Justification Logics with Probability Operators

Kokkinis, Ioannis; Savic, Nenad; Studer, Thomas (2020). Justification Logics with Probability Operators. In: Ognjanović, Zoran (ed.) Probabilistic Extensions of Various Logical Systems (pp. 215-234). Springer 10.1007/978-3-030-52954-3_8

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In this chapter we present a formal system that results from the combination of two well known formalisms for knowledge representation: probabilistic logic and justification logic. This framework, called probabilistic justification logic, allows the analysis of epistemic situations with incomplete information. We present two sound and strongly complete probabilistic justification logics, which are defined by adding probability operators to the minimal justification logic J. The first logic does not allow nesting of the probability operators and can be used to express statements like “t is a justification for A with probability at least 30%”. The second logic allows iterations of the probability operators and can be used to express statements like “I am uncertain for the fact that t is a justification for a coin being counterfeit” or to describe more complex epistemic situations like Kyburg’s Lottery Paradox. We also present tight complexity bounds for the satisfiability problem in the aforementioned logics which are obtained with the help of the theory of linear programming and by applying a tableau procedure. Finally, we present two more extensions of the logic J.

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