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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
Belief Revision in Structured Probabilistic Argumentation
In real-world applications, knowledge bases consisting of all the information
at hand for a specific domain, along with the current state of affairs, are
bound to contain contradictory data coming from different sources, as well as
data with varying degrees of uncertainty attached. Likewise, an important
aspect of the effort associated with maintaining knowledge bases is deciding
what information is no longer useful; pieces of information (such as
intelligence reports) may be outdated, may come from sources that have recently
been discovered to be of low quality, or abundant evidence may be available
that contradicts them. In this paper, we propose a probabilistic structured
argumentation framework that arises from the extension of Presumptive
Defeasible Logic Programming (PreDeLP) with probabilistic models, and argue
that this formalism is capable of addressing the basic issues of handling
contradictory and uncertain data. Then, to address the last issue, we focus on
the study of non-prioritized belief revision operations over probabilistic
PreDeLP programs. We propose a set of rationality postulates -- based on
well-known ones developed for classical knowledge bases -- that characterize
how such operations should behave, and study a class of operators along with
theoretical relationships with the proposed postulates, including a
representation theorem stating the equivalence between this class and the class
of operators characterized by the postulates
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