Computing least common subsumers (lcs) and most speci c concepts (msc) are inference tasks that can be used to support the \bottom up" construction of knowledge bases for KR systems based on description logic. For the description logic ALN , the msc need not always exist if one restricts the attention to acyclic concept descriptions. In this paper, we extend the notions lcs and msc to cyclic de...

Computing least common subsumers (lcs) and most speciic concepts (msc) are inference tasks that can be used to support the \bottom up" construction of knowledge bases for KR systems based on description logic. For the description logic ALN, the msc need not always exist if one restricts the attention to acyclic concept descriptions. In this paper, we extend the notions lcs and msc to cyclic des...

We consider the modal-calculus due to Kozen, which is a nitary modal logic with least and greatest xed points of monotone operators. We extend the existing duality between the category of modal algebras with homomorphisms and the category of descriptive modal frames with contractions to the case of having xed point operators. As a corollary, we obtain a completeness result for Kozen's original ...

In fractal image compression, the code is given by a contractive aane mapping whose xed point is an approximation to the original image. Usually, the mapping is found by the collage coding method. We propose an algorithm that starts from an initial mapping obtained by collage coding and iteratively provides a sequence of contractive mappings whose xed points are monotonically approaching the or...

The deenition of concepts is a central problem in commonsense reasoning. Many themes in nonmonotonic reasoning concern implicit and explicit deenability. Implicit deenability in nonmonotonic logic is always relative to the context-the current theory of the world. We show that xed point equations provide a generalization of explicit deenability, which correctly captures the relativized context. ...

The existence of stationary solutions to the Povzner equation is established for a class of problems in bounded domains with smooth boundaries. The result holds for general type collision kernels under assumptions of angular cutoo. The boundary conditions with xed in-data and with a linear operator of diiuse reeection type are considered. The method is based on constructing approximate solution...

Computing least common subsumers (lcs) and most speci c concepts (msc) are inference tasks that can be used to support the \bottom up" construction of knowledge bases for KR systems based on description logic. For the description logic ALN , the msc need not always exist if one restricts the attention to acyclic concept descriptions. In this paper, we extend the notions lcs and msc to cyclic de...

We analyze a renormalization group transformation R for partially analytic Hamiltonians, with emphasis on what seems to be needed for the construction of non-integrable xed points. Under certain assumptions, which are supported by numerical data in the golden mean case, we prove that such a xed point has a critical invariant torus. The proof is constructive and can be used for numerical computa...