Speaker: Ana Lucia Vargas-Sandoval
Date and Time: Thursday, May 3rd 2018, 16:00-17:30
Venue: ILLC Seminar Room F1.15, Science Park 107.
Title: Arbitrary Announcement Logic with Memory is better.
Abstract. Arbitrary Public Announcement logic (APAL) and its relatives are natural extensions of Public Announcement Logic obtained by adding an arbitrary announcement operator. These logics are of great interest both philosophically and from the point of view of applications. Motivations range from modelling notions of knowability to modelling inductive learnability in empirical science. One problem with APAL formalisms is that they use infinitary axiomatisations, therefore it is not guaranteed that the validities of these logics are recursively enumerable. The question of whether Arbitrary Public Announcement logic has a finitary axiomatisation remains open since almost a decade.
In this talk we present an APAL-style logic for which a recursive axiomatisation is guaranteed. We expose the problem of the original APAL and explain our solution: equipping APAL with a memory mechanism. We introduce Arbitrary Public Announcement Logic with Memory (APALM), obtained by adding to the models a memory of the initial states, representing the information before any communication took place, and adding to the syntax operators that can access this memory. We give a sound and complete axiomatisation for APALM that is recursive, our recursive axiomatisation uses a natural finitary rule. If time permits we will also discuss expressivity results and some connections of APALM with other logics.