JuDAS: a theory of rational belief revision
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JuDAS: a theory of rational belief revision Gordian Haas1 Received: 13 May 2018 / Accepted: 20 September 2018 © Springer Nature B.V. 2018
Abstract Although the AGM theory established a paradigm for the theory of belief revision, which is generally regarded as a kind of standard in the field, it is also frequently criticized as inadequate because it neglects justificational structures. Other theories of belief revision are similarly remiss in this regard. So far, little has been done to address this shortcoming. This paper aims to fill this gap. Following a critical analysis of the AGM theory, a justification operator is introduced as a formal means to incorporate justificational structures into a belief revision theory. An AGM style belief revision theory is proposed that is based on such a justification operator. The theory is presented in an axiomatic form. Representation theorems link the axioms with constructive belief change mechanisms. The proposed theory addresses the problems of the AGM theory and similar approaches that neglect justificational structures. Keywords Epistemic justification · Belief revision · AGM · Theory change · Justificational structures · Reason
1 Introduction In their groundbreaking paper On the Logic of Theory Change: Partial Meet Contraction and Revision Functions, Carlos Alchourrón, Peter Gärdenfors, and David Makinson (henceforth: AGM) establish a paradigm for the theory of belief revision, which is generally regarded as a kind of standard in the field.1 The AGM theory is, however, often criticized as being inadequate because it neglects justificational structures. Other theories of belief revision are similarly remiss in this regard. So far, little has been done to address this shortcoming. This paper therefore aims to fill this gap. Section 2 provides a brief overview of the AGM theory, while Sect. 3 points to some arguments in favor of taking justificational structures into account to arrive at 1 I would like to thank two anonymous reviewers for their valuable comments on an earlier drafts of this paper. Cf. Alchourrón et al. (1985) and Gärdenfors (1988).
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Gordian Haas [email protected] Institut für Philosophie, Universität Bayreuth, 95440 Bayreuth, Germany
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an adequate belief revision theory. In Sect. 4, a justification operator is introduced as a formal means to incorporate justificational structures into belief revision theory. Sections 5 and 6, propose AGM style belief expansion and revision procedures that are based on such a justification operator. In Sect. 7, I demonstrate that this theory—which I call the JuDAS theory—avoids the problems associated with the AGM theory and similar approaches that neglect justificational structures.
2 AGM: the standard theory of belief revision AGM model the epistemic state of a subject as a set of sentences A, the intended interpretation of course being that the set consists of precisely those sentences accepted by the epistemic subject. As rationality constraints AGM require a set of sentences to be dedu
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