Terminological reasoning with constraint handling rules

Constraint handling rules (CHRs) are a flexible means to implement \u27user-defined\u27 constraints on top of existing host languages (like Prolog and Lisp). Recently, M. Schmidt-Schauß and G. Smolka proposed a new methodology for constructing sound and complete inference algorithms for terminological knowledge representation formalisms in the tradition of KLONE. We propose CHRs as a flexible implementation language for the consistency test of assertions, which is the basis for all terminological reasoning services. The implementation results in a natural combination of three layers: (i) a constraint layer that reasons in well- understood domains such as rationals or finite domains, (ii) a terminological layer providing a tailored, validated vocabulary on which (iii) the application layer can rely. The flexibility of the approach will be illustrated by extending the formalism, its implementation and an application example (solving configuration problems) with attributes, a new quantifier and concrete domains

Confluence of CHR Revisited:Invariants and Modulo Equivalence

Abstract simulation of one transition system by another is introduced as a means to simulate a potentially infinite class of similar transition sequences within a single transition sequence. This is useful for proving confluence under invariants of a given system, as it may reduce the number of proof cases to consider from infinity to a finite number. The classical confluence results for Constraint Handling Rules (CHR) can be explained in this way, using CHR as a simulation of itself. Using an abstract simulation based on a ground representation, we extend these results to include confluence under invariant and modulo equivalence, which have not been done in a satisfactory way before.Comment: Pre-proceedings paper presented at the 28th International Symposium on Logic-Based Program Synthesis and Transformation (LOPSTR 2018), Frankfurt am Main, Germany, 4-6 September 2018 (arXiv:1808.03326