Abstract

A non-transitive distributed knowledge logic TnD, obtained from multi-modal logic Tn by adding distributed knowledge operator, is considered. Sound and complete loop-check-free sequent calculus for this logic is proposed. Termination of derivations in proposed calculus is justified.

Highlights

  • To consider properties of distributed systems logics of knowledge with distributed knowledge operator were introduced

  • If we have only one agent the distributed knowledge reduces to knowledge

  • Traditional techniques used to ensure termination of a decision procedure in nonclassical sequent calculi is based on loopcheck [2]

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Summary

Introduction

To consider properties of distributed systems logics of knowledge with distributed knowledge operator were introduced. Traditional techniques used to ensure termination of a decision procedure in nonclassical (e.g., knowledge-based) sequent (and tableau) calculi is based on loopcheck [2]. For modal logic T loop-check-free sequent calculus is presented in [3] using sequents with two halves. In this paper non-transitive distributed knowledge logic TnD (obtained from multimodal logic Tn by adding distributed knowledge operator) is considered. In the paper a loop-check-free sequent calculus for distributed knowledge logic TnD is constructed. This calculus does not require sequents in a certain normal form and does not use sequents with two halves. To avoid loop-check, applications of reflexivity rules are restricted using marked knowledge and distributed knowledge operators. More efficient loop-check-free specialization of reflexivity rules, different from [4] is presented

Initial Gentzen-style calculus for the logic T nD
Loop-check-free sequent calculus for T nD
Termination of derivations in G1T nD

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