This technical note describes a monotone and continuous fixpoint operator to compute the answer sets of programs with aggregates. The fixpoint operator relies on the notion of aggregate solution. Under certain conditions, this operator behaves identically to the three-valued immediate consequence operator Φ P for aggregate programs, independently proposed in (Pelov 2004; Pelov et al. 2004). Thi...

We investigate a generalization of weight-constraint programs with stable semantics, as implemented in the ASP solver smodels. Our programs admit atoms of the form 〈X,F〉 where X is a finite set of propositional atoms and F is an arbitrary family of subsets of X. We call such atoms set constaints and show that the concept of stable model can be generalized to programs admitting set constraints b...

In this paper we present a new rule-based approach for consistency preserving view updating in deductive databases. Based on rule transformations performed during schema design, fixpoint evaluations of these rules at run time compute consistent realizations of view update requests. Alternative realizations are expressed using disjunctive Datalog internally. The approach extends and integrates s...

Compton, K.J., Stratified least fixpoint logic, Theoretical Computer Science 131 (1994) 95-120. Stratified least jixpoint logic, or SLFP, characterizes the expressibility of stratified logic programs and, in a different formulation, has been used as a logic of imperative programs. These two formulations of SLFP are proved to be equivalent. A complete sequent calculus with one infinitary rule is...

We present a practical algorithm for computing exact least solutions of systems of equations over the rationals with addition, multiplication with positive constants, minimum and maximum. The algorithm is based on strategy improvement combined with solving linear programming problems for each selected strategy. We apply our technique to compute the abstract least fixpoint semantics of affine pr...

In this paper, we discuss the main problems of inductive query languages and optimisation issues. We present a logic-based inductive query language and illustrate the use of aggregates and exploit a new join operator to model specific data mining tasks. We show how a fixpoint operator works for association rule mining and a clustering method. A preliminary experimental result shows that fixpoin...

In [10], hybrid MKNF knowledge bases have been proposed for combining open and closed world reasoning within the logics of minimal knowledge and negation as failure ([8]). For this powerful framework, we define a three-valued semantics and provide an alternating fixpoint construction for nondisjunctive hybrid MKNF knowledge bases. We thus provide a well-founded semantics which is a sound approx...

We present a novel procedure FixIt(ALC) for deciding knowledge base satisfiability in the Fuzzy Description Logic (FDL) ALC. FixIt(ALC) does not search for tree-structured models as in tableau-based proof procedures, but embodies a fixpoint-computation of canonical models that are not necessarily tree-structured. Conceptually, the procedure is based on a type-elimination process. Soundness, com...