Temporal Type Theory

@article{Schultz2019TemporalTT,
  title={Temporal Type Theory},
  author={Patrick Schultz and David I. Spivak},
  journal={Progress in Computer Science and Applied Logic},
  year={2019}
}
This book introduces a temporal type theory, the first of its kind as far as we know. It is based on a standard core, and as such it can be formalized in a proof assistant such as Coq or Lean by adding a number of axioms. Well-known temporal logics---such as Linear and Metric Temporal Logic (LTL and MTL)---embed within the logic of temporal type theory. The types in this theory represent "behavior types". The language is rich enough to allow one to define arbitrary hybrid dynamical systems… 
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16 Citations
Background Citations
6
Methods Citations
3

16 Citations

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The specification of branching dependency structures, which exist in fields from knowledge-representation to package management, to the specification of semantics of concurrent computation, and how such constructions may relate to important questions in complexity theory, including solutions of satisfiability problems are discussed.
Dynamical Systems and Sheaves
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A categorical framework for modeling and analyzing systems in a broad sense, which includes lax monoidal functors, which provide a language of compositionality, as well as sheaf theory, which flexibly captures the crucial notion of time.
Behavioral Mereology (Proofs and Properties).
Mereology is the study of parts and the relationships that hold between them. We introduce a behavioral approach to mereology, in which systems and their parts are known only by the types of behavior…
Topos Semantics for a Higher-Order Temporal Logic of Actions
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This work uses categorical techniques to recast a real-time semantics for TLA in terms of the actions of a group of time dilations, or "stutters," and an extension by a monoid incorporating delays, or 'falters.
Behavioral Mereology: A Modal Logic for Passing Constraints
TLDR
A behavioral approach to mereology is introduced, in which systems and their parts are known only by the types of behavior they can exhibit, and an inter-modal logic is given that generalizes the usual alethic modalities in the setting of symmetric accessibility.
A cost-aware logical framework
TLDR
It is argued that the cost structure of programs motivates a phase distinction between intension and extension, which contributes a synthetic account of cost structure as a computational effect in which cost-aware programs enjoy an internal noninterference property: input/output behavior cannot depend on cost.
Chapter IV : Modal homotopy type theory
We now proceed to take the final step in our journey towards modal homotopy type theory. Analytic philosophers have put modal logic to extensive use in their exploration of so-called alethic,…
Bisimulation maps in presheaf categories
Temporal Landscapes: A Graphical Temporal Logic for Reasoning
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…
Behavioral Mereology
Mereology is the study of parts and the relationships that hold between them. We introduce a behavioral approach to mereology, in which systems and their parts are known only by the types of behavior…
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