Problem Of Belief Revision Research Articles

A quantitative approach to belief revision in structured probabilistic argumentation

Many real-world knowledge-based systems must deal with information coming from different sources that invariably leads to incompleteness, overspecification, or inherently uncertain content. The presence of these varying levels of uncertainty doesn't mean that the information is worthless --- rather, these are hurdles that the knowledge engineer must learn to work with. In this paper, we continue work on an argumentation-based framework that extends the well-known Defeasible Logic Programming (DeLP) language with probabilistic uncertainty, giving rise to the Defeasible Logic Programming with Presumptions and Probabilistic Environments (DeLP3E) model. Our prior work focused on the problem of belief revision in DeLP3E, where we proposed a non-prioritized class of revision operators called AFO (Annotation Function-based Operators) to solve this problem. In this paper, we further study this class and argue that in some cases it may be desirable to define revision operators that take quantitative aspects into account, such as how the probabilities of certain literals or formulas of interest change after the revision takes place. To the best of our knowledge, this problem has not been addressed in the argumentation literature to date. We propose the QAFO (Quantitative Annotation Function-based Operators) class of operators, a subclass of AFO, and then go on to study the complexity of several problems related to their specification and application in revising knowledge bases. Finally, we present an algorithm for computing the probability that a literal is warranted in a DeLP3E knowledge base, and discuss how it could be applied towards implementing QAFO-style operators that compute approximations rather than exact operations.

Characterization of logic program revision as an extension of propositional revision

AbstractWe address the problem of belief revision of logic programs (LPs), i.e., how to incorporate to a LP P a new LP Q. Based on the structure of SE interpretations, Delgrande et al. (2008. Proc. of the 11th International Conference on Principles of Knowledge Representation and Reasoning (KR'08), 411–421; 2013b. Proc. of the 12th International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR'13), 264–276) adapted the well-known AGM framework (Alchourrón et al. 1985. Journal of Symbolic Logic 50, 2, 510–530) to LP revision. They identified the rational behavior of LP revision and introduced some specific operators. In this paper, a constructive characterization of all rational LP revision operators is given in terms of orderings over propositional interpretations with some further conditions specific to SE interpretations. It provides an intuitive, complete procedure for the construction of all rational LP revision operators and makes easier the comprehension of their semantic and computational properties. We give a particular consideration to LPs of very general form, i.e., the generalized logic programs (GLPs). We show that every rational GLP revision operator is derived from a propositional revision operator satisfying the original AGM postulates. Interestingly, the further conditions specific to GLP revision are independent from the propositional revision operator on which a GLP revision operator is based. Taking advantage of our characterization result, we embed the GLP revision operators into structures of Boolean lattices, that allow us to bring to light some potential weaknesses in the adapted AGM postulates. To illustrate our claim, we introduce and characterize axiomatically two specific classes of (rational) GLP revision operators which arguably have a drastic behavior. We additionally consider two more restricted forms of LPs, i.e., the disjunctive logic programs (DLPs) and the normal logic programs (NLPs) and adapt our characterization result to disjunctive logic program and normal logic program revision operators.

Dynamic inference and everyday conditional reasoning in the new paradigm

One of the principal motivations for the new paradigm in reasoning was a reaction to the old (binary truth functional) paradigm's inability to deal with everyday non-monotonic inference. Within the new paradigm the problem of non-monotonicity is recast as the problem of belief revision or dynamic inference; that is, what happens when the probability distribution over which inferences are made changes from Pr0 to Pr1. Non-monotonicity arises when the new distribution, conditional on new information, I, changes the relevant probabilities, so that Pr0(x) ≠ Pr1(x), i.e., Pr0(x) ≠ Pr0(x|I). In this paper we first introduce the general problem of dynamic inference. We then consider the specific problems for dynamic conditional inference, in particular for modus tollens (MT). We then turn to possible reactions to these problems, looking at Oaksford and Chater's (2007) learning approach and causal Bayes nets. We conclude that most of the recent research on the non-monotonic effects observed in casual conditional inference and the suppression effect require a dynamic approach. However, the rational constraints on the transition from Pr0 to Pr1, when Pr0(x) ≠ Pr0(x|I), remain unclear.

Three Scenarios for the Revision of Epistemic States

This position paper discusses the difficulty of interpreting the iterated belief revision problem. Axioms of iterated belief revision are often presented as extensions of the AGM axioms, upon receiving a sequence of inputs, likely to alter not only the belief set, but also the epistemic entrenchment relation underlying the revision operator. Iterated belief revision presupposes that more recent inputs have priority over less recent ones. We argue that this view of iterated revision is at odds with the suggestion of Gardenfors and Makinson, that belief revision and non-monotonic reasoning are two sides of the same coin. It is not clear that non-monotonic reasoning modifies the ranking of possible worlds implicit in default rules. We lay bare three different paradigms of revision based on specific interpretations of the epistemic entrenchment implicitly at work and of the input information. If the epistemic entrenchment stems from default rules and the input is a specific piece of evidence, then AGM revision is a matter of changing plausible conclusions, and iterated revision makes no sense. However, if the epistemic entrenchment encodes uncertain factual evidence and the input information as well, then iterated revision reduces to prioritized merging. A third problem where iteration makes sense corresponds to the revision, by the addition of new default rules, of a conditional knowledge base describing background information. The three scenarios are compared with similar problems in the framework of probabilistic reasoning.

Belief change as propositional update

This study examines the problem of belief revision, defined as deciding which of several initially accepted sentences to disbelieve, when new information presents a logical inconsistency with the initial set. In the first three experiments, the initial sentence set included a conditional sentence, a non-conditional (ground) sentence, and an inferred conclusion drawn from the first two. The new information contradicted the inferred conclusion. Results indicated that conditional sentences were more readily abandoned than ground sentences, even when either choice would lead to a consistent belief state, and that this preference was more pronounced when problems used natural language cover stories rather than symbols. The pattern of belief revision choices differed depending on whether the contradicted conclusion from the initial belief set had been a modus ponens or modus tollens inference. Two additional experiments examined alternative model-theoretic definitions of minimal change to a belief state, using problems that contained multiple models of the initial belief state and of the new information that provided the contradiction. The results indicated that people did not follow any of four formal definitions of minimal change on these problems. The new information and the contradiction it offered was not, for example, used to select a particular model of the initial belief state as a way of reconciling the contradiction. The preferred revision was to retain only those initial sentences that had the same, unambiguous truth value within and across both the initial and new information sets. The study and results are presented in the context of certain logic-based formalizations of belief revision, syntactic and model-theoretic representations of belief states, and performance models of human deduction. Principles by which some types of sentences might be more “entrenched” than others in the face of contradiction are also discussed from the perspective of induction and theory revision.

Belief Change as Propositional Update

This study examines the problem of belief revision, defined as deciding which of several initially accepted sentences to disbelieve, when new information presents a logical inconsistency with the initial set. In the first three experiments, the initial sentence set included a conditional sentence, a non‐conditional (ground) sentence, and an inferred conclusion drawn from the first two. The new information contradicted the inferred conclusion. Results indicated that conditional sentences were more readily abandoned than ground sentences, even when either choice would lead to a consistent belief state, and that this preference was more pronounced when problems used natural language cover stories rather than symbols. The pattern of belief revision choices differed depending on whether the contradicted conclusion from the initial belief set had been a modus ponens or modus tollens inference. Two additional experiments examined alternative model‐theoretic definitions of minimal change to a belief state, using problems that contained multiple models of the initial belief state and of the new information that provided the contradiction. The results indicated that people did not follow any of four formal definitions of minimal change on these problems. The new information and the contradiction it offered was not, for example, used to select a particular model of the initial belief state as a way of reconciling the contradiction. The preferred revision was to retain only those initial sentences that had the same, unambiguous truth value within and across both the initial and new information sets. The study and results are presented in the context of certain logic‐based formalizations of belief revision, syntactic and model‐theoretic representations of belief states, and performance models of human deduction. Principles by which some types of sentences might be more “entrenched” than others in the face of contradiction are also discussed from the perspective of induction and theory revision.

A framework for controlling model-based diagnosis systems with multiple actions

In recent years reasoning about structure and function of physical systems for the purpose of diagnosis has seen a dramatic increase in activities. New exciting results concerning modelling issues, diagnostic inference patterns and inferential power have emerged. A state of the art diagnosis agent now has a considerable toolset at hand. A main obstacle for building large diagnosis systems, however, remains. How can we controlwhen to usewhich inference pattern or representation? We argue that the actions available to a diagnosis agent can be understood in terms of change ofworking hypotheses. The control problem then becomes a belief revision problem: when to adopt or drop beliefs. Our approach proceeds in two steps. First, we adopt the principle of informational economy from Gardenfors, Knowledge in Flux (MIT Press, 1988) as kind of a law of inertia for diagnostic processes, that helps us identify candidates for revised belief states. In a second step we employ specificdiagnostic knowledge to actually choose the next belief state. We demonstrate the use of our concepts on an example in the domain of ballast tank systems as e.g. used in offshore plants.

Belief revision ? an axiomatic approach

Belief revision systems aim at keeping a database consistent. They mostly concentrate on how to record and maintain dependencies. We propose an axiomatic system, called MFOT, as a solution to the problem of belief revision. MFOT has a set of proper axioms which selects a set of most plausible and consistent input beliefs. The proposed nonmonotonic inference rule further maintains consistency while generating the consequences of input beliefs. It also permits multiple property inheritance with exceptions. We have also examined some important properties of the proposed axiomatic system. We also propose a belief revision model that is object-centered. The relevance of such a model in maintaining the beliefs of a physician is examined.

Skeptical reason maintenance and belief revision

The skeptical semantics is a three-valued semantics for reason maintenance based on an extension of the well-known two-valued grounded or stable model semantics. Unlike the latter, however, the skeptical semantics has a computationally attractive feature: the skeptical model can be computed in O( n 2) time. The skeptical semantics can also be used to give a better account of the belief revision problem in reason maintenance. A recent logical reconstruction of dependency-directed backtracking (DDB) offers the possibility to represent different DDB strategies by different extensions of a reason maintenance system. Given a reason maintenance system D, we can distinguish a class of extensions, representing all possible DDB strategies for D. We will prove that within this class there exists a unique extension whose skeptical model can be used as a canonical, information-minimal belief revision model. This skeptical belief revision model has some important advantages: 1. (1) The arbitrariness of solutions found by classical dependency-directed backtracking methods can be avoided. 2. (2) The semantics guarantees a (tractable) incremental updating method, and this method satisfies—contrary to standard belief revision techniques—a weak rationality postulate ensuring the minimality of performed changes. 3. (3) Skeptical belief revision is a complete belief revision strategy and is easy to compute, having a worst-case complexity O( n 3).

Automatic belief revision in a plausibility-driven design environment

Truth maintenance systems (TMSs) offer the most elaborate approach to the belief revision problem and are thus ideal candidates for automating belief revision during the course of plausibility-driven design evolution. However, the theory of plausible design (TPD) necessitates multivalued belief propagation while conventional TMSs are two-valued (IN/OUT) systems. Due to this mismatch, the encoding of constraint dependency graphs (CDGs) in conventional TMSs requires an exponential number of justifications. A belief revision system for TPD called the theory of plausible design belief revision system (TPD-BRS) is proposed. TPD-BRS uses a modified version of the assumption-based TMS label propagation algorithm in conjunction with a label interpreter to support automated belief revision in TPD efficiently.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>