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An Axiomatisation of the Probabilistic -Calculus

Junnan Xu,Wanwei Liu,David N. Jansen,Lijun Zhang

Formal Methods and Software Engineering: 21st International Conference on Formal Engineering Methods, ICFEM 2019, Shenzhen, China, November 5–9, 2019, Proceedings（2019）

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Abstract
The probabilistic -calculus (PTL) is a simple and succinct probabilistic extension of the propositional -calculus, by extending the ‘next’-operator with a probabilistic quantifier. We extend the approach developed by Walukiewicz for propositional -calculus and provide an axiomatisation of PTL. Our main contributions are a sound axiom system for PTL, and a proof of its completeness for aconjunctive formulae.
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