The study of fixpoints has long been at the heart of logic programming. However, whereas least fixpoint semantics works well for SLD-refutations (i.e. is sound and complete), there is no satisfactory (i.e. complete) fixpoint semantics for infinite derivations. In this paper, we focus on this problem. Standard approaches in this area consist in concentrating on infinite derivations that can be s...

A general functorial framework for recursive deenitions is presented in which simulation of a deenition scheme by another one implies an ordering between the values deened by these schemes in an arbitrary model. Under mild conditions on the functor involved, the converse implication also holds: a model is constructed such that, if the values deened are ordered, there is a simulation between the...

It is desirable to answer queries' posed to deductive databases by computing fixpoints because such computations are directly amenable to set-oriented fact processing. However, the classical fixpoint procedures based on bottom-up processingthe naive and semi-naive methodsare rather primitive and often inefficient. In this article, we rely on bottom-up meta-interpretation for formalizing a new f...

Verification techniques for Timed Automata [2] built in tools like Kronos [7] are based on the fixpoint calculus of an appropriate operator. In this work, we present different alternatives to calculate that fixpoint, which have direct impact in the number of iterations needed to converge.

In this paper, symmetry-based choice mechanisms are exploited to compute deterministic queries. We investigate a particular form of these choice mechanisms, called specified symmetry choice. This mechanism is efficient (i.e. computable in polynomial time) and can be added to Fixpoint Logic to give a language that is more powerful than the extension of Fixpoint with Counting.

We prove a generic completeness result for a class of modal fixpoint logics corresponding to flat fragments of the two-way mu-calculus, extending earlier work by Santocanale and Venema. We observe that Santocanale and Venema’s proof that least fixpoints in the Lindenbaum-Tarski algebra of certain flat fixpoint logics are constructive, using finitary adjoints, no longer works when the converse m...

It is well known that, under certain conditions, it is possible to split logic programs under stable model semantics, i.e. to divide such a program into a number of different “levels”, such that the models of the entire program can be constructed by incrementally constructing models for each level. Similar results exist for other non-monotonic formalisms, such as auto-epistemic logic and defaul...