This paper presents a logical approach to nonmonotonic reasoning based on the notion of a nonmonotonic consequence relation A condi tional knowledge base consisting of a set of conditional assertions of the type if then represents the explicit defeasible knowledge an agent has about the way the world generally behaves We look for a plausible de nition of the set of all conditional assertions en...

A new algorithm for rational interpolation is proposed. Given the data set, the algorithm generates a set of orthogonal polynomials by the classical threeterm recurrence relation and then uses Newton interpolation to find the numerator and the denominator polynomials of the rational interpolating function. The number of arithmetic operations of the algorithm to find a particular rational interp...

In multi-agent environments where agents independently generate and execute plans to satisfy their goals, the resulting plans may sometimes overlap. In this paper, we propose a collaboration mechanism using social law, through which rational agents can smoothly delegate and receive the execution of the overlapping parts of plans in order to reduce the cost of plan execution. Also, we consider c...

— We give hère a proof of the « cross section theorem » that is slightly différent from the original one. This allows us not only to show the existence of a rational cross section ofany rational set but also to describe such a cross section by means ofthe lexicographie ordering of the words. With some examples we also show that if we use the ordering ofwords by length, instead of the lexicograp...

A tree of height and cardinality ω 1 is satiable if it has a new branch in some ω 1-preserving outer model. If V is a standard transitive model of ZFC, say that W is an outer model of V if W ⊇ V is also a standard transitive model of ZFC and V ∩ OR = W ∩ OR. In this section, " tree " will mean normal, everbranching tree of height ω 1 with unique limit nodes. Precise definitions of these terms a...

We provide an introduction to logarithmic potential theory in the complex plane that particularly emphasizes its usefulness in the theory of polynomial and rational approximation. The reader is invited to explore the notions of Fekete points, logarithmic capacity, and Chebyshev constant through a variety of examples and exercises. Many of the fundamental theorems of potential theory, such as Fr...

The paper presents a new algorithmic construction of a finite generating set of rational invariants for the rational action of an algebraic group on the affine space. The construction provides an algebraic counterpart of the moving frame method in differential geometry. The generating set of rational invariants appears as the coefficients of a Gröbner basis, reduction with respect to which allo...

Let f be a rational function such that the multipliers of all repelling periodic points are real. We prove that the Julia set of such a function belongs to a circle. Combining this with a result of Fatou we conclude that whenever J(f) belongs to a smooth curve, it also belongs to a circle. Then we discuss rational functions whose Julia sets belong to a circle. MSC classes: 37F10, 30D05. A simpl...

Makienko's conjecture, a proposed addition to Sul-livan's dictionary, can be stated as follows: The Julia set of a rational function R : C ∞ → C ∞ has buried points if and only if no component of the Fatou set is completely invariant under the second iterate of R. We prove Makienko's conjecture for rational functions with Julia sets that are decomposable continua. This is a very broad collectio...

We give an example of two rational functions with non-equal Julia sets that generate a rational semigroup whose completely invariant Julia set is a closed line segment. We also give an example of polynomials with unequal Julia sets that generate a non nearly Abelian polynomial semigroup with the property that the Julia set of one generator is equal to the Julia set of the semigroup. These examp...