Temporal Landscapes: A Graphical Logic of Behavior

Brendan Fong
(Topos Institute)
Alberto Speranzon
(Honeywell Aerospace)
David I. Spivak
(Topos Institute & MIT LIDS)

We present an elementary introduction to a new logic for reasoning about behaviors that occur over time. This logic is based on temporal type theory. The syntax of the logic is similar to the usual first-order logic; what differs is the notion of truth value. Instead of reasoning about whether formulas are true or false, our logic reasons about temporal landscapes. A temporal landscape may be thought of as representing the set of durations over which a statement is true. To help understand the practical implications of this approach, we give a wide variety of examples where this logic is used to reason about autonomous agents.

In Kohei Kishida: Proceedings of the Fourth International Conference on Applied Category Theory (ACT 2021), Cambridge, United Kingdom, 12-16th July 2021, Electronic Proceedings in Theoretical Computer Science 372, pp. 276–288.
Published: 3rd November 2022.

ArXived at: http://dx.doi.org/10.4204/EPTCS.372.20 bibtex PDF

Comments and questions to: eptcs@eptcs.org
For website issues: webmaster@eptcs.org