Epistemic Learning Programs A Calculus for Describing Epistemic Action Models Mohammad Ardeshir and Rasoul Ramezanian Department of Mathematical Sciences, Sharif University of Technology, P. O. Box 11365-9415, Tehran, Iran mardeshir@sharif.edu, ramezanian@sharif.edu Abstract Dynamic Epistemic Logic makes it possible to model and reason about information change in multi-agent systems. Information change is mathematically modeled through epistemic action Kripke models introduced by Baltag et al. Also, van Ditmarsch inter- prets the information change as a relation between epistemic states and sets of epistemic states and to describe it formally, he considers a special constructor L B called learning operator. Inspired by this, it seems natural to us that the basic source of information change in a multi-agent system should be learning an announcement by some agents together, privately, concurrently or even wrongly. Hence moving along this path, we introduce the notion of a learning program and prove that all finite K45 action models can be described by our learning programs. 1 Introduction A computable function over strings of a finite alphabet is a function that can be computed by a Turing machine. A Turing machine takes a string as input, performs a sequence of elementary changes on the string and if it halts, it provides another string as output of the function. In recursion theory all Turing computable function can be obtained via some initial functions : zero, successor, and projections through applying some basic operations such as composition, primitive recursion and least search. In this paper, our goal is to develop a similar methodology for a class of epistemic functions. Following the same terminology, an epistemic function is a function that takes the epistemic state of a multi-agent system as input and yields a new epistemic state as output. The notion of epistemic function is the focus of Dynamic Epistemic Logic, Baltag et al. [4, 5], and is formalized in action models. These functions act on Kripke models via an update operator and produce an update Kripke model. In this paper, we concentrate on those epistemic functions which can be coded as K45 action models. K45 models are those models which accessibly relations transitive and Euclidian. We claim that there are possible information changes which are not possible to encode them by KD45 or S 5 action models. Consequently K45 action models are more powerful to describe epistemic functions than KD45 and S 5 action models. It is why we consider K45 action models instead of S 5 or KD45 models. So far no one has looked at it from a computational aspect to answer the following question what are the initial functions and the basic operations by which all K45 epis- temic functions can be obtained? 1 arXiv:1304.6276v1 [cs.LO] 23 Apr 2013