Evidence elimination in multi-agent justification logic
Proceedings of the 12th Conference on Theoretical Aspects of Rationality and Knowledge
The Ontology of Justifications in the Logical Setting
Studia Logica
Distributed knowledge with justifications
ESSLLI'10 Proceedings of the 2010 international conference on New Directions in Logic, Language and Computation
Arguing with justifications between collaborating agents
ArgMAS'11 Proceedings of the 8th international conference on Argumentation in Multi-Agent Systems
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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 $\mathsf{S4}^{2}$.