Complexity Jumps In Multiagent Justification Logic Under Interacting Justifications

The Logic of Proofs, LP, and its successor, Justification Logic, is a refinement of the modal logic approach to epistemology in which proofs/justifications are taken into account. In 2000 Kuznets showed that satisfiability for LP is in the second level of the polynomial hierarchy, a result which has been successfully repeated for all other one-agent justification logics whose complexity is known. We introduce a family of multi-agent justification logics with interactions between the agents' justifications, by extending and generalizing the two-agent versions of the Logic of Proofs introduced by Yavorskaya in 2008. Known concepts and tools from the single-agent justification setting are adjusted for this multiple agent case. We present tableau rules and some preliminary complexity results. In several cases the satisfiability problem for these logics remains in the second level of the polynomial hierarchy, while for others it is PSPACE or EXP-hard. Furthermore, this problem becomes PSPACE-hard even for certain two-agent logics, while there are EXP-hard logics of three agents

Weak Arithmetical Interpretations for the Logic of Proofs

Artemov established an arithmetical interpretation for the Logics of Proofs LPCS, which yields a classical provability semantics for the modal logic S4. These Logics of Proofs are parameterized by so-called constant specifications CS that state which axioms can be used in the reasoning process, and the arithmetical interpretation relies on the constant specifications being finite. In this paper, we remove this restriction by introducing weak arithmetical interpretations that are sound and complete for a wide class of constant specifications, including infinite ones. In particular, they interpret the full Logic of Proofs LP. Keywords: Logic of Proofs, arithmetical interpretation, BHK semantic

Decidability for some justification logics with negative introspection

Justification logics are modal logics that include justifications for the agent's knowledge. So far, there are no decidability results available for justification logics with negative introspection. In this paper, we develop a novel model construction for such logics and show that justification logics with negative introspection are decidable for finite constant specifications

TR-2014003: On the Complexity of Two-Agent Justification Logic

We investigate the complexity of derivability for two-agent Justification Logic. For this purpose we revisit Yavorskaya’s two-agent LP with interactions (2008), we simplify the syntax and provide natural extensions. We consider two-agent versions of other justification logics as well as ways to combine two justification logics. For most of these cases we prove that the upper complexity bound 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 complex-ity jump to PSPACE-completeness, which is a new phenomenon for Justification Logic

Uncertain Reasoning in Justification Logic

This thesis studies the combination of two well known formal systems for knowledge representation: probabilistic logic and justification logic. Our aim is to design a formal framework that allows the analysis of epistemic situations with incomplete information. In order to achieve this we introduce two probabilistic justification logics, which are defined by adding probability operators to the minimal justification logic J. We prove soundness and completeness theorems for our logics and establish decidability procedures. Both our logics rely on an infinitary rule so that strong completeness can be achieved. One of the most interesting mathematical results for our logics is the fact that adding only one iteration of the probability operator to the justification logic J does not increase the computational complexity of the logic