EAN: 9783030007034

TEMPORAL TYPE THEORY - PATRICK SCHULTZ DAVID I ...

This innovative monograph explores a new mathematical formalism in higher-order temporal logic
for proving properties about the behavior of systems. Developed by the authors  the goal of
this novel approach is to explain what occurs when multiple  distinct system components
interact by using a category-theoretic description of behavior types based on sheaves. The
authors demonstrate how to analyze the behaviors of elements in continuous and discrete
dynamical systems so that each can be translated and compared to one another. Their temporal
logic is also flexible enough that it can serve as a framework for other logics that work with
similar models. The book begins with a discussion of behavior types  interval domains  and
translation invariance  which serves as the groundwork for temporal type theory. From there 
the authors lay out the logical preliminaries they need for their temporal modalities and
explain the soundness of those logical semantics. These results are then applied to hybrid
dynamical systems  differential equations  and labeled transition systems. A case study
involving aircraft separation within the National Airspace System is provided to illustrate
temporal type theory in action. Researchers in computer science  logic  and mathematics
interested in topos-theoretic and category-theory-friendly approaches to system behavior will
find this monograph to be an important resource. It can also serve as a supplemental text for a
specialized graduate topics course.

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