-1), and by CNPq/CAPES (Casadinho/PROCAD 2011).Peer reviewedPreprin

Transforming Normal Programs by Replacement

The replacement transformation operation, already defined in [28], is studied wrt normal programs. We give applicability conditions able to ensure the correctness of the operation wrt Fitting's and Kunen's semantics. We show how replacement can mimic other transformation operations such as thinning, fattening and folding, thus producing applicability conditions for them too. Furthermore we characterize a transformation sequence for which the preservation of Fitting's and Kunen's semantics is ensured