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Foundational Belief Change
 Journal of Philosophical Logic
, 1992
"... : This paper is concerned with the construction of a base contraction (revision) operation such that the theory contraction (revision) operation generated by it will be fully AGMrational. It is shown that the theory contraction operation generated by Fuhrmann's minimal base contraction operati ..."
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Cited by 21 (3 self)
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: This paper is concerned with the construction of a base contraction (revision) operation such that the theory contraction (revision) operation generated by it will be fully AGMrational. It is shown that the theory contraction operation generated by Fuhrmann's minimal base contraction operation, even under quite strong restrictions, fails to satisfy the "supplementary postulates" of belief contraction. Finally Fuhrmann's construction is appropriately modified so as to yield the desired properties. The new construction may be described as involving a modification of safe (base) contraction so as to make it maxichoice. Descriptors: belief, change, contraction, revision, base, theory. We often change our beliefs. We learn new things, occasionally things that conflict with our current beliefs. On such occasions new beliefs replace the old ones. It is as if this process is completed in two steps: (1) first we identify and throw out the beliefs that conflict with the new information and t...
A ConsistencyBased Approach for Belief Change
, 2003
"... This paper presents a general, consistencybased framework for expressing belief change. ..."
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Cited by 16 (7 self)
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This paper presents a general, consistencybased framework for expressing belief change.
Ten philosophical problems in belief revision
 Journal of Logic and Computation
, 2003
"... The paper introduces ten open problems in belief revision theory, related to the representation of the belief state, to different notions of degrees of belief, and to the nature of change operations. It is argued that these problems are all issues in philosopical logic, in the strong sense of requir ..."
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Cited by 13 (0 self)
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The paper introduces ten open problems in belief revision theory, related to the representation of the belief state, to different notions of degrees of belief, and to the nature of change operations. It is argued that these problems are all issues in philosopical logic, in the strong sense of requiring inputs from both logic and philosophy for their solution. 1
Infinitary belief revision
 Journal of Philosophical Logic
, 2001
"... Abstract This paper aims to extend the AGM theory of belief revision to accommodate infinitary belief change. We generalize the AGM theory both in axiomatization and modeling. We show that most properties of the AGM belief change operations are preserved by the generalized operations whereas the inf ..."
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Cited by 10 (5 self)
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Abstract This paper aims to extend the AGM theory of belief revision to accommodate infinitary belief change. We generalize the AGM theory both in axiomatization and modeling. We show that most properties of the AGM belief change operations are preserved by the generalized operations whereas the infinitary belief change operations have their special properties. We prove that the extended axiomatic system for the generalized belief change operators with a Limit Postulate properly specifies infinite belief change. This framework forms a base for firstorder belief revision and the theory of revising a belief state by a belief state.
Diamonds are a Philosopher's Best Friends. The Knowability Paradox and Modal Epistemic Relevance Logic (Extended Abstract)
 Journal of Philosophical Logic
, 2002
"... Heinrich Wansing Dresden University of Technology The knowability paradox is an instance of a remarkable reasoning pattern (actually, a pair of such patterns), in the course of which an occurrence of the possibility operator, the diamond, disappears. In the present paper, it is pointed out how the ..."
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Cited by 6 (0 self)
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Heinrich Wansing Dresden University of Technology The knowability paradox is an instance of a remarkable reasoning pattern (actually, a pair of such patterns), in the course of which an occurrence of the possibility operator, the diamond, disappears. In the present paper, it is pointed out how the unwanted disappearance of the diamond may be escaped. The emphasis is not laid on a discussion of the contentious premise of the knowability paradox, namely that all truths are possibly known, but on how from this assumption the conclusion is derived that all truths are, in fact, known. Nevertheless, the solution o#ered is in the spirit of the constructivist attitude usually maintained by defenders of the antirealist premise. In order to avoid the paradoxical reasoning, a paraconsistent constructive relevant modal epistemic logic with strong negation is defined semantically. The system is axiomatized and shown to be complete.
COBA 2.0: A ConsistencyBased Belief Change System
"... We describe COBA 2.0, an implementation of a consistencybased framework for expressing belief change, focusing here on revision and contraction, with the possible incorporation of integrity constraints. This general framework was first proposed in [1]; following a review of this work, we present ..."
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Cited by 3 (1 self)
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We describe COBA 2.0, an implementation of a consistencybased framework for expressing belief change, focusing here on revision and contraction, with the possible incorporation of integrity constraints. This general framework was first proposed in [1]; following a review of this work, we present COBA 2.0’s highlevel algorithm, work through several examples, and describe our experiments. A distinguishing feature of COBA 2.0 is that it builds on SATtechnology by using a module comprising a stateoftheart SATsolver for consistency checking. As well, it allows for the simultaneous specification of revision, multiple contractions, along with integrity constraints, with respect to a given knowledge base.
A ConsistencyBased System for . . .
, 2006
"... The ability to change one’s beliefs consistently is essential for sound reasoning in a world where the new information one acquires may invalidate or augment one’s current beliefs. Belief revision is the process wherein an agent modifies its beliefs to incorporate the new information received, and k ..."
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The ability to change one’s beliefs consistently is essential for sound reasoning in a world where the new information one acquires may invalidate or augment one’s current beliefs. Belief revision is the process wherein an agent modifies its beliefs to incorporate the new information received, and knowledge base merging the process wherein the agent is given two or more knowledge bases to merge. We present a binary decision diagram (BDD) based implementation of Delgrande and Schaub’s consistencybased belief change framework. Our system focuses on knowledge base merging with the possible incorporation of integrity constraints, using a BDD solver for consistency checking. We show that the result of merging finite knowledge bases can be represented as a finite formula, and that merging can be streamlined algorithmically by restricting attention to a subset of the vocabulary of the propositional formulas involved. Experimental results and comparisons with related systems are also given.
Sten Lindström A SEMANTIC APPROACH TO NONMONOTONIC REASONING: INFERENCE OPERATIONS AND CHOICE *
"... This paper presents a uniform semantic treatment of nonmonotonic inference operations that allow for inferences from infinite sets of premisses. The semantics is formulated in terms of selection functions and is a generalization of the preferential semantics of Shoham (1987), (1988), Kraus, Lehman, ..."
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This paper presents a uniform semantic treatment of nonmonotonic inference operations that allow for inferences from infinite sets of premisses. The semantics is formulated in terms of selection functions and is a generalization of the preferential semantics of Shoham (1987), (1988), Kraus, Lehman, and Magidor (1990) and Makinson (1989), (1993). A selection function picks out from a given set of possible states (worlds, situations, models) a subset consisting of those states that are, in some sense, the most preferred ones. A proposition α is a nonmonotonic consequence of a set of propositions Γ iff α holds in all the most preferred Γstates. In the literature on revealed preference theory, there are a number of wellknown theorems concerning the representability of selection functions, satisfying certain properties, in terms of underlying preference relations. Such theorems are utilized here to give corresponding representation theorems for nonmonotonic inference operations. At the end of the paper, the connection between nonmonotonic inference and belief revision, in the sense of Alchourrón, Gärdenfors, and Makinson, is explored. In this connection, infinitary belief revision operations, that allow for the revision of a theory with a possibly infinite set of propositions, are introduced and characterized axiomatically. Several semantic representation theorems are proved for operations of this kind. 1.
Belief Change: Partial Epistemic Priorities and Logical NonOmniscience
, 1992
"... In many database applications, designers can easily provide at least some information about the relative importance of the information to be stored and manipulated. While of potentially high value, the ordering information is typically only partial. Here we address the issue of updates in such parti ..."
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In many database applications, designers can easily provide at least some information about the relative importance of the information to be stored and manipulated. While of potentially high value, the ordering information is typically only partial. Here we address the issue of updates in such partially ordered situations, which we call epistemically stratified databases. In the current database theory literature, Alchourr'on, Gardenfors and Makinson (AGM) have proposed a collection of rationality postulates that define rational updates to deductively closed databases. We reformulate the AGM framework to accomodate empistemically stratified databases, and to relax the closure requirement. Our immediate goal is to exploit the use of partial ordering information and to relax the logical omniscient flavour of the closure condition. A more ambitious goal is only hinted at; it is motivated by a desire to develop a more general theory of updates that integrates the naturally related ideas i...