30,647 research outputs found
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
Handling Defeasibilities in Action Domains
Representing defeasibility is an important issue in common sense reasoning.
In reasoning about action and change, this issue becomes more difficult because
domain and action related defeasible information may conflict with general
inertia rules. Furthermore, different types of defeasible information may also
interfere with each other during the reasoning. In this paper, we develop a
prioritized logic programming approach to handle defeasibilities in reasoning
about action. In particular, we propose three action languages {\cal AT}^{0},
{\cal AT}^{1} and {\cal AT}^{2} which handle three types of defeasibilities in
action domains named defeasible constraints, defeasible observations and
actions with defeasible and abnormal effects respectively. Each language with a
higher superscript can be viewed as an extension of the language with a lower
superscript. These action languages inherit the simple syntax of {\cal A}
language but their semantics is developed in terms of transition systems where
transition functions are defined based on prioritized logic programs. By
illustrating various examples, we show that our approach eventually provides a
powerful mechanism to handle various defeasibilities in temporal prediction and
postdiction. We also investigate semantic properties of these three action
languages and characterize classes of action domains that present more
desirable solutions in reasoning about action within the underlying action
languages.Comment: 49 pages, 1 figure, to be appeared in journal Theory and Practice
Logic Programmin
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