LP-1994-01: Introducing Some Classical Elements of Modal Logic to the Propositional Logics of Qualitative Probabilities

LP-1994-01: Gelev, Dimitar (1994) Introducing Some Classical Elements of Modal Logic to the Propositional Logics of Qualitative Probabilities. [Report]

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Abstract

Introducing Some Classical Elements of Modal Logic to the Propositional Logics of Qualitative Probabilities Dimitar P. Gelev This paper presents the construction of canonical models for a number of logics of qualitative probabilities by introducing a conservative infinitary rule into their axiomatizations. These logics include the minimal logic of qualitative probabilities and a new multioperator propositional logic, that contains qualitative probabilistic analogons of operations essential to propositional dynamic logic. These operations capture some basic laws for stochastic processes into this new logic's semantics and are given a complete axiomatization. The paper also presents qualitative probabilistic versions of the modal logic techniques of unravelling and filtration. All the constructs and arguments in this paper are suitable to be combined with their counterparts for other propositional, e.g. modal logics, and can possibly be incorporated in proofs of completeness and decidability of logics containing both qualitative probabilistic and other propositional operators for application purposes.

Item Type: Report
Report Nr: LP-1994-01
Series Name: Logic, Philosophy and Linguistics (LP)
Year: 1994
Uncontrolled Keywords: probabilistic logic, propositional logic, modal logic techniques, dynamic logic, stochastic processes.
Subjects: Logic
Date Deposited: 12 Oct 2016 14:39
Last Modified: 12 Oct 2016 14:39
URI: https://eprints.illc.uva.nl/id/eprint/1203

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