Antje Rumberg: Pruning the Tree of Possibilities: Axiomatizability Results for Transition Semantics
Time: Wed 2019-05-15 10.00 - 11.45
Lecturer: Antje Rumberg
Location: Room 16, building 5, Kräftriket, Department of Mathematics, Stockholm University
In my talk, I will give an overview of transition semantics for branching time, which I have developed in my dissertation, and sketch some axiomatizability results, drawing on joint work with Alberto Zanardo.
The theory of branching time, pioneered by Prior, depicts the future as genuinely open. The picture is that of a tree, whose branches represent possibilities for the future. The distinctive feature of transition semantics is that it provides a local approach to branching time: building on local future possibilities, viz. transitions, rather than on complete possible courses of events, it allows for a fine-grained, dynamic picture of the interrelation of modality and time, and it generalizes and extends extant accounts.
In the first part of my talk, I will motivate the basic idea underlying transition semantics and introduce the overall framework. It will become apparent that the semantics is set-theoretically rather complex. In the second part, I will then show that the set-theoretic complexity can be evaded – owing to the notion of a pruning. Based on this notion, I will provide a class of first-order definable Kripke structures that preserves validity, which naturally leads to axiomatizability results.