Choice revision is a sort of non-prioritized multiple revision, in which the agent partially accepts the new information represented by a set of sentences. We investigate the construction of choice revision based on a new approach to belief change called descriptor revision. We prove that each of two variants of choice revision based on such construction is axiomatically characterized with a set of plausible postulates, assuming that the object language is finite. Furthermore, we introduce an alternative modelling for choice revision, (...) which is based on a type of relation on sets of sentences, named multiple believability relation. We show without assuming a finite language that choice revision constructed from such relations is axiomatically characterized with the same sets of postulates that we proposed for the choice revision based on descriptor revision, whenever the relations satisfy certain rationality conditions. (shrink)

We introduce a new operator, called rational evaluation, in belief change. The operator evaluates new information according to the agent’s core beliefs, and then exports the plausible part of the new information. It belongs to the decision module in belief change. We characterize rational evaluation by axiomatic postulates and propose two functional constructions for it, based on the well-known constructions of kernel sets and remainder sets, respectively. The main results of the paper are two representation theorems with respect to the (...) two functional constructions. We also compare and connect the evaluation operator with some related operators in belief revision, including contraction, set contraction, and prioritized multiple revision. (shrink)

When an agent can not recognize, immediately, the implausible part of new information received, she will usually first expand her belief state by the new information, and then she may encounter some belief conflicts, and find the implausible information based on her criteria to consolidate her belief state. This process indicates a new kind of non-prioritized multiple revision, called metabolic revision. I give some axiomatic postulates for metabolic revision and propose two functional constructions for it, namely kernel metabolic revision and (...) partial meet metabolic revision, with respect to which the representation theorems are proved. I also compare metabolic revision with some related works in the literature, including semi-revision, merging with integrity constraints, evaluation, and evaluative multiple revision. (shrink)

In the literature of belief revision, it is widely accepted that: there is only one revision phase in belief revision which is well characterized by the Bayes’ Rule, Jeffrey’s Rule, etc.. However, as I argue in this article, there are at least four successive phases in belief revision, namely first/second order evaluation and first/second order revision. To characterize these phases, I propose mainly four rules of belief revision based on agent’s criteria, and make one composition rule to characterize belief revision (...) as a whole. (shrink)

This article investigates the properties of multistate top revision, a dichotomous model of belief revision that is based on an underlying model of probability revision. A proposition is included in the belief set if and only if its probability is either 1 or infinitesimally close to 1. Infinitesimal probabilities are used to keep track of propositions that are currently considered to have negligible probability, so that they are available if future information makes them more plausible. Multistate top revision satisfies a (...) slightly modified version of the set of basic and supplementary AGM postulates, except the inclusion and success postulates. This result shows that hyperreal probabilities can provide us with efficient tools for overcoming the well known difficulties in combining dichotomous and probabilistic models of belief change. (shrink)

Belief revision theories aim to model the dynamics of epistemic states. Besides beliefs, epistemic states comprise most importantly justificational structures. Typically, belief revision theories, however, model the dynamics of beliefs while neglecting justificational structures over and above logical relations. Despite some awareness that this approach is problematic, how devastating the consequences of this neglect are has not yet been fully grasped. In this paper, I argue that taking justificational structures into account could solve four well-known problems of belief revision.

The AGM success postulates for belief expansions and revisions have been widely criticized. This has resulted in the development of a number of non-prioritized belief change theories that violate these postulates. It is shown that we must also discard the monotony postulate for belief expansions if we abandon the success postulates. Non-prioritized belief change theories should instead fulfill a weaker postulate, which we call Conditional Monotony.

We propose a revision operator on a stratified belief base, i.e., a belief base that stores beliefs in different strata corresponding to the value an agent assigns to these beliefs. Furthermore, the operator will be defined as to perform the revision in such a way that information is never lost upon revision but stored in a stratum or layer containing information perceived as having a lower value. In this manner, if the revision of one layer leads to the rejection of (...) some information to maintain consistency, instead of being withdrawn it will be kept and introduced in a different layer with lower value. Throughout this development we will follow the principle of minimal change, being one of the important principles proposed in belief change theory, particularly emphasized in the AGM model. Regarding the reasoning part from the stratified belief base, the agent will obtain the inferences using an argumentative formalism. Thus, the argumentation framework will decide which information prevails when sentences of different layers are used for entailing conflicting beliefs. We will also illustrate how inferences are changed and how the status of arguments can be modified after a revision process. (shrink)

This work considers the formalisation of the merging process of stratified belief bases, where beliefs are stored in different layers or strata. Their strata are ranked, following a total order, employing the value the agent using the belief base assigns to these beliefs. The agent uses an argumentation mechanism to reason from the belief base and obtain the final inferences. We present two ways of merging stratified belief bases: the first is defined by merging two strata without belief preservation, and (...) the second by merging two strata with belief preservation. For these operators, as layers merge, it is possible that some information has to be deleted from the stratum to maintain consistency. The latter merge operator will be defined as performing their actions so that information removed from the stratum is preserved after the merging by moving it to a stratum containing information perceived as having a lower value and where those beliefs may trigger a new revision, possibly starting a cascading effect. (shrink)

The problem of knowledge evolution has received considerable attention over the years. Mainly, the study of the dynamics of knowledge has been addressed in the area of Belief Revision, a field emerging as the convergence of the efforts in Philosophy, Logic, and more recently Computer Science, where research efforts usually involve “flat” knowledge bases where there is no additional information about the formulas stored in it. Even when this may be a good fit for particular applications, in many real-world scenarios (...) different information items may be attached to formulas. For instance, when the reliability of the source of the piece of information is attached to it as a measure of some quality (e.g., strength) of the piece of information itself, or when some characteristic informs us on the desirability of the item (e.g., the potential benefit that could be obtained from it). If this type of information is available, we can use it to guide how the belief base is to be modified when new information arrives. In this work, we present a novel approach to the contraction of knowledge bases where formulas have values attached that measure some quality linked to those formulas, exploiting it to define their desirability, and uses such desirability to define which formulas need to be removed to solve conflicts. In this context, we introduce a set of properties for contraction operators by extending classic approaches. We also show how the local treatment of minimal conflicts can induce some counter-intuitive contractions, and we present a way to avoid them by considering optimal resolutions of conflicts using the additional information encoded. We show how the proposed formalization captures any contraction that is optimal under a set of features. Finally, we present a refinement based on the identification of related minimal conflicts that performs contraction in optimal ways without looking into the entire knowledge base. The approach is based on the use of the accrual of beliefs where several formulas collaboratively use their respective values to prevail in the resolution of conflicts. (shrink)

This thesis investigates a sort of non-prioritized multiple revision, the operation of making up one's mind, and its generalization, the operation of choice revision. Making up one's mind about a sentence is a belief change that takes the agent to a belief state in which either the sentence or its negation is believed. In choice revision, the input information is represented by a set of sentences, and the agent should make a choice on which sentences to be accepted. Apart from (...) being practically important, these operations are technically interesting since the standard approach of intersecting a set of optimal outcomes is not workable. Paper I provides a construction based on descriptor revision in which the operation of making up one's mind can be modelled in a ``select-direct'' way, which is different from the traditional ``select-and-intersect'' methodology employed in the AGM model. The article shows that this construction is axiomatically characterized with a set of plausible postulates, and investigates the additional postulates that correlate with properties of the construction. Paper II investigates a new modelling for sentential belief revision operations, which is based on a set of relations on sentences named believability relations. It demonstrates that two special kinds of such relations, i.e. H-believability relations and basic believability relations, are faithful alternative models of two typical sentential revision generated from descriptor revision. It also shows that traditional AGM revision operations can be reconstructed from a strengthened variant of the basic believability relation and there exists a close connection between this strengthened believability relation and the standard epistemic entrenchment relation. Paper III studies the constructions of choice revision based on descriptor revision and multiple believability relations, which extends the domain of believability relations from sentences to sets of sentences. It is shown that each of two variants of choice revision based on descriptor revision is axiomatically characterized with a set of plausible postulates, assuming that the object language is finite. Furthermore, without assuming a finite language, it is shown that choice revision constructed from multiple believability relations is axiomatically characterized with the same sets of postulates proposed for choice revision derived from descriptor revision, whenever these relations satisfy certain rationality conditions. Paper IV explores choice revision on belief bases. A generalized version of expansion operation called partial expansion is introduced for developing models of this kind of choice revision. Based on the partial expansion as well as two multiple contraction operations from the literature, two kinds of choice revision operators on belief bases are constructed. This paper proposes several postulates for such two operators and shows that they can be axiomatically characterized by such postulates. Furthermore, it investigates two kinds of making up one's mind operators generated from these two choice revision operators and presents the axiomatic characterizations of them. (shrink)