A. Tarskiego kryterium monotoniczności operatora konsekwencji w międzykulturowych badaniach systemów wniskowań

In this article I refer to the issue of comparative research methodology and methods of philosophical argumentation systems with different cultural areas. In relation to that shown by A. Tarski logical consequence operator, will establish criteria for the comparative analysis of systems inferences different cultural areas of the property based on the operator monotonic consequences.

Well-founded and stable semantics of logic programs with aggregates

In this paper, we present a framework for the semantics and the computation of aggregates in the context of logic programming. In our study, an aggregate can be an arbitrary interpreted second order predicate or function. We define extensions of the Kripke-Kleene, the well-founded and the stable semantics for aggregate programs. The semantics is based on the concept of a three-valuedimmediate consequence operatorof an aggregate program. Such an operatorapproximatesthe standard two-valued immediate consequence operator of the program, and induces a unique Kripke-Kleene model, a unique well-founded model and a collection of stable models. We study different ways of defining such operators and thus obtain a framework of semantics, offering different trade-offs betweenprecisionandtractability. In particular, we investigate conditions on the operator that guarantee that the computation of the three types of semantics remains on the same level as for logic programs without aggregates. Other results show that, in practice, even efficient three-valued immediate consequence operators which are very low in the precision hierarchy, still provide optimal precision.

A Constructive semantic characterization of aggregates in answer set programming

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 ofaggregate solution. Under certain conditions, this operator behaves identically to the three-valued immediate consequence operator ΦaggrPfor aggregate programs, independently proposed in Pelov (2004) and Pelovet al.(2004). This operator allows us to closely tie the computational complexity of the answer set checking and answer sets existence problems to the cost of checking a solution of the aggregates in the program. Finally, we relate the semantics described by the operator to other proposals for logic programming with aggregates.

ON THE RELATION BETWEEN FUZZY PREORDERS AND FUZZY CONSEQUENCE OPERATORS

The purpose of this paper is to analyze the operators induced by relations and conversely the relations induced by operators in fuzzy logic. Given a t-norm * and given a non-empty universal set X, it is well known that if R is a fuzzy *-preorder on X then the operator induced by R, [Formula: see text], is a fuzzy consequence operator (FCO). In fact, [Formula: see text] is a *-coherent FCO. It is also known that if C is a *-coherent FCO then the relation induced by C, RC, is a fuzzy *-preorder. We explore the *-coherence axiom because we do not know in the literature any example of non-coherent operator. Then, several families of these operators will be shown. Moreover we prove that the equivalence between fuzzy preorders and fuzzy consequence operators is held in only one way. As a result, a characterization of the *-preorder concept using the induced operator is given. Also some characterizations which show when an operator induces a *-preorder are proved. Finally, we will show that the characterization of the operators induced by relations given for finite universes cannot be generalized for infinite universes.