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The Topology of Belief, Belief Revision and Defeasible Knowledge [chapter]

Alexandru Baltag, Nick Bezhanishvili, Aybüke Özgün, Sonja Smets
2013 Lecture Notes in Computer Science  
We show that our topological notions fit well with the defeasibility analysis of knowledge: topological knowledge coincides with undefeated true belief.  ...  We also give a topological semantics for conditional belief and show its connection to the operation of updating with "hard information" (modeled by restricting the topology to a subspace).  ...  of knowledge) and the defeasibility analysis.  ... 
doi:10.1007/978-3-642-40948-6_3 fatcat:fhjlhz4uxzgrvhla5awifd57ce

On a plausible concept-wise multipreference semantics and its relations with self-organising maps [article]

Laura Giordano, Valentina Gliozzi, Daniele Theseider Dupré
2020 arXiv   pre-print
Inthispaperwedescribeaconcept-wisemulti-preferencesemantics for description logic which has its root in the preferential approach for modeling defeasible reasoning in knowledge representation.  ...  We argue that this proposal, beside satisfying some desired properties, such as KLM postulates, and avoiding the drowning problem, also defines a plausible notion of semantics.  ...  The knowledge base K (the set of all the strict and defeasible inclusions satisfied in M som , can then be regarded as the knowledge base obtained from K 0 through a sequence of revision steps, i.e., K  ... 
arXiv:2008.13278v1 fatcat:ppvnpbtmjfa7rp3d6z4y7sjpvy

Forthcoming Papers

2002 Artificial Intelligence  
We identify the computational complexity of conditional independence and of all these related independence relations.  2002 Published by Elsevier Science B.V.  ...  Independence-the study of what is relevant to a given problem of reasoning-is an important AI topic.  ...  Simari, Explanations, belief revision and defeasible reasoning We present different constructions for non-prioritized belief revision, that is, belief changes in which the input sentences are not always  ... 
doi:10.1016/s0004-3702(02)00313-2 fatcat:hemfnxilxrdorbzhnfbf7ary5a

Reasoning about Perception

Daniela Musto, Kurt Konolige
1993 AI Communications  
The process of formation of beliefs involves a form of inference that is defeasible. We represent this kind of inference by means of well-known techniques of non-monotonic reasoning.  ...  We outlines the basics of a formal theory of belief that is sensitive to the way in which beliefs are formed through perception.  ...  Acknowledgments We would like to thank David Israel, Leonard Wesley, Alessandro Saffiotti, Alvaro del Val and Moshe Tannenholtz for providing useful discussions.  ... 
doi:10.3233/aic-1993-63-404 fatcat:is5qxsulinfrjklph4jqt26ym4

Page 6739 of Mathematical Reviews Vol. , Issue 98K [page]

1998 Mathematical Reviews  
Summary: “In this paper we compare the logical, the game- theoretical and the topological approach to knowledge and com- mon knowledge. Aumann’s theorem [R. J. Aumann, Ann.  ...  In the present paper, the discussion of a result by C. B. Cross [in Knowledge representation and defeasible reasoning (Rochester, NY, 1988), 223-244, Kluwer Acad.  ... 

A Topological Approach to Full Belief

Alexandru Baltag, Nick Bezhanishvili, Aybüke Özgün, Sonja Smets
2018 Journal of Philosophical Logic  
This semantics extends the standard topological interpretation of knowledge (as the interior operator) with a new topological semantics for belief.  ...  In this paper, we provide a topological semantics for belief, in particular, for Stalnaker's notion of belief defined as 'epistemic possibility of knowledge', in terms of the closure of the interior operator  ...  of static belief revision.  ... 
doi:10.1007/s10992-018-9463-4 pmid:30956353 pmcid:PMC6423016 fatcat:se5zhba22ja7fg7z4wga7swlae

Logic and Topology for Knowledge, Knowability, and Belief - Extended Abstract

Adam Bjorndahl, Aybüke Özgün
2017 Electronic Proceedings in Theoretical Computer Science  
Our analysis leads to a trimodal logic of knowledge, knowability, and belief interpreted in topological subset spaces in which belief is definable in terms of knowledge and knowability.  ...  More precisely, we argue that the plausibility of the principles Stalnaker proposes relating knowledge and belief relies on a subtle equivocation between an "evidence-in-hand" conception of knowledge and  ...  Acknowledgements We thank Alexandru Baltag for feedback and discussions on the topic of this paper. We also thank the anonymous reviewers of TARK 2017 for their valuable comments.  ... 
doi:10.4204/eptcs.251.7 fatcat:2hjpv5gwfvexnpramwhuu7cfxe

Three Scenarios for the Revision of Epistemic States

D. Dubois
2008 Journal of Logic and Computation  
We argue that this view of iterated revision is at odds with the claim, made by Gärdenfors and Makinson, that belief revision and non-monotonic reasoning are two sides of the same coin.  ...  In this case, iteration makes sense, and it corresponds to the revision of a conditional knowledge base describing background information by the addition of new default rules.  ...  is like revising a Bayes net (changing the probability tables and/or the topology of the graph).  ... 
doi:10.1093/logcom/exm092 fatcat:6hs23ipoq5aolgdzn642tesaea

Page 1186 of Mathematical Reviews Vol. , Issue 90B [page]

1990 Mathematical Reviews  
syntax for first order inference (pp. 289-300); Bernhard Nebel, A knowledge level analysis of belief revision (pp. 301-311).  ...  Foo, Formal theories of belief revision (pp. 369-380); Manny Rayner, Did Newton solve the “extended predic- tion problem”? (pp. 381-385); Stanley J.  ... 

An Awareness Epistemic Framework for Belief, Argumentation and Their Dynamics

Alfredo Burrieza, Antonio Yuste-Ginel
2021 Electronic Proceedings in Theoretical Computer Science  
The notion of argumentation and the one of belief stand in a problematic relation to one another.  ...  On the one hand, argumentation is crucial for belief formation: as the outcome of a process of arguing, an agent might come to (justifiably) believe that something is the case.  ...  As for [36] , their choice of modelling arguments semantically (as opens of a topology), permits a transparent axiomatisation of their notion of argument-based beliefs, which is easily guaranteed to be  ... 
doi:10.4204/eptcs.335.6 fatcat:zerugoziyzcqvhm2hdc4ph3r4u

Generalizations of Rough Sets: From Crisp to Fuzzy Cases [chapter]

Masahiro Inuiguchi
2004 Lecture Notes in Computer Science  
Approximation Spaces and Information Granulation p. 116 Granular Language and Its Applications in Problem Solving p. 127 Belief Reasoning, Revision and Fusion by Matrix Algebra p. 133 Rough and  ...  and Belief Revision p. 95 A Note on Ziarko's Variable Precision Rough Set Model and Nonmonotonic Reasoning p. 103 Fuzzy Reasoning Based on Propositional Modal Logic p. 109 Granular Computing  ... 
doi:10.1007/978-3-540-25929-9_3 fatcat:saiacsrpovgphlh5zzhoq4tcrq

Page 1839 of Mathematical Reviews Vol. , Issue 98C [page]

1998 Mathematical Reviews  
Shankar, Bayesian approximation and invariance of Bayesian belief func- tions (251-258). J. Kohlas, P. A. Monney, R. Haenni and N.  ...  1839 vanni Guida and Silvano Mussi, Modeling uncertain relational knowledge: the AV-quantified production rules approach (18-27); Mario R. F.  ... 

Logic and Topology for Knowledge, Knowability, and Belief [article]

Adam Bjorndahl, Aybüke Özgün
2017 arXiv   pre-print
Our analysis leads to a trimodal logic of knowledge, knowability, and belief interpreted in topological subset spaces in which belief is definable in terms of knowledge and knowability.  ...  More precisely, we argue that the plausibility of the principles Stalnaker proposes relating knowledge and belief relies on a subtle equivocation between an "evidence-in-hand" conception of knowledge and  ...  (They also consider a weaker, defeasible type of knowledge, correctly justified belief, and obtain topological semantics for it under which Stalnaker's original system Stal is sound and complete.)  ... 
arXiv:1612.02055v2 fatcat:zb65p3bqijenfm24iv4ulwylje

Page 5720 of Mathematical Reviews Vol. , Issue 2003h [page]

2003 Mathematical Reviews  
In the model theory of belief revision, belief contraction and nonmonotonic inference alike, a cluster of difficult problems arise around the question of injectivity.  ...  A special epistemic ingredient is also enclosed in the proposed semantic analysis, viz. belief complexes (consisting of agents’ belief sets, along with their corresponding knowledge sets), with the aim  ... 

A conditional, a fuzzy and a probabilistic interpretation of self-organising maps [article]

Laura Giordano, Valentina Gliozzi, Daniele Theseider Dupré
2021 arXiv   pre-print
Properties of the network can be proven by model checking on the fuzzy or on the preferential interpretation.  ...  on a concept-wise multipreference semantics, which takes into account preferences with respect to different concepts and has been recently proposed for ranked and for weighted defeasible description logics  ...  Acknowledgement: We thank the anonymous referees for their helpful comments and suggestions that helped to improve the paper. This research has been partially supported by INDAM-GNCS Project 2020.  ... 
arXiv:2103.06854v2 fatcat:df5kf433xbbajbc7n7ndrerj6m
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