Temporal Landscapes: A Graphical Temporal Logic for Reasoning

 arXiv:1904.01081v1  [math.LO]  1 Apr 2019 

Brendan Fong∗ Alberto Speranzon Abstract David I. Spivak˚ 

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 syntaxofthelogicissimilartotheusualfirst-orderlogic; whatdiffersisthenotion 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 systems.