Roman Kuznets

Logical omniscience via proof complexity

The Hintikka-style modal logic approach to knowledge contains a well-known defect of logical omniscience, i.e., the unrealistic feature that an agent knows all logical consequences of her assumptions. In this paper, we suggest the following Logical Omniscience Test (LOT): an epistemic system E is not logically omniscient if for any valid in E knowledge assertion

Logical omniscience as a computational complexity problem

\mathcal{A}

Partial realization in dynamic justification logic

of type ‘Fis known,’ there is a proof of F in E, the complexity of which is bounded by some polynomial in the length of

Update as Evidence: Belief Expansion

\mathcal{A}

Realizing public announcements by justifications

. We show that the usual epistemic modal logics are logically omniscient (modulo some common complexity assumptions). We also apply LOT to evidence-based knowledge systems, which, along with the usual knowledge operator Ki(F) (‘agent iknows F’), contain evidence assertions t:F (‘t is a justification for F’). In evidence-based systems, the evidence part is an appropriate extension of the Logic of Proofs LP, which guarantees that the collection of evidence terms t is rich enough to match modal logic. We show that evidence-based knowledge systems are logically omniscient w.r.t. the usual knowledge and are not logically omniscient w.r.t. evidence-based knowledge.

The NP-Completeness of Reflected Fragments of Justification Logics

The logical omniscience feature assumes that an epistemic agent knows all logical consequences of her assumptions. This paper offers a general theoretical framework that views logical omniscience as a computational complexity problem. We suggest the following approach: we assume that the knowledge of an agent is represented by an epistemic logical system E; we call such an agent not logically omniscient if for any valid knowledge assertion A of type F is known, a proof of F in E can be found in polynomial time in the size of A. We show that agents represented by major modal logics of knowledge and belief are logically omniscient, whereas agents represented by justification logic systems are not logically omniscient with respect to t is a justification for F.

Logical omniscience as infeasibility

Justification logic is an epistemic framework that provides a way to express explicit justifications for the agents belief. In this paper, we present OPAL, a dynamic justification logic that includes term operators to reflect public announcements on the level of justifications. We create dynamic epistemic semantics for OPAL. We also elaborate on the relationship of dynamic justification logics to Gerbrandy-Groenevelds PAL by providing a partial realization theorem.

Two Ways to Common Knowledge

We introduce a justification logic with a novel constructor for evidence terms, according to which the new information itself serves as evidence for believing it. We provide a sound and complete axiomatization for belief expansion and minimal change and explain how the minimality can be graded according to the strength of reasoning. We also provide an evidential analog of the Ramsey axiom.

Modal interpolation via nested sequents

Abstract Modal public announcement logics study how beliefs change after public announcements. However, these logics cannot express the reason for a new belief. Justification logics fill this gap since they can formally represent evidence and justifications for an agents belief. We present OPAL ( K ) and JPAL ( K ) , two alternative justification counterparts of Gerbrandy–Groenevelds public announcement logic PAL ( K ) . We show that PAL ( K ) is the forgetful projection of both OPAL ( K ) and JPAL ( K ) . We also establish that JPAL ( K ) partially realizes PAL ( K ) . The question whether a similar result holds for OPAL ( K ) is still open.

Grafting hypersequents onto nested sequents

Justification Logic studies epistemic and provability phenomena by introducing justifications/proofs into the language in the form of justification terms. Pure justification logics serve as counterparts of traditional modal epistemic logics, and hybrid logics combine epistemic modalities with justification terms. The computational complexity of pure justification logics is typically lower than that of the corresponding modal logics. Moreover, the so-called reflected fragments, which still contain complete information about the respective justification logics, are known to be in NP for a wide range of justification logics, pure and hybrid alike. This paper shows that, under reasonable additional restrictions, these reflected fragments are NP-complete, thereby proving a matching lower bound.