The well-founded semantics for normal logic programs is deened in a constructive way through the use of a xpoint operator and in general is not computable. We propose an approach for approximating through abstract interpretation the concrete behavior of normal logic programs described by the well-founded semantics. We provide also an abstract well-founded semantics scheme, based on an abstract ...

This paper is an investigation of S. Wolfram’s Principle of Computational Equivalence’ – that (discrete) systems in the natural world should be thought of as performing computations. We take a logical approach, and demonstrate that under almost trivial (physically reasonable) assumptions, discrete evolving physical systems give a class of logical models. Moreover, these models are of intuitioni...

Lutz [7] has recently developed a constructive version of Hausdorff dimension, using it to assign to every sequence A ∈ C a constructive dimension dim(A) ∈ [0,1]. Classical Hausdorff dimension [3] is an augmentation of Lebesgue measure, and in the same way constructive dimension augments Martin– Löf randomness. All Martin–Löf random sequences have constructive dimension 1, while in the case of ...

In this paper we apply abstract interpretation to systematically derive, compose and compare semantics according to their expressive power. The main results are: (1) a deenition of a hierarchy of collecting semantics , including well known semantics for logic programs, where semantics can be related to each other by abstract interpretation; (2) a characterization of collecting and abstract sema...