On the one hand, termination analysis of logic programs is now a fairly established research topic within the logic programming community. On the other hand, non-termination analysis seems to remain a much less attractive subject. If we divide this line of research into two kinds of approaches, dynamic versus static analysis, this paper belongs to the latter. It proposes a criterion for detecting non-terminating atomic queries with respect to binary constraint logic programming (CLP) rules, which strictly generalizes our previous works on this subject. We give a generic operational definition and an implemented logical form of this criterion. Then we show that the logical form is correct and complete with respect to the operational definition.

This paper investigates the relationship between the Logical Algorithms (LA) language of Ganzinger and McAllester and Constraint Handling Rules (CHR). We present a translation schema from LA to CHRrp: CHR with rule priorities, and show that the meta-complexity theorem for LA can be applied to a subset of CHRrp via inverse translation. Inspired by the high-level implementation proposal for Logical Algorithm by Ganzinger and McAllester and based on a new scheduling algorithm, we propose an alternative implementation for CHRrp that gives strong complexity guarantees and results in a new and accurate meta-complexity theorem for CHRrp. It is furthermore shown that the translation from Logical Algorithms to CHRrp combined with the new CHRrp implementation satisfies the required complexity for the Logical Algorithms meta-complexity result to hold.

Disjunctive finitary programs are a class of logic programs admitting function symbols and hence infinite domains. They have very good computational properties; for example, ground queries are decidable, while in the general case the stable model semantics are Π11-hard. In this paper we prove that a larger class of programs, called finitely recursive programs, preserve most of the good properties of finitary programs under the stable model semantics, which are as follows: (i) finitely recursive programs enjoy a compactness property; (ii) inconsistency checking and skeptical reasoning are semidecidable; (iii) skeptical resolution is complete for normal finitely recursive programs. Moreover, we show how to check inconsistency and answer skeptical queries using finite subsets of the ground program instantiation. We achieve this by extending the splitting sequence theorem by Lifschitz and Turner: we prove that if the input program P is finitely recursive, then the partial stable models determined by any smooth splitting ω-sequence converge to a stable model of P.