Notions of relevance for modeling the dynamics of belief

We identify different kinds of relevance relations between formulas that emerge in the process of belief revision. Informal definitions for alternative notions of relevance are suggested and a set of schemas and intuitive postulates for formalizing these notions are proposed. The notions of relevance proposed here are shown to be good candidates for modeling the process of belief revision.Eje: Programación lógicaRed de Universidades con Carreras en Informática (RedUNCI

The Irreducibility of Iterated to Single Revision

After a number of decades of research into the dynamics of rational belief, the belief revision theory community remains split on the appropriate handling of sequences of changes in view, the issue of so-called iterated revision. It has long been suggested that the matter is at least partly settled by facts pertaining to the results of various single revisions of one’s initial state of belief. Recent work has pushed this thesis further, offering various strong principles that ultimately result in a wholesale reduction of iterated to one-shot revision. The present paper offers grounds to hold that these principles should be significantly weakened and that the reductionist thesis should ultimately be rejected. Furthermore, the considerations provided suggest a close connection between the logic of iterated belief change and the logic of evidential relevance

Improving Assumption based Distributed Belief Revision

Belief revision is a critical issue in real world DAI applications. A Multi-Agent System not only has to cope with the intrinsic incompleteness and the constant change of the available knowledge (as in the case of its stand alone counterparts), but also has to deal with possible conflicts between the agents’ perspectives. Each semi-autonomous agent, designed as a combination of a problem solver – assumption based truth maintenance system (ATMS), was enriched with improved capabilities: a distributed context management facility allowing the user to dynamically focus on the more pertinent contexts, and a distributed belief revision algorithm with two levels of consistency. This work contributions include: (i) a concise representation of the shared external facts; (ii) a simple and innovative methodology to achieve distributed context management; and (iii) a reduced inter-agent data exchange format. The different levels of consistency adopted were based on the relevance of the data under consideration: higher relevance data (detected inconsistencies) was granted global consistency while less relevant data (system facts) was assigned local consistency. These abilities are fully supported by the ATMS standard functionalities

Observations on darwiche and Pearl's approach for iterated belief revision

© 2019 International Joint Conferences on Artificial Intelligence. All rights reserved. Notwithstanding the extensive work on iterated belief revision, there is, still, no fully satisfactory solution within the classical AGM paradigm. The seminal work of Darwiche and Pearl (DP approach, for short) remains the most dominant, despite its well-documented shortcomings. In this article, we make further observations on the DP approach. Firstly, 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 (P). Lastly, we show that the DP postulates allow for more revision polices than the ones that can be captured by identifying belief states with total preorders over possible worlds, a fact implying that a preference ordering (over possible worlds) is an insufficient representation for a belief state

Full characterization of Parikh's Relevance-Sensitive Axiom for Belief Revision

© 2019 AI Access Foundation. In this article, the epistemic-entrenchment and partial-meet characterizations of Parikh's relevance-sensitive axiom for belief revision, known as axiom (P), are provided. In short, axiom (P) states that, if a belief set K can be divided into two disjoint compartments, and the new information ' relates only to the first compartment, then the revision of K by ' should not affect the second compartment. Accordingly, we identify the subclass of epistemic-entrenchment and that of selection-function preorders, inducing AGM revision functions that satisfy axiom (P). Hence, together with the faithful-preorders characterization of (P) that has already been provided, Parikh's axiom is fully characterized in terms of all popular constructive models of Belief Revision. Since the notions of relevance and local change are inherent in almost all intellectual activity, the completion of the constructive view of (P) has a significant impact on many theoretical, as well as applied, domains of Artificial Intelligence

Notions of relevance for modeling the dynamics of belief

We identify different kinds of relevance relations between formulas that emerge in the process of belief revision. Informal definitions for alternative notions of relevance are suggested and a set of schemas and intuitive postulates for formalizing these notions are proposed. The notions of relevance proposed here are shown to be good candidates for modeling the process of belief revision.Eje: Programación lógicaRed de Universidades con Carreras en Informática (RedUNCI

An Epistemological Study of Theory Change

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

AGM-Like Paraconsistent Belief Change

Two systems of belief change based on paraconsistent logics are introduced in this article by means of AGM-like postulates. The first one, AGMp, is defined over any paraconsistent logic which extends classical logic such that the law of excluded middle holds w.r.t. the paraconsistent negation. The second one, AGMo , is specifically designed for paraconsistent logics known as Logics of Formal Inconsistency (LFIs), which have a formal consistency operator that allows to recover all the classical inferences. Besides the three usual operations over belief sets, namely expansion, contraction and revision (which is obtained from contraction by the Levi identity), the underlying paraconsistent logic allows us to define additional operations involving (non-explosive) contradictions. Thus, it is defined external revision (which is obtained from contraction by the reverse Levi identity), consolidation and semi-revision, all of them over belief sets. It is worth noting that the latter operations, introduced by S. Hansson, involve the temporary acceptance of contradictory beliefs, and so they were originally defined only for belief bases. Unlike to previous proposals in the literature, only defined for specific paraconsistent logics, the present approach can be applied to a general class of paraconsistent logics which are supraclassical, thus preserving the spirit of AGM. Moreover, representation theorems w.r.t. constructions based on selection functions are obtained for all the operations