Belief Revision in Non-Classical Logics

Ribeiro, Márcio Moretto

doi:10.1007/978-1-4471-4186-0

Cited by 16 publications

(18 citation statements)

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“…Inductive reasoning is a powerful tool to cope with noise, but there are other solutions to explore in the next years. Looking at deductive reasoning techniques, inconsistency repair [7,88] and belief revision [109,111] offer solid foundations to build framework to identify noise and to decide the proper actions to be taken. The challenge for researchers is to find algorithms able to use them in the context of stream processing.…”

Section: Coping With Noisementioning

confidence: 99%

Stream reasoning: A survey and outlook

et al. 2017

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Stream reasoning studies the application of inference techniques to data characterised by being highly dynamic. It can find application in several settings, from Smart Cities to Industry 4.0, from Internet of Things to Social Media analytics. This year stream reasoning turns ten, and in this article we analyse its growth. In the first part, we trace the main results obtained so far, by presenting the most prominent studies. We start by an overview of the most relevant studies developed in the context of semantic web, and then we extend the analysis to include contributions from adjacent areas, such as database and artificial intelligence. Looking at the past is useful to prepare for the future: in the second part, we present a set of open challenges and issues that stream reasoning will face in the next future.

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Section: Coping With Noisementioning

confidence: 99%

Stream reasoning: A survey and outlook

et al. 2017

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“…In this paper, we focus on the most interesting one: belief revision. There is an extensive literature on the theory of belief revision . Actually, it was started with the work of Alchourrón et al .…”

Section: Introductionmentioning

confidence: 99%

A Fuzzy Dynamic Belief Logic System

Jing

Luo

Zhang

2014

Int. J. Intell. Syst.

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In this paper, we develop a fuzzy dynamic belief revision logic system. In our system, propositions take truth values in a set of multiple fuzzy linguistic terms, which people use in everyday life. And we use a uninorm operator to aggregate the linguistic truth values of the same proposition but drawn from two different rules because uninorms can reflect well that the aggregated result of two somehow negative truth values of the same proposition should be more negative, the aggregated result of two somehow positive ones should be more positive, and the result of a negative one and a positive one is a compromise. In this system, the belief on a proposition is the linguistic truth of the proposition in the most possible world according to the current preference over all possible worlds. In the light of new information, the preference degrees of possible worlds will be updated. Accordingly, the most possible world will be changed to another and thus an old belief on a propositional formula will be changed to the linguistic truth of the proposition in the new most possible world. Moreover, we prove the soundness and completeness of our fuzzy dynamic belief revision system. In addition, we also prove that our belief revision method in fuzzy environment satisfies some relevant ones of standard AGM postulates (named after the names of their proponents, Alchourrón, Gärdenfors, and Makinson).

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“…Logic and some classes of Description Logics. To workaround this limitation, Ribeiro (2013) has devised an alternative theory of belief change for logics that do not cope with AGM postulates, precisely classes of Description Logics that are not closed under classical negation.…”

Section: Belief Change In Formal Methodsmentioning

confidence: 99%

“…The AGM theory dictates what revisions and contraction functions must satisfy and was originally proposed for logics which satisfy the AGM assumptions -we discussed the AGM assumptions in Section 2.2. However, as shown in (Ribeiro, 2013), in some interesting logics, such as Description…”

Section: Agm Compliancementioning

confidence: 99%

“…There are two main reasons for the hurdle: whereas in some logics, the standard belief change operators do not satisfy the rationality postulates, in other logics it is not even possible to dene belief change operators that behave accordingly to the rationality postulates. The latter is the case of logics such as Horn Logic, Intuitionist Logics and classes of Descriptions Logics (Ribeiro, 2013).…”

Section: Introductionmentioning

confidence: 99%

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Belief change without compactness

Ribeiro¹

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One of the main goals of Articial Intelligence (AI) is to build rational agents that are capable of taking rational decisions autonomously. For this, it is essential to devise mechanisms to properly represent knowledge, and reason about the knowledge that an agent has about the world. However, an agent's knowledge is not static-it gets updated as the agent acquires new information. One of the big challenges involving knowledge representation is how an agent ought to change its own knowledge and beliefs in response to any new information it acquires. This, in short, is the problem of belief change. Standard approaches of Belief Change come in two avours: a set of rationality postulates that prescribes epistemic behaviours for an agent, and a collection of constructions, or functions, to perform such rational changes. The two foremost paradigms of Belief Change are the AGM paradigm (for belief change in a static environment) and the KM paradigm (for belief change in a dynamic environment). Both these paradigms make strong assumptions about the underlying logic used to express an agent beliefs, such as Supraclassicality and Compactness. Relying on these assumptions, however, is rather restrictive, since many logics that are important for both AI and Computer Science applications do not have them. This thesis focuses on extending Belief Change to the realm of non-compact logics. One of the side eects of dispensing with compactness is that standard constructions of both the AGM and the KM paradigms no longer nicely connect with the respective rationality postulates. In this work, I identify the reasons behind this breakdown. This in turn helps us identify some minimal conditions under which the existence of rational AGM and KM belief change operations is guaranteed. Subsequently we provide constructive accounts of AGM-and KM-rational belief change operations without the compactness assumption, and we oer full accounts of belief change for both the paradigms. The main dierence of our approach from the standard ones relies on the way epistemic preference of an agent is represented: instead of remainders and Grove's Systems of Spheres, we consider maximal complete theories and genuine partial relations over worlds. Furthermore, we also consider the connection between AGM revision and non-monotonic reasoning (NMR) systems, often viewed to be two sides of the same coin. We demonstrate that the bridge between belief revision and NMR breaks down in the absence of compactness. We then identify the basis of this breakdown, and present a new non-monotonic system that appropriately connects with the AGM revision postulates even in absence of compactness. Signicantly, this connection with the AGM paradigm is independent of any specic constructions (such as systems of spheres), and is directly established between the AGM postulates and the axioms of the proposed non-monotonic system.

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Belief Revision in Non-Classical Logics

Cited by 16 publications

References 0 publications

Stream reasoning: A survey and outlook

Stream reasoning: A survey and outlook

A Fuzzy Dynamic Belief Logic System

Belief change without compactness

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