Two Sides of the Same Coin: Belief Revision and Enforcing Arguments

We study a type of change on knowledge bases inspired by the dynamics of formal argumentation systems, where the goal is to enforce acceptance of certain arguments. We put forward that enforcing acceptance of arguments can be viewed as a member of the wider family of belief change operations, and that an axiomatic treatment of it is therefore desirable. In our case, laying down axioms enables a precise account of the close connection between enforcing arguments and belief revision. Our analysis of enforcing arguments proceeds by (i) axiomatizing it as an operation in propositional logic and providing a representation result in terms of rankings on sets of interpretations, (ii) showing that it stands in close relationship to belief revision, and (iii) using it as a gateway towards a principled treatment of enforcement in abstract argumentation.

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Horn Clause Contraction Functions

Journal of Artificial Intelligence Research ◽

10.1613/jair.4031 ◽

2013 ◽

Vol 48 ◽

pp. 475-511 ◽

Cited By ~ 7

Author(s):

J. P. Delgrande ◽

R. Wassermann

Keyword(s):

Propositional Logic ◽

Belief Change ◽

Description Logics ◽

Knowledge Bases ◽

Classical Propositional Logic ◽

Horn Clauses ◽

Related Notion ◽

Starting Point ◽

Representation Result ◽

Obvious Extension

In classical, AGM-style belief change, it is assumed that the underlying logic contains classical propositional logic. This is clearly a limiting assumption, particularly in Artificial Intelligence. Consequently there has been recent interest in studying belief change in approaches where the full expressivity of classical propositional logic is not obtained. In this paper we investigate belief contraction in Horn knowledge bases. We point out that the obvious extension to the Horn case, involving Horn remainder sets as a starting point, is problematic. Not only do Horn remainder sets have undesirable properties, but also some desirable Horn contraction functions are not captured by this approach. For Horn belief set contraction, we develop an account in terms of a model-theoretic characterisation involving weak remainder sets. Maxichoice and partial meet Horn contraction is specified, and we show that the problems arising with earlier work are resolved by these approaches. As well, constructions of the specific operators and sets of postulates are provided, and representation results are obtained. We also examine Horn package contraction, or contraction by a set of formulas. Again, we give a construction and postulate set, linking them via a representation result. Last, we investigate the closely-related notion of forgetting in Horn clauses. This work is arguably interesting since Horn clauses have found widespread use in AI; as well, the results given here may potentially be extended to other areas which make use of Horn-like reasoning, such as logic programming, rule-based systems, and description logics. Finally, since Horn reasoning is weaker than classical reasoning, this work sheds light on the foundations of belief change

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A Weighted-Logic Representation of C-Revising Ordinal Conditional Functions

International Journal of Uncertainty Fuzziness and Knowledge-Based Systems ◽

10.1142/s0218488520500245 ◽

2020 ◽

Vol 28 (04) ◽

pp. 569-589

Author(s):

Safia Laaziz ◽

Younes Zeboudj ◽

Salem Benferhat ◽

Faiza Haned Khellaf

Keyword(s):

Information System ◽

Belief Revision ◽

Belief Change ◽

Possibility Theory ◽

Knowledge Bases ◽

Compact Representation ◽

Natural Representation ◽

Uncertainty Distribution ◽

Semantic Level ◽

New Information

The problem of belief change is considered as a major issue in managing the dynamics of an information system. It consists in modifying an uncertainty distribution, representing agents’ beliefs, in the light of a new information. In this paper, we focus on the so-called multiple iterated belief revision or C-revision, proposed for conditioning or revising uncertain distributions under uncertain inputs. Uncertainty distributions are represented in terms of ordinal conditional functions. We will use prioritized or weighted knowledge bases as a compact representation of uncertainty distributions. The input information leading to a revision of an uncertainty distribution is also represented by a set of consistent weighted formulas. This paper shows that C-revision, defined at a semantic level using ordinal conditional functions, has a very natural representation using weighted knowledge bases. We propose simple syntactic methods for revising weighted knowledge bases, that are semantically meaningful in the frameworks of possibility theory and ordinal conditional functions. In particular, we show that the space complexity of the proposed syntactic C-revision is linear with respect to the size of initial weighted knowledge bases.

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Belief Update within Propositional Fragments

Journal of Artificial Intelligence Research ◽

10.1613/jair.5541 ◽

2018 ◽

Vol 61 ◽

pp. 807-834 ◽

Cited By ~ 1

Author(s):

Nadia Creignou ◽

Raïda Ktari ◽

Odile Papini

Keyword(s):

Knowledge Representation ◽

Belief Revision ◽

Classical Logic ◽

Propositional Logic ◽

Belief Change ◽

Research Area ◽

Belief Contraction ◽

Belief Merging ◽

Change Operation ◽

Horn Fragment

Belief change within the framework of fragments of propositional logic is one of the main and recent challenges in the knowledge representation research area. While previous research works focused on belief revision, belief merging, and belief contraction, the problem of belief update within fragments of classical logic has not been addressed so far. In the context of revision, it has been proposed to refine existing operators so that they operate within propositional fragments, and that the result of revision remains in the fragment under consideration. This approach is not restricted to the Horn fragment but also applicable to other propositional fragments like Krom and affine fragments. We generalize this notion of refinement to any belief change operator. We then focus on a specific belief change operation, namely belief update. We investigate the behavior of the refined update operators with respect to satisfaction of the KM postulates and highlight differences between revision and update in this context.

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Belief Update in the Horn Fragment

Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence ◽

10.24963/ijcai.2018/246 ◽

2018 ◽

Author(s):

Nadia Creignou ◽

Adrian Haret ◽

Odile Papini ◽

Stefan Woltran

Keyword(s):

Recent Work ◽

Propositional Logic ◽

Possible Worlds ◽

Belief Change ◽

Representation Result ◽

Total Preorders ◽

Horn Fragment ◽

Shed Light

In line with recent work on belief change in fragments of propositional logic, we study belief update in the Horn fragment. We start from the standard KM postulates used to axiomatize belief update operators; these postulates lend themselves to semantic characterizations in terms of partial (resp. total) preorders on possible worlds. Since the Horn fragment is not closed under disjunction, the standard postulates have to be adapted for the Horn fragment. Moreover, a restriction on the preorders (i.e., Horn compliance) and additional postulates are needed to obtain sensible characterizations for the Horn fragment, and this leads to our main contribution: a representation result which shows that the class of update operators captured by Horn compliant partial (resp. total) preorders over possible worlds is precisely that given by the adapted and augmented Horn update postulates. With these results at hand, we provide concrete Horn update operators and are able to shed light on Horn revision operators based on partial preorders.

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Dynamics of knowledge in DeLP through Argument Theory Change

Theory and Practice of Logic Programming ◽

10.1017/s1471068411000603 ◽

2012 ◽

Vol 13 (6) ◽

pp. 893-957 ◽

Cited By ~ 6

Author(s):

MARTÍN O. MOGUILLANSKY ◽

NICOLÁS D. ROTSTEIN ◽

MARCELO A. FALAPPA ◽

ALEJANDRO J. GARCÍA ◽

GUILLERMO R. SIMARI

Keyword(s):

Theory Change ◽

Knowledge Bases ◽

Minimal Change ◽

Logic Programs ◽

Rule Based ◽

Defeasible Logic ◽

Abstract Argumentation ◽

Revision Operations ◽

Argumentation Systems ◽

Article Abstract

AbstractThis article is devoted to the study of methods to change defeasible logic programs (de.l.p.s) which are the knowledge bases used by the Defeasible Logic Programming (DeLP) interpreter. DeLP is an argumentation formalism that allows to reason over potentially inconsistent de.l.p.s. Argument Theory Change (ATC) studies certain aspects of belief revision in order to make them suitable for abstract argumentation systems. In this article, abstract arguments are rendered concrete by using the particular rule-based defeasible logic adopted by DeLP. The objective of our proposal is to define prioritized argument revision operators à la ATC for de.l.p.s, in such a way that the newly inserted argument ends up undefeated after the revision, thus warranting its conclusion. In order to ensure this warrant, the de.l.p. has to be changed in concordance with a minimal change principle. To this end, we discuss different minimal change criteria that could be adopted. Finally, an algorithm is presented, implementing the argument revision operations.

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(DIS)BELIEF CHANGE AND ARGUED FEED-BACK DIALOG

International Journal of Uncertainty Fuzziness and Knowledge-Based Systems ◽

10.1142/s0218488505003631 ◽

2005 ◽

Vol 13 (05) ◽

pp. 511-538

Author(s):

LAURENT PERRUSSEL ◽

JEAN-MARC THÉVENIN

Keyword(s):

Belief Revision ◽

Belief Change ◽

Preference Relation ◽

Belief State ◽

Temporal Aspects ◽

Incoming Information ◽

Multi Agent

This paper focuses on the features of belief change in a multi-agent context where agents consider beliefs and disbeliefs. Disbeliefs represent explicit ignorance and are useful to prevent agents to entail conclusions due to their ignorance. Agents receive messages holding information from other agents and change their belief state accordingly. An agent may refuse to adopt incoming information if it prefers its own (dis)beliefs. For this, each agent maintains a preference relation over its own beliefs and disbeliefs in order to decide if it accepts or rejects incoming information whenever inconsistencies occur. This preference relation may be built by considering several criteria such as the reliability of the sender of statements or temporal aspects. This process leads to non-prioritized belief revision. In this context we first present the * and − operators which allow an agent to revise, respectively contract, its belief state in a non-prioritized way when it receives an incoming belief, respectively disbelief. We show that these operators behave properly. Based on this we then illustrate how the receiver and the sender may argue when the incoming (dis)belief is refused. We describe pieces of dialog where (i) the sender tries to convince the receiver by sending arguments in favor of the original (dis)belief and (ii) the receiver justifies its refusal by sending arguments against the original (dis)belief. We show that the notion of acceptability of these arguments can be represented in a simple way by using the non-prioritized change operators * and −. The advantage of argumentation dialogs is twofold. First whenever arguments are acceptable the sender or the receiver reconsider its belief state; the main result is an improvement of the reconsidered belief state. Second the sender may not be aware of some sets of rules which act as constraints to reach a specific conclusion and discover them through argumentation dialogs.

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Modeling Belief in Dynamic Systems, Part II: Revision and Update

Journal of Artificial Intelligence Research ◽

10.1613/jair.506 ◽

1999 ◽

Vol 10 ◽

pp. 117-167 ◽

Cited By ~ 20

Author(s):

N. Friedman ◽

J. Y. Halpern

Keyword(s):

Artificial Intelligence ◽

Belief Revision ◽

Dynamic Systems ◽

Belief Change ◽

Companion Paper ◽

Minimal Change ◽

Special Cases ◽

Epistemic Modalities ◽

Over Time ◽

New Framework

The study of belief change has been an active area in philosophy and AI. In recent years two special cases of belief change, belief revision and belief update, have been studied in detail. In a companion paper (Friedman & Halpern, 1997), we introduce a new framework to model belief change. This framework combines temporal and epistemic modalities with a notion of plausibility, allowing us to examine the change of beliefs over time. In this paper, we show how belief revision and belief update can be captured in our framework. This allows us to compare the assumptions made by each method, and to better understand the principles underlying them. In particular, it shows that Katsuno and Mendelzon's notion of belief update (Katsuno & Mendelzon, 1991a) depends on several strong assumptions that may limit its applicability in artificial intelligence. Finally, our analysis allow us to identify a notion of minimal change that underlies a broad range of belief change operations including revision and update.

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