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

REVISION PROGRAMMING: A KNOWLEDGE REPRESENTATION FORMALISM

The topic of the dissertation is revision programming. It is a knowledge representation formalismfor describing constraints on databases, knowledge bases, and belief sets, and providing acomputational mechanism to enforce them. Constraints are represented by sets of revision rules.Revision rules could be quite complex and are usually in a form of conditions (for instance, ifthese elements are present and those elements are absent, then this element must be absent). Inaddition to being a logical constraint, a revision rule specify a preferred way to satisfy the constraint.Justified revisions semantics assigns to any database a set (possibly empty) of revisions.Each revision satisfies the constraints, and all deletions and additions of elements in a transitionfrom initial database to the revision are derived from revision rules.Revision programming and logic programming are closely related. We established an elegantembedding of revision programs into logic programs, which does not increase the size of a program.Initial database is used in transformation of a revision program into the corresponding logicprogram, but it is not represented in the logic program.The connection naturally led to extensions of revision programming formalism which correspondto existing extensions of logic programming. More specific, a disjunctive and a nestedversions of revision programming were introduced.Also, we studied annotated revision programs, which allow annotations like confidence factors,multiple experts, etc. Annotations were assumed to be elements of a complete infinitely distributivelattice. We proposed a justified revisions semantics for annotated revision programs which agreedwith intuitions.Next, we introduced definitions of well-founded semantics for revision programming. It assignsto a revision problem a single intended model which is computable in polynomial time.Finally, we extended syntax of revision problems by allowing variables and implemented translatorsof revision programs into logic programs and a grounder for revision programs. The implementationallows us to compute justified revisions using existing implementations of the stablemodel semantics for logic programs

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