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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