Annotated revision programs

Revision programming is a formalism to describe and enforce updates of belief sets and databases. That formalism was extended by Fitting who assigned annotations to revision atoms. Annotations provide a way to quantify the confidence (probability) that a revision atom holds. The main goal of our paper is to reexamine the work of Fitting, argue that his semantics does not always provide results consistent with intuition, and to propose an alternative treatment of annotated revision programs. Our approach differs from that proposed by Fitting in two key aspects: we change the notion of a model of a program and we change the notion of a justified revision. We show that under this new approach fundamental properties of justified revisions of standard revision programs extend to the annotated case.Comment: 30 pages, to appear in Artificial Intelligence Journa

Ultimate approximations in nonmonotonic knowledge representation systems

We study fixpoints of operators on lattices. To this end we introduce the notion of an approximation of an operator. We order approximations by means of a precision ordering. We show that each lattice operator O has a unique most precise or ultimate approximation. We demonstrate that fixpoints of this ultimate approximation provide useful insights into fixpoints of the operator O. We apply our theory to logic programming and introduce the ultimate Kripke-Kleene, well-founded and stable semantics. We show that the ultimate Kripke-Kleene and well-founded semantics are more precise then their standard counterparts We argue that ultimate semantics for logic programming have attractive epistemological properties and that, while in general they are computationally more complex than the standard semantics, for many classes of theories, their complexity is no worse.Comment: This paper was published in Principles of Knowledge Representation and Reasoning, Proceedings of the Eighth International Conference (KR2002

Morphology and internal structure of Antarctic cosmic dust spherules: Possible links to meteorite fusion crusts

Petrographic and SEM comparison of the outer morphology of different Antarctic spherules with their internal structure helped to distinguish those spherules that resulted from melting of micrometeorites from the ablation products of meteorites. A chain of possible transformations beginning with unmelted micrometeorites was recognized. Such structural transformations could begin from unmelted cosmic dust of olivine aggregates through granular spherules, to vitrophyric spherules with ghost-olivine glassy ovoidal objects, to vitrophyric, and to skeletal spherules. The fusion crusts of meteorites studied, showed that ablation can also produce a variety of spherules. Achondrites could produce glassy smooth, and internally compact holohyaline spherules, whereas chondrites could generate spherules of the rough glazed, dendrite decorated morphological types

Normal Form Theorem for Logic Programs with Cardinality Constraints

We discuss proof schemes, a kind of context-dependent proofs for logic programs. We show usefullness of these constructs both in the context of normal logic programs and their generalizations due to Niemela and collaborators. As an application we show the following result. For every cardinality-constraint logic program P there is a logic program P´ with the same heads, but with bodies consisting of atoms and negated atoms such that P and P´ have same stable models. It is worth noting that another proof of same result can be obtained from the results by Lifschitz and collaborators