Belief Contraction in Non-classical logics as Hyperintensional Belief Change

2021 ◽  
Author(s):  
Marlo Souza ◽  
Renata Wassermann
Keyword(s):  
Belief Revision ◽  
General Framework ◽  
Belief Change ◽  
Description Logics ◽  
Belief Contraction

AGM's belief revision is one of the main paradigms in the study of belief change operations. Despite its popularity and importance to the area, it is well recognised that AGM's work relies on a strong idealisation of the agent's capabilities and the nature of beliefs themselves. Particularly, it is recognised in the literature that Belief and Knowledge are hyperintensional attitudes, i.e. they can differentiate between contents that are necessarily equivalent, but to our knowledge, only a few works have explicitly considered how hyperintensionality affects belief change. This work investigates abstract operations of hyperintensional belief change and their connection to belief change in non-classical logics, such as belief contraction operations for Horn Logics and Description Logics. Our work points to hyperintensional belief change as a general framework to unify results in belief change for non-classical logics.

scholarly journals Belief Update within Propositional Fragments

2018 ◽  
Vol 61 ◽  
pp. 807-834 ◽  
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.

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.

(DIS)BELIEF CHANGE AND ARGUED FEED-BACK DIALOG

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.

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

1999 ◽  
Vol 10 ◽  
pp. 117-167 ◽  
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.

OUTCOME LEVEL ANALYSIS OF BELIEF CONTRACTION

2013 ◽  
Vol 6 (2) ◽  
pp. 183-204 ◽  
Author(s):  
SVEN OVE HANSSON
Keyword(s):  
Belief Change ◽  
Belief Contraction ◽  
Axiomatic Characterizations ◽  
Outcome Set ◽  
Level Analysis

AbstractThe outcome set of a belief change operator is the set of outcomes that can be obtained with it. Axiomatic characterizations are reported for the outcome sets of the standard AGM contraction operators and eight types of base-generated contraction. These results throw new light on the properties of some of these operators.

Belief contraction as nonmonotonic inference

2000 ◽  
Vol 65 (2) ◽  
pp. 605-626 ◽  
Author(s):  
Alexander Bochman
Keyword(s):  
Belief Change ◽  
Epistemic State ◽  
Belief Contraction ◽  
Nonmonotonic Inference

AbstractA notion of an epistemic state is introduced as a generalization of common representations suggested for belief change. Based on it, a new kind of nonmonotonic inference relation corresponding to belief contractions is defined. A number of representation results is established that cover both traditional AGM contractions and contractions that do not satisfy recovery.

scholarly journals Horn Clause Contraction Functions

2013 ◽  
Vol 48 ◽  
pp. 475-511 ◽  
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

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 A Semantics for Hyperintensional Belief Revision Based on Information Bases

Studia Logica ◽  
2021 ◽  
Author(s):  
Sena Bozdag
Keyword(s):  
Belief Revision ◽  
Epistemic Logic ◽  
Belief Change ◽  
Dynamic Epistemic Logic ◽  
Doxastic Logic ◽  
Dynamic Operation ◽  
Belief Dynamics ◽  
Dynamic Doxastic Logic ◽  
New Framework

AbstractI propose a novel hyperintensional semantics for belief revision and a corresponding system of dynamic doxastic logic. The main goal of the framework is to reduce some of the idealisations that are common in the belief revision literature and in dynamic epistemic logic. The models of the new framework are primarily based on potentially incomplete or inconsistent collections of information, represented by situations in a situation space. I propose that by shifting the representational focus of doxastic models from belief sets to collections of information, and by defining changes of beliefs as artifacts of changes of information, we can achieve a more realistic account of belief representation and belief change. The proposed dynamic operation suggests a non-classical way of changing beliefs: belief revision occurs in non-explosive environments which allow for a non-monotonic and hyperintensional belief dynamics. A logic that is sound with respect to the semantics is also provided.

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