### Abstract

This theory provides a formalisation of linear temporal logic (LTL) and unifies previous formalisations within the AFP. This entry establishes syntax and semantics for this logic and decouples it from existing entries, yielding a common environment for theories reasoning about LTL. Furthermore a parser written in SML and an executable simplifier are provided.

### License

BSD License

### History

March 12, 2019
  Support for additional operators, implementation of common equivalence relations, definition of syntactic fragments of LTL and the minimal disjunctive normal form.

### Topics

- Logic/General logic/Temporal logic
- Computer science/Automata and formal languages

### Session LTL

- LTL
- Rewriting
- Equivalence_Relations
- Disjunctive_Normal_Form
- Code_Equations
- Example

### Depends on

- Boolean Expression Checkers

### Used by

- An Efficient Normalisation Procedure for Linear Temporal Logic: Isabelle/HOL Formalisation
- A Compositional and Unified Translation of LTL into ω-Automata
- Converting Linear Temporal Logic to Deterministic (Generalized) Rabin Automata
- Converting Linear-Time Temporal Logic to Generalized Büchi Automata
- Promela Formalization
- Stuttering Equivalence

### Auto-related entries

- Formalization of a Monitoring Algorithm for Metric First-Order Temporal Logic
- A Compositional and Unified Translation of LTL into ω-Automata
- Formalization of Refinement Calculus for Reactive Systems

## Cite

×

LTL-AFP

    @article{LTL-AFP,
      author  = {Salomon Sickert},
      title   = {Linear Temporal Logic},
      journal = {Archive of Formal Proofs},
      month   = {March},
      year    = {2016},
      note    = {\url{https://isa-afp.org/entries/LTL.html},
                 Formal proof development},
      ISSN    = {2150-914x},
    }

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Older releases:

- Sep 13, 2023 : Isabelle2023
- Oct 27, 2022 : Isabelle2022
- Dec 14, 2021 : Isabelle2021-1
- Feb 23, 2021 : Isabelle2021
- Apr 20, 2020 : Isabelle2020
- Jun 11, 2019 : Isabelle2019
- Aug 16, 2018 : Isabelle2018
- Oct 10, 2017 : Isabelle2017
- Dec 17, 2016 : Isabelle2016-1
- Mar 2, 2016 : Isabelle2016