NEXP-completeness and Universal Hardness Results for Justification Logic

We provide a lower complexity bound for the satisfiability problem of a multi-agent justification logic, establishing that the general NEXP upper bound from our previous work is tight. We then use a simple modification of the corresponding reduction to prove that satisfiability for all multi-agent justification logics from there is hard for the Sigma 2 p class of the second level of the polynomial hierarchy - given certain reasonable conditions. Our methods improve on these required conditions for the same lower bound for the single-agent justification logics, proven by Buss and Kuznets in 2009, thus answering one of their open questions.Comment: Shorter version has been accepted for publication by CSR 201

The Complexity of Non-Iterated Probabilistic Justification Logic

The logic PJ is a probabilistic logic defined by adding (noniterated) 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 complexity of the derivability problem in PJ remains the same as the complexity of the derivability problem in the underlying logic J, which is π[p/2] -complete. This implies that the probability operators do not increase the complexity of the logic, although they arguably enrich the expressiveness of the language

The NP-Completeness of Reflected Fragments of Justification Logics

Abstract. 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. 1 Introduction and Main Definitions Justification Logic is an emerging field that studies provability, knowledge, and belief via explicit proofs or justifications that are part of the language. A justificatio

A Complexity Question in Justification Logic

Bounds for the computational complexity of major justification logics were found in papers by Buss, N. Krupski, Kuznets, and Milnikel: logicsJ,J4, JT,LPandJD,wereestablishedtobeΣ p 2-complete. A corresponding lower bound is also known for JD4, the system that includes the consistency axiom and positive introspection. However, no upper bound has been established so far for this logic. Here, the missing upper bound for the complexity of JD4 is established through an alternating algorithm. It is shown that using Fitting models of only two worlds is adequate to describe JD4; this helps to produce an effective tableau procedure and essentially is what distinguishes the new algorithm from existing ones.

Tracking evidence

In this case study we describe an approach to a general logical framework for tracking evidence within epistemic contexts. We consider as basic an example which features two justifications for a true statement, one which is correct and one which is not. We formalize this example in a system of Justification Logic with two knowers: the object agent and the observer, and we show that whereas the object agent does not logically distinguish between factive and non-factive justifications, such distinctions can be attained at the observer level by analyzing the structure of evidence terms. Basic logic properties of the corresponding two-agent Justification Logic system have been established, which include Kripke-Fitting completeness. We also argue that a similar evidence-tracking approach can be applied to analyzing paraconsistent systems.