The Complexity of Non-Iterated Probabilistic Justification Logic

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

Abstract

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.

Keywords

Justification logic Probabilistic logic Complexity Derivability Satisfiability 

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Institute of Computer ScienceUniversity of BernBernSwitzerland

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