Actions and resources in epistemic logic

• Authors: Mehrnoosh Sadrzadeh
• Venue: Actions and resources in epistemic logic
• Year: 2006

Reasoning about knowledge has been a central issue in epistemology since Plato defined knowledge as justified true belief. In the twentieth century, the discussion was renewed by the use of formal logic and modal operators in Hintikka's epistemic logic. This logic has found applications in computer science and economics, but has defects: it is mono-modal, static and has no sense of resources. In this thesis we present a logic to reason about knowledge and the change induced to it as a result of communication actions between agents in a multi-agent systems. The semantics of this logic is an algebra of propositions paired with an algebra of actions. Both have structure preserving appearance maps whose adjoints stand for knowledge of agents. The algebra of actions is a quantale, thus actions are treated as the qualitative resources of Linear Logic: they are not accessible to all agents to acquire new information. Agents themselves act as qualitative resources to other agents: their nested appearances of a context has an effect in the reasoning of other agents. We also present a sequent calculus for our semantics, in the style of Lambek Calculus and Non-commutative Intuitionistic Linear Logic. We prove the soundness and completeness of this sequent calculus with regard to the algebra and apply the setting to reason about safety of security protocols. We connect our approach to the existing literature by showing that models of dynamic epistemic logic of Baltag-Moss-Solecki are instances of our logic.Key words. Actions, Resources, Knowledge, Logic, Security Protocols