The Complexity of Non-Iterated Probabilistic Justification Logic

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9616)


The logic \(\mathsf {PJ}\) is a probabilistic logic defined by adding (non-iterated) probability operators to the basic justification logic \(\mathsf {J}\). In this paper we establish upper and lower bounds for the complexity of the derivability problem in the logic \(\mathsf {PJ}\). The main result of the paper is that the complexity of the derivability problem in \(\mathsf {PJ}\) remains the same as the complexity of the derivability problem in the underlying logic \(\mathsf {J}\), which is \(\varPi _2^p\)-complete. This implies hat the probability operators do not increase the complexity of the logic, although they arguably enrich the expressiveness of the language.


Justification logic Probabilistic logic Complexity Derivability Satisfiability 


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© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Institute of Computer ScienceUniversity of BernBernSwitzerland

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