Rational Defeasible Belief Change

2020 ◽  
Author(s):  
Giovanni Casini ◽  
Thomas Meyer ◽  
Ivan Varzinczak
Keyword(s):  
Belief Change ◽  
Nonmonotonic Reasoning ◽  
Logical Consistency ◽  
Iterated Revision ◽  
Reasoning System ◽  
Classical Work ◽  
Formal Framework ◽  
Important Notion ◽  
Iterated Contraction ◽  
Recent Attention

We present a formal framework for modelling belief change within a nonmonotonic reasoning system. Belief change and non-monotonic reasoning are two areas that are formally closely related, with recent attention being paid towards the analysis of belief change within a non-monotonic environment. In this paper we consider the classical AGM belief change operators, contraction and revision, applied to a defeasible setting in the style of Kraus, Lehmann, and Magidor. The investigation leads us to the consideration of the problem of iterated change, generalising the classical work of Darwiche and Pearl. We characterise a family of operators for iterated revision, followed by an analogous characterisation of operators for iterated contraction. We start considering belief change operators aimed at preserving logical consistency, and then characterise analogous operators aimed at the preservation of coherence—an important notion within the field of logic-based ontologies.

scholarly journals Incompatibilities Between Iterated and Relevance-Sensitive Belief Revision

2020 ◽  
Vol 69 ◽  
pp. 85-108
Author(s):  
Theofanis Aravanis ◽  
Pavlos Peppas ◽  
Mary-Anne Williams
Keyword(s):  
Belief Revision ◽  
Belief Change ◽  
Strong Sense ◽  
Revision Process ◽  
Entire Class ◽  
Iterated Revision ◽  
Formal Framework ◽  
Knowledge Dynamics

The AGM paradigm for belief change, as originally introduced by Alchourron, Gärdenfors and Makinson, lacks any guidelines for the process of iterated revision. One of the most influential work addressing this problem is Darwiche and Pearl's approach (DP approach, for short), which, despite its well-documented shortcomings, remains to this date the most dominant. In this article, we make further observations on the DP approach. In particular, we prove that the DP postulates are, in a strong sense, inconsistent with Parikh's relevance-sensitive axiom (P), extending previous initial conflicts. Immediate consequences of this result are that an entire class of intuitive revision operators, which includes Dalal's operator, violates the DP postulates, as well as that the Independence postulate and Spohn's conditionalization are inconsistent with axiom (P). The whole study, essentially, indicates that two fundamental aspects of the revision process, namely, iteration and relevance, are in deep conflict, and opens the discussion for a potential reconciliation towards a comprehensive formal framework for knowledge dynamics.

scholarly journals Reasoning about Cardinal Directions between 3-Dimensional Extended Objects using Answer Set Programming

2020 ◽  
Vol 20 (6) ◽  
pp. 942-957
Author(s):  
Yusuf Izmirlioglu ◽  
Esra Erdem
Keyword(s):  
Nonmonotonic Reasoning ◽  
Answer Set Programming ◽  
3 Dimensional ◽  
3D Space ◽  
Formal Framework ◽  
Different Types ◽  
New Type ◽  
Cardinal Directions ◽  
Answer Set

AbstractWe propose a novel formal framework (called 3D-NCDC-ASP) to represent and reason about cardinal directions between extended objects in 3-dimensional (3D) space, using Answer Set Programming (ASP). 3D-NCDC-ASP extends Cardinal Directional Calculus (CDC) with a new type of default constraints, and NCDC-ASP to 3D. 3D-NCDC-ASP provides a flexible platform offering different types of reasoning: Nonmonotonic reasoning with defaults, checking consistency of a set of constraints on 3D cardinal directions between objects, explaining inconsistencies, and inferring missing CDC relations. We prove the soundness of 3D-NCDC-ASP, and illustrate its usefulness with applications.

An analysis of a logical consistency model of belief change.

1970 ◽  
Vol 15 (2) ◽  
pp. 133-143 ◽  
Author(s):  
Sam G. McFarland ◽  
Donald L. Thistlethwaite
Keyword(s):  
Belief Change ◽  
Logical Consistency ◽  
Consistency Model

On uniform belief revision

2020 ◽  
Vol 30 (7) ◽  
pp. 1357-1376
Author(s):  
Theofanis Aravanis
Keyword(s):  
Present Article ◽  
Belief Revision ◽  
Possible Worlds ◽  
Belief Change ◽  
Rational Belief ◽  
Iterated Revision ◽  
Interesting Class ◽  
Total Preorder ◽  
Revision Function

Abstract Rational belief-change policies are encoded in the so-called AGM revision functions, defined in the prominent work of Alchourrón, Gärdenfors and Makinson. The present article studies an interesting class of well-behaved AGM revision functions, called herein uniform-revision operators (or UR operators, for short). Each UR operator is uniquely defined by means of a single total preorder over all possible worlds, a fact that in turn entails a significantly lower representational cost, relative to an arbitrary AGM revision function, and an embedded solution to the iterated-revision problem, at no extra representational cost. Herein, we first demonstrate how weaker, more expressive—yet, more representationally expensive—types of uniform revision can be defined. Furthermore, we prove that UR operators, essentially, generalize a significant type of belief change, namely, parametrized-difference revision. Lastly, we show that they are (to some extent) relevance-sensitive, as well as that they respect the so-called principle of kinetic consistency.

scholarly journals Belief Change in a Preferential Non-monotonic Framework

2017 ◽  
Author(s):  
Giovanni Casini ◽  
Thomas Meyer
Keyword(s):  
Belief Change ◽  
The Other ◽  
Definition Of ◽  
Important Notion ◽  
Two Sides

Belief change and non-monotonic reasoning are usually viewed as two sides of the same coin, with results showing that one can formally be defined in terms of the other. In this paper we show that it also makes sense to analyse belief change within a (preferential) non-monotonic framework. We consider belief change operators in a non-monotonic propositional setting with a view towards preserving consistency. We show that the results obtained can also be applied to the preservation of coherence— an important notion within the field of logic-based ontologies. We adopt the AGM approach to belief change and show that standard AGM can be adapted to a preferential non-monotonic framework, with the definition of expansion, contraction, and revision operators, and corresponding representation results.

scholarly journals Iterated contraction of propositions and conditionals under the principle of conditional preservation

10.29007/3q8l ◽  
2018 ◽  
Author(s):  
Gabriele Kern-Isberner ◽  
Tanja Bock ◽  
Kai Sauerwald ◽  
Christoph Beierle
Keyword(s):  
Belief Revision ◽  
Belief Change ◽  
Ranking Function ◽  
Ranking Functions ◽  
Belief Contraction ◽  
Seminal Work ◽  
Iterated Belief Revision ◽  
Iterated Contraction

Research on iterated belief change has focussed mostly on belief revision, only few papers have addressed iterated belief contraction. Most prominently, Darwiche and Pearl published seminal work on iterated belief revision the leading paradigm of which is the so-called principle of conditional preservation. In this paper, we use this principle in a thoroughly axiomatized form to develop iterated belief contraction operators for Spohn's ranking functions. We show that it allows for setting up constructive approaches to tackling the problem of how to contract a ranking function by a proposition or a conditional, respectively, and that semantic principles can also be derived from it for the purely qualitative case.

scholarly journals An Epistemological Study of Theory Change

2021 ◽  
Author(s):  
Theofanis Aravanis
Keyword(s):  
Belief Revision ◽  
Belief Change ◽  
Theory Change ◽  
Rational Belief ◽  
Dominant Model ◽  
Traditional Philosophy ◽  
New Information ◽  
Formal Framework ◽  
The Face ◽  
Main Shortcoming

Belief Revision is a well-established field of research that deals with how agents rationally change their minds in the face of new information. The milestone of Belief Revision is a general and versatile formal framework introduced by Alchourrón, Gärdenfors and Makinson, known as the AGM paradigm, which has been, to this date, the dominant model within the field. A main shortcoming of the AGM paradigm, as originally proposed, is its lack of any guidelines for relevant change. To remedy this weakness, Parikh proposed a relevance-sensitive axiom, which applies on splittable theories; i.e., theories that can be divided into syntax-disjoint compartments. The aim of this article is to provide an epistemological interpretation of the dynamics (revision) of splittable theories, from the perspective of Kuhn's inuential work on the evolution of scientific knowledge, through the consideration of principal belief-change scenarios. The whole study establishes a conceptual bridge between rational belief revision and traditional philosophy of science, which sheds light on the application of formal epistemological tools on the dynamics of knowledge.

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