The Complexity of Non-Iterated Probabilistic Justification Logic

TL;DR

This paper investigates the computational complexity of the probabilistic logic PJ, showing that adding probability operators does not increase the complexity beyond that of the base logic J, which is {a}p2-complete.

Contribution

It establishes that the derivability problem in PJ has the same complexity as in the underlying logic J, providing bounds and showing no increase in complexity.

Findings

The derivability problem in PJ is {a}p2-complete.

Probability operators do not increase the complexity of the logic.

The paper provides upper and lower bounds for the complexity of PJ.

Abstract

The logic PJ is a probabilistic logic defined by adding (non-iterated) probability operators to the basic justification logic J. In this paper we establish upper and lower bounds for the complexity of the derivability problem in the logic PJ. The main result of the paper is that the complex- ity of the derivability problem in PJ remains the same as the complexity of the derivability problem in the underlying logic J, which is {\Pi}p2-complete. This implies hat the probability operators do not increase the complex- ity of the logic, although they arguably enrich the expressiveness of the language.