A Probabilistic Temporal Epistemic Logic: Strong Completeness

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Logic Journal of the IGPL (forthcoming)
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Abstract

The paper offers a formalization of reasoning about distributed multi-agent systems. The presented propositional probabilistic temporal epistemic logic |$\textbf {PTEL}$| is developed in full detail: syntax, semantics, soundness and strong completeness theorems. As an example, we prove consistency of the blockchain protocol with respect to the given set of axioms expressed in the formal language of the logic. We explain how to extend |$\textbf {PTEL}$| to axiomatize the corresponding first-order logic.

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10.1093/jigpal/jzac072

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References found in this work

The completeness of the first-order functional calculus.Leon Henkin - 1949 - Journal of Symbolic Logic 14 (3):159-166.
Syntactic cut-elimination for common knowledge.Kai Brünnler & Thomas Studer - 2009 - Annals of Pure and Applied Logic 160 (1):82-95.
First order common knowledge logics.Frank Wolter - 2000 - Studia Logica 65 (2):249-271.

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