@MISC{Antonakos06justifiedknowledge, author = {Evangelia Antonakos}, title = {Justified Knowledge is Sufficient}, year = {2006} }

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Abstract

Three formal approaches to public knowledge are “any fool ” knowledge by McCarthy (1970), Common Knowledge by Halpern and Moses (1990), and Justified Knowledge by Artemov (2004). We compare them to mathematically address the observation that the light-weight systems of Justified Knowledge and ‘any fool knows ’ suffice to solve standard epistemic puzzles for which heavier solutions based on Common Knowledge are offered by standard textbooks. Specifically we show that epistemic systems with Common Knowledge modality C are conservative with respect to Justified Knowledge systems on formulas χ∧Cϕ → ψ, where χ, ϕ, and ψ are C-free. We then notice that formalization of standard epistemic puzzles can be made in the aforementioned form, hence each time there is a solution within a Common Knowledge system, there is a solution in the corresponding Justified Knowledge system. 1 Multi-agent Logics The logics Tn, S4n, and S5n are logics in which each of the finitely many (n) agents has a knowledge operator Ki which is T, or S4, or S5 respectively. We only consider cases where all agents ’ modalities are of the same logical strength.