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On Properties of Update Sequences Based on Causal Rejection
We consider an approach to update nonmonotonic knowledge bases represented as
extended logic programs under answer set semantics. New information is
incorporated into the current knowledge base subject to a causal rejection
principle enforcing that, in case of conflicts, more recent rules are preferred
and older rules are overridden. Such a rejection principle is also exploited in
other approaches to update logic programs, e.g., in dynamic logic programming
by Alferes et al. We give a thorough analysis of properties of our approach, to
get a better understanding of the causal rejection principle. We review
postulates for update and revision operators from the area of theory change and
nonmonotonic reasoning, and some new properties are considered as well. We then
consider refinements of our semantics which incorporate a notion of minimality
of change. As well, we investigate the relationship to other approaches,
showing that our approach is semantically equivalent to inheritance programs by
Buccafurri et al. and that it coincides with certain classes of dynamic logic
programs, for which we provide characterizations in terms of graph conditions.
Therefore, most of our results about properties of causal rejection principle
apply to these approaches as well. Finally, we deal with computational
complexity of our approach, and outline how the update semantics and its
refinements can be implemented on top of existing logic programming engines.Comment: 59 pages, 2 figures, 3 tables, to be published in "Theory and
Practice of Logic Programming
A Program-Level Approach to Revising Logic Programs under the Answer Set Semantics
An approach to the revision of logic programs under the answer set semantics
is presented. For programs P and Q, the goal is to determine the answer sets
that correspond to the revision of P by Q, denoted P * Q. A fundamental
principle of classical (AGM) revision, and the one that guides the approach
here, is the success postulate. In AGM revision, this stipulates that A is in K
* A. By analogy with the success postulate, for programs P and Q, this means
that the answer sets of Q will in some sense be contained in those of P * Q.
The essential idea is that for P * Q, a three-valued answer set for Q,
consisting of positive and negative literals, is first determined. The positive
literals constitute a regular answer set, while the negated literals make up a
minimal set of naf literals required to produce the answer set from Q. These
literals are propagated to the program P, along with those rules of Q that are
not decided by these literals. The approach differs from work in update logic
programs in two main respects. First, we ensure that the revising logic program
has higher priority, and so we satisfy the success postulate; second, for the
preference implicit in a revision P * Q, the program Q as a whole takes
precedence over P, unlike update logic programs, since answer sets of Q are
propagated to P. We show that a core group of the AGM postulates are satisfied,
as are the postulates that have been proposed for update logic programs
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