Modal Logics of Ordered Trees

From this page you may download my PhD thesis on Modal Logics of Ordered Trees, which was supervised by Dov Gabbay at King's College London and which I submitted to the University of London in January 2003 (defended in February 2003).

Abstract: In this thesis, we develop a new modal logic that is suitable to model complex systems evolving over time in a modular fashion. This logic may be regarded as the result of extending propositional linear temporal logic by a second dimension that allows us to "zoom" into states and thereby to further refine the specification of events associated with these states. In this sense, our logic may be described as an extended temporal logic that combines features from both point-based temporal logics and modal interval logics. From a more abstract point of view, our logic is best described as a modal logic based on frames that are ordered trees.

We give both a semantic and an axiomatic characterisation of our modal logic of ordered trees, discuss its expressive power, and prove its decidability. The thesis also includes an expository introduction to elementary modal logics.