Theory of Computing Systems

, Volume 43, Issue 2, pp 272–293 | Cite as

Interacting Explicit Evidence Systems

Article

Abstract

Logic of proofs \(\mathsf{LP}\) , introduced by S. Artemov, originally designed for describing properties of formal proofs, now became a basis for the theory of knowledge with justification (cf. S. Artemov, Evidence-based common knowledge, Technical report TR–2004018, CUNY Ph.D. Program in Computer Science, 2005). So far, in epistemic systems with justification the corresponding “evidence part”, even for multi-agent systems, consisted of a single explicit evidence logic. In this paper we introduce logics describing two interacting explicit evidence systems. We find an appropriate formalization of the intended semantics and prove the completeness of these logics with respect to both symbolic and arithmetical models. Also, we find the forgetful projections for the two-agent justification logics which are extensions of the bimodal logic \(\mathsf{S4}^{2}\) .

Keywords

Justification logic Explicit evidence Logic of proofs Multi-modal logic Epistemic logic 

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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Department of Mathematical Logic and Theory of Algorithms, Faculty of Mechanics and MathematicsMoscow State UniversityMoscowRussia

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