Epistemic Actions as Resources

13 years 4 months ago

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We provide algebraic semantics together with a sound and complete sequent calculus for information update due to epistemic actions. This semantics is ﬂexible enough to accommodate incomplete as well as wrong information e.g. deceit. We give a purely algebraic treatment of the muddy children puzzle, which moreover extends to situations where the children are allowed to lie and cheat. Epistemic actions, that is, information exchanges between agents A, B, . . . ∈ A, are modeled as elements of a quantale, hence conceiving them as resources. Indeed, quantales are to locales what monoidal closed categories are to Cartesian closed categories, respectively providing semantics for Intuitionistic Logic, and for non-commutative Intuitionistic Linear Logic, including Lambek calculus. The quantale (Q, , •) acts on an underlying Q-right module (M, ) of epistemic propositions and facts. The epistemic content is encoded by appearance maps, one pair fM A : M → M and fQ A : Q → Q of (lax) mor...

Alexandru Baltag, Bob Coecke, Mehrnoosh Sadrzadeh

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