REFLECTIVE WELL-FOUNDED RELATIONS

Well-Founded Recursive Relations

We give a short constructive proof of the fact that certain binary relations > are well-founded, given a lifting à la Ferreira-Zantema and a wellfounded relation .. This construction generalizes several variants of the recursive path ordering on terms and of the Knuth-Bendix ordering. It also applies to other domains, of graphs, of infinite terms, of word and tree automata notably. We then exte...

On the Union of Well-Founded Relations

We give a criterion for the union of well-founded (i.e., noetherian) relations to be well-founded, generalizing results of Geser and of Bachmair-Dershowitz. The proof is written in a calculational style and is conducted entirely in regular algebra.

Termination and Abstract Reduction Systems 1.1 Well-founded Relations

Then (N, R) is well-founded. Note that R is not transitive. Example 1.3 Consider (N × N, <) with the lexicographic order (a, b) < (c, d) iff a < c or a = c and b < d. We have (0, 0) <′ (0, 1) <′ · · · <′ (0, n) <′ · · · <′ (1, 0) <′ (1, 1) <′ · · · (2, 0) <′ · · · <′ (m, 0). This relation is well-founded. For suppose (an+1, bn+1) < ′ (an, bn) for all n. Then the sequence (an) is eventually cons...

Ramsey Theorem as an Intuitionistic Property of Well Founded Relations

Efficient Approximation of Well-Founded Justification and Well-Founded Domination

Many native ASP solvers exploit unfounded sets to compute consequences of a logic program via some form of well-founded negation, but disregard its contrapositive, well-founded justification (WFJ), due to computational cost. However, we demonstrate that this can hinder propagation of many relevant conditions such as reachability. In order to perform WFJ with low computational cost, we devise a ...