Studies on non-prioritized multiple belief revision

What kind of independence do we need for multiple iterated belief change?

In this paper we investigate the properties of iterated multiple belief revision. We examine several typical assumptions for iterated revision operations with an ontology where an agent assigns ordinals to beliefs, representing strength or firmness of beliefs. A notion of minimal change is introduced to express the idea that if no evidence to show how a belief set should be reordered after it is revised, the changes on the ordering should be minimal. It has been shown that under the assumption of minimal change, the multiple version of Darwiche and Pearl’s postulate (C1) holds no matter in what degree new information is accepted. Moreover, under the same assumption, Boutilier’s postulate (CB) holds if and only if new information is always accepted in the lowest degree of firmness while Nayak et al.’s postulate (CN) holds if and only if new information is always accepted in the highest degree. These results provide an ontological base for analyzing the rationality of postulates of iterated belief revision.

Multiple Belief Change extends the classical AGM framework for Belief Revision introduced by Alchourron, Gardenfors, and Makinson in the early ’80s. The extended framework includes epistemic input represented as a (possibly infinite) set of sentences , as opposed to a single sentence assumed in the original framework. The transition from single to multiple epistemic input worked out well for the operation of belief revision. The AGM postulates and the system-of-spheres model were adequately generalized and so was the representation result connecting the two. In the case of belief contraction however, the transition was not as smooth. The generalized postulates for contraction, which were shown to correspond precisely to the generalized partial meet model , failed to match up to the generalized epistemic entrenchment model . The mismatch was fixed with the addition of an extra postulate, called the limit postulate , that relates contraction by multiple epistemic input to a series of contractions by single epistemic input. The new postulate however creates problems on other fronts. First, the limit postulate needs to be mapped into appropriate constraints in the partial meet model. Second, via the Levi and Harper Identities, the new postulate translates into an extra postulate for multiple revision, which in turn needs to be characterized in terms of systems of spheres. Both these open problems are addressed in this article. In addition, the limit postulate is compared with a similar condition in the literature, called (K*F), and is shown to be strictly weaker than it. An interesting aspect of our results is that they reveal a profound connection between rationality in multiple belief change and the notion of an elementary set of possible worlds (closely related to the notion of an elementary class of models from classical logic).

This report documents the programme and outcomes of Dagstuhl Seminar 13231 Belief Change and Argumentation in Multi-Agent Scenarios. The seminar brought together researchers from the fields of argumentation theory and belief revision, both from philosophy and computer science, to present recent research results and exchange ideas for combining argumentation and belief revision. A key objective of the seminar, moreover, has been to shed light on the applicability of these two fields in the area of multi-agent systems: Can both argumentation and belief revision be combined and used in a rational agent? Before revising its beliefs, how should an agent decide what, or what part of the new information should be believed? Can this deliberation before the proper revision process be performed by argumentation? The unique atmosphere of Dagstuhl provided again a perfect environment for leading researchers from a wide variety of backgrounds to discuss future directions of argumentation, belief revision and their applications in multi-agent systems.

We consider the connections between belief revision, conditional logic and nonmonotonic reasoning, using as a foundation the approach to theory change developed by Alchourron, Gardenfors and Makinson (the AGM approach). This is first generalized to allow the iteration of theory change operations to capture the dynamics of epistemic states according to a principle of minimal change of entrenchment. The iterative operations of expansion, contraction and revision are characterized both by a set of postulates and by Grove’s construction based on total pre-orders on the set of complete theories of the belief logic. We present a sound and complete conditional logic whose semantics is based on our iterative revision operation, but which avoids Gardenfors’s triviality result because of a severely restricted language of beliefs and hence the weakened scope of our extended postulates. In the second part of the paper, we develop a computational approach to theory dynamics using Rott’s E-bases as a representation for epistemic states. Under this approach, a ranked E-base is interpreted as standing for the most conservative entrenchment compatible with the base, reflecting a kind of foundationalism in the acceptance of evidence for a belief. Algorithms for the computation of our iterative versions of expansion, contraction and revision are presented. Finally, we consider the relationship between nonmonotonic reasoning and both conditional logic and belief revision. Adapting the approach of Delgrande, we show that the unique extension of a default theory expressed in our conditional logic of belief revision corresponds to the most conservative belief state which respects the theory: however, this correspondence is limited to propositional default theories. Considering first order default theories, we present a belief revision algorithm which incorporates the assumption of independence of default instances and propose the use of a base logic for default reasoning which incorporates uniqueness of names. We conclude with an examination of the behavior of an implemented system on some of Lifschitz’s benchmark problems in nonmonotonic reasoning.

BackgroundDeep prosthetic joint infection (PJI) is a devastating complication of joint replacement surgery. It is difficult to treat, and patients often require multiple major revision surgeries to eradicate the infection. Treatment can have negative and long‐term impact on patients' quality of life. Understanding current service provision provides valuable information needed to design and evaluate support interventions for patients.AimThis survey aimed to identify usual care pathways and support in UK National Health Service (NHS) orthopaedic centres for patients receiving revision surgery for PJI after hip or knee replacement.MethodsThe 20 highest volume NHS orthopaedic centres treating prosthetic joint infection after hip or knee replacement were approached. Consultant orthopaedic surgeons specializing in treating PJI were invited to participate in a telephone or email survey about usual care provision and support for PJI.FindingsSixteen centres completed the survey. Findings showed a high degree of variation nationally in follow‐up time‐points after revision surgery. Multidisciplinary approaches to care focused more on clinical care and physical rehabilitation than social and psychological care. Patient management and referral to support services also varied and barriers to referrals included lack of availability or access to services, lack of knowledge of services, shortage of staff, and complexities of referring outside of the hospital catchment area.ConclusionsOur findings suggest that future development of interventions should focus on more inclusive and patient‐centred multidisciplinary approaches to care. Such interventions could more completely address psychological and social as well as physical aspects of patients' recovery.

Belief merging aims at combining information from multiple sources while belief revision studies strategies for retracting information in order to maintain consistency when the addition of new evidence to a belief base makes it inconsistent. An ordering of the sentences in the belief base is used to determine priorities among sentences so that those with lower priority can be identified and retracted. This ordering can be difficult to generate and maintain. To address this difficulty, in this paper we show how to generate automatically an ordering of the belief base sentences through the implementation of a belief merging operator. We extend the Δps (PS-Merge) belief merging operator in order to consider constraints, then we use this extension, called Δps-μ (Δps under constraints), as a strategy for belief revision. We treat new evidence as a constraint and apply the extended merging operator to obtain the revised belief base. We propose several properties of this operator when compared to other two belief revision operators solving four examples described as real-life scenarios. Finally we show a software prototype based on this approach, called Belief Reviser, freely accessible online.

In real-world applications, knowledge bases consisting of all the available information for a specific domain, along with the current state of affairs, will typically contain contradictory data, coming from different sources, as well as data with varying degrees of uncertainty attached. An important aspect of the effort associated with maintaining such knowledge bases is deciding what information is no longer useful; pieces of information may be outdated; may come from sources that have recently been discovered to be of low quality; or abundant evidence may be available that contradicts them. In this paper, we propose a probabilistic structured argumentation framework that arises from the extension of Presumptive Defeasible Logic Programming (PreDeLP) with probabilistic models, and argue that this formalism is capable of addressing these basic issues. The formalism is capable of handling contradictory and uncertain data, and we study non-prioritized belief revision over probabilistic PreDeLP programs that can help with knowledge-base maintenance. For belief revision, we propose a set of rationality postulates -- based on well-known ones developed for classical knowledge bases -- that characterize how these belief revision operations should behave, and study classes of operators along with theoretical relationships with the proposed postulates, including representation theorems stating the equivalence between classes of operators and their associated postulates. We then demonstrate how our framework can be used to address the attribution problem in cyber security/cyber warfare.

Transfusion and Post-Hospital Discharge Outcomes In Elective Total Hip Replacement (THR) or Total Knee Replacement (TKR) Surgery Among Adults <65 Years of Age.

In an earlier paper [Rational choice and AGM belief revision, Artificial Intelligence, 2009] a correspondence was established between the set-theoretic structures of revealed-preference theory (developed in economics) and the syntactic belief revision functions of the AGM theory (developed in philosophy and computer science). In this paper we extend the re-interpretation of those structures in terms of one-shot belief revision by relating them to the trichotomous attitude towards information studied in Garapa (Rev Symb Logic, 1–21, 2020) where information may be either (1) fully accepted or (2) rejected or (3) taken seriously but not fully accepted. We begin by introducing the syntactic notion of filtered belief revision and providing a characterization of it in terms of a mixture of both AGM revision and contraction. We then establish a correspondence between the proposed notion of filtered belief revision and the above-mentioned set-theoretic structures, interpreted as semantic partial belief revision structures. We also provide an interpretation of the trichotomous attitude towards information in terms of the degree of implausibility of the information.

Conditionals are not only central items for knowledge representation, but also play an important part in belief revision, in particular when dealing with iterated belief revision. To handle conditional beliefs appropriately, epistemic states instead of propositional belief sets have to be considered. Within this framework, the preservation of conditional beliefs turns out to be a principal concern, corresponding to the paradigm of minimal propositional change to be found in AGM theory. In this paper, we deal with the revision of epistemic states by conditional beliefs, thus extending the usual framework of only taking propositional or factual beliefs as new information. We present a thorough formalization of the principle of conditional preservation under revision for ordinal conditional functions, commonly regarded as appropriate representations of epistemic states. Though apparently quite simple and elementary, this formal principle will be shown to imply the postulates dealing with conditional preservation stated in other papers.

In this paper, we present a revision strategy of revising a conditional probabilistic logic program (PLP) when new information is received (which is in the form of probabilistic formulae), through the technique of variable forgetting. We first extend the traditional forgetting method to forget a conditional event in PLPs. We then propose two revision operators to revise a PLP based on our forgetting method. By revision through forgetting, the irrelevant knowledge in the original PLP is retained according to the minimal change principle. We prove that our revision operators satisfy most of the postulates for probabilistic belief revision. A main advantage of our revision operators is that a new PLP is explicitly obtained after revision, since our revision operator performs forgetting a conditional event at the syntax level.

We present a framework for incorporating perception-induced beliefs into the knowledge base of a rational agent. Normally, the agent accepts the propositional content of perception and other propositions that follow from it. Given the fallibility of perception, this may result in contradictory beliefs. Hence, we model high-level perception as belief revision. Adopting a classical AGM-style belief revision operator is problematic, since it implies that, as a result of perception, the agent will come to believe everything that follows from its new set of beliefs. We overcome this difficulty in two ways. First, we adopt a belief revision operator based on relevance logic, thus limiting the derived beliefs to those that relevantly follow from the new percept. Second, we focus belief revision on only a subset of the agent's set of beliefs--those that we take to be within the agent's current focus of attention.

The situation of belief change in numerical uncertainty frameworks differs from the situation in classical logic in two respects: on the one hand, uncertainty theories are tailored to representing epistemic states involving shades of belief and are more expressive than classical logic in that respect. Indeed, considering a propositional belief set (a set of accepted beliefs) from the standpoint of uncertainty, a proposition is only surely true (it belongs to the belief set), surely false (its negation belongs to the belief set) or unknown (neither the proposition nor its negation belong to the belief set). Uncertainty theories express the extent to which an ultimately true or false proposition is believed. On the other hand, many logical-oriented belief revision theories are syntax-dependent (e.g., [Nebel, 1992], and in this book)—although they are semantically meaningful—while uncertainty theories adopt a semantic representation of epistemic states. In syntax-dependent theories of revision two logically equivalent, syntactically distinct, belief bases are generally not revised in the same way. The syntactic dimension of logical approaches introduces a level of increased complexity and expressiveness that cannot be grasped in the usual uncertainty theories. So, uncertainty theories are altogether more refined and less expressive than logical syntax-dependent approaches for the purpose of belief change.

Fiscal Targets. A Guide to Forecasters?