ABS Khosravi Rad(Latin)

ABSTRACT:

   Dynamic Epistemic Logic (DEL) is PDL-style logic to reason about epistemic actions and updates in a multi-agent system. It focuses in particular on epistemic programs, i.e. programs that update the information states of agents and it has applications to modelling and reasoning about information-flow and information exchange between agents. This is a major problem in several fields such as secure communication. Where one has to deal with the privacy and authentication of communication protocols, artificial Intelligence where agents are to be provided with reliable tools to reason about their environment and each other's knowledge, and e-commerce where agents need to have knowledge acquisition strategies over complex networks. The standard approach to information flow in a multi-agent system has been presented but it does not present a formal description of epistemic programs and their updates.

   In this thesis we study a generalization Boolean DEL by introducing the notion of an abstract epistemic system. This generalization goes hand-in-hand with the introduction of non-determinism for states and actions and brings algebraic clarity to the semantics. The particular algebraic objects which we introduce area refinement of previously used objects tailored to study concurrency in computer science and the dynamics and interaction of physical systems. Such an abstract epistemic system consists of a quantal Q of epistemic programs, a Q-right module M of epistemic propositions and each agent is encoded by an appearance map i.e., an endomorphism of the ­ (M, Q)-structure.   We show that the Boolean DEL is a concrete example of such an abstract epistemic system. The axioms of the modal operators follow immediately from abstract properties of a quantales and modules over them.   Crucial notions of DEL are definable abstractly and some new notions emerge naturally. The passage to the non-Boolean theory also provides a new insight into epistemic programs such as public announcement and of a surprisingly different status, public refutation.   We sketch an analysis of the muddy children puzzles and of a cryptographic attach in our setting and also provide a motivating example for the passage to a non-Boolean theory. We also provide a corresponding sequent calculus in which sequence will typically look like