Abstract
Justification Logic provides a refined version of epistemic modal logic in which the proofs/justifications are taken into account. As a practical tool, Justification Logic has the ability to model argumentation and track evidence in the full logic context, to measure the complexity of the arguments, to keep the logical omniscience at bay, etc. The complexity of single-agent justification logics has been well-studied and shown to be generally lower than the complexity of their modal counterparts. In this paper we investigate the complexity of two-agent Justification Logic. We show that for most cases the upper complexity bounds established for the single-agent cases are maintained: these logics’ derivability problem is in the second step of the polynomial hierarchy. For certain logics, though, we discover a complexity jump to PSPACE-completeness, which is a new phenomenon for Justification Logic.
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