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Possibilistic conditioning framed in fuzzy logics

Possibilistic conditioning framed in fuzzy logics
Possibilistic conditioning framed in fuzzy logics
The notion of conditional possibility derived from marginal possibility measures has received different treatments. As shown by Bouchon-Meunier et al., conditional possibility can be introduced as a primitive notion generalizing simple possibility measures. In this paper, following an approach already adopted by the author w.r.t. conditional probability, we build up the fuzzy modal logic FC??, relying on Rational Pavelka Logic RPL, so as to reason about coherent conditional possibilities and necessities. First, we apply a modal operator {white diamond suit} over conditional events ??{symbol}{divides}?? to obtain modal formulas of the type (??{symbol}{divides}??){white diamond suit} whose reading is "??{symbol}{divides}?? is possible". Then, we define the truth-value of the modal formulas as corresponding to a conditional possibility measure. The logic FC?? is shown to be strongly complete for finite theories w.r.t. to the class of the introduced conditional possibility Kripke structures. Then, we show that any rational assessment of conditional possibilities is coherent iff a suitably defined theory over FC?? is consistent. We also prove compactness for rational coherent assessments of conditional possibilities. We derive the notion of generalized conditional necessity from the notion of generalized conditional possibility, and we show and discuss how to represent those concepts introducing some logics generalizing FC??. Finally we show how to frame qualitative comparative relations in this logical framework. ?? 2006 Elsevier Inc. All rights reserved.
Coherence, Compactness, Comparative conditional possibility, Conditional possibility, Fuzzy logics, Possibility theory
0888-613X
133-165
Marchioni, Enrico
729c9984-5949-438e-8de7-0e079bdb9f96
Marchioni, Enrico
729c9984-5949-438e-8de7-0e079bdb9f96

Marchioni, Enrico (2006) Possibilistic conditioning framed in fuzzy logics. International Journal of Approximate Reasoning, 43 (2), 133-165. (doi:10.1016/j.ijar.2006.03.002).

Record type: Article

Abstract

The notion of conditional possibility derived from marginal possibility measures has received different treatments. As shown by Bouchon-Meunier et al., conditional possibility can be introduced as a primitive notion generalizing simple possibility measures. In this paper, following an approach already adopted by the author w.r.t. conditional probability, we build up the fuzzy modal logic FC??, relying on Rational Pavelka Logic RPL, so as to reason about coherent conditional possibilities and necessities. First, we apply a modal operator {white diamond suit} over conditional events ??{symbol}{divides}?? to obtain modal formulas of the type (??{symbol}{divides}??){white diamond suit} whose reading is "??{symbol}{divides}?? is possible". Then, we define the truth-value of the modal formulas as corresponding to a conditional possibility measure. The logic FC?? is shown to be strongly complete for finite theories w.r.t. to the class of the introduced conditional possibility Kripke structures. Then, we show that any rational assessment of conditional possibilities is coherent iff a suitably defined theory over FC?? is consistent. We also prove compactness for rational coherent assessments of conditional possibilities. We derive the notion of generalized conditional necessity from the notion of generalized conditional possibility, and we show and discuss how to represent those concepts introducing some logics generalizing FC??. Finally we show how to frame qualitative comparative relations in this logical framework. ?? 2006 Elsevier Inc. All rights reserved.

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More information

Accepted/In Press date: 30 March 2006
e-pub ahead of print date: 25 April 2006
Published date: October 2006
Keywords: Coherence, Compactness, Comparative conditional possibility, Conditional possibility, Fuzzy logics, Possibility theory

Identifiers

Local EPrints ID: 417391
URI: http://eprints.soton.ac.uk/id/eprint/417391
ISSN: 0888-613X
PURE UUID: b1d0245c-21eb-4c09-9c04-4065b10ded59

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Date deposited: 30 Jan 2018 17:31
Last modified: 13 Mar 2019 19:04

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