Algebra and Sequent Calculus for Epistemic Actions

  • Authors:
  • Alexandru Baltag;Bob Coecke;Mehrnoosh Sadrzadeh

  • Affiliations:
  • Computing laboratory, Oxford University, Oxford, U.K.;Computing laboratory, Oxford University, Oxford, U.K.;Department of Philosophy, Université du Québec À Montréal, Montreal, Canada

  • Venue:
  • Electronic Notes in Theoretical Computer Science (ENTCS)
  • Year:
  • 2005

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Abstract

We introduce an algebraic approach to Dynamic Epistemic Logic. This approach has the advantage that: (i) its semantics is a transparent algebraic object with a minimal set of primitives from which most ingredients of Dynamic Epistemic Logic arise, (ii) it goes with the introduction of non-determinism, (iii) it naturally extends beyond boolean sets of propositions, up to intuitionistic and non-distributive situations, hence allowing to accommodate constructive computational, information-theoretic as well as non-classical physical settings, and (iv) introduces a structure on the actions, which now constitute a quantale. We also introduce a corresponding sequent calculus (which extends Lambek calculus), in which propositions, actions as well as agents appear as resources in a resource-sensitive dynamic-epistemic logic.