A tableau for temporal logic over the reals
A tableau for temporal logic over the reals Mark Reynolds School of Computer Science and Software Engineering The University of Western Australia
AiML 2014, Groningen
uwacrest
Reynolds (UWA)
Tableau over the reals
AiML 2014, Groningen
1 / 24
Advances in Modal Logic 2014 University of Groningen Wednesday 6th August 11:55 until 12:20
uwacrest
Reynolds (UWA)
Tableau over the reals
AiML 2014, Groningen
2 / 24
Abstract We provide a simple, sound, complete and terminating tableau decision procedure for the temporal logic of until and since over the real numbers model of time. This logic is an important basis for reasoning about concurrency, metric constraints and planning. Despite its usefulness and long history, there are no existing implementable reasoning techniques for it. The tableau uses a mosaic-based technique to translate the satisfiability problem into a question about the way that intervals of a real-flowed model relate to each other. It builds on top of recently developed reasoning tools for general linear time by applying some interesting but computationally simple checks. uwacrest
Reynolds (UWA)
Tableau over the reals
AiML 2014, Groningen
3 / 24
Outline
1
Introduction
2
RTL
3
Mosaics
4
Tableaux
5
Conclusion and Future Work
uwacrest
Reynolds (UWA)
Tableau over the reals
AiML 2014, Groningen
4 / 24
What we want and why Consider a collection of boolean signals switching between off and on over time. They might represent an abstraction of some combination of hardware, software, or wetware: eg a communication protocol, workflow, a multi-agent system, a physical system, or a distributed system. For many applications time is the real numbers: dense and continuous. Is a candidate description of behaviour even possible? Useful for sanity checks, synthesis of synchronisation skeletons, counter-examples, ... The RTLSAT problem answers these questions. uwacrest
Reynolds (UWA)
Tableau over the reals
AiML 2014, Groningen
5 / 24
RTL Fix a countable set L of propositional atoms.
Definition A real frame (R,
AiML 2014, Groningen
uwacrest
Reynolds (UWA)
Tableau over the reals
AiML 2014, Groningen
1 / 24
Advances in Modal Logic 2014 University of Groningen Wednesday 6th August 11:55 until 12:20
uwacrest
Reynolds (UWA)
Tableau over the reals
AiML 2014, Groningen
2 / 24
Abstract We provide a simple, sound, complete and terminating tableau decision procedure for the temporal logic of until and since over the real numbers model of time. This logic is an important basis for reasoning about concurrency, metric constraints and planning. Despite its usefulness and long history, there are no existing implementable reasoning techniques for it. The tableau uses a mosaic-based technique to translate the satisfiability problem into a question about the way that intervals of a real-flowed model relate to each other. It builds on top of recently developed reasoning tools for general linear time by applying some interesting but computationally simple checks. uwacrest
Reynolds (UWA)
Tableau over the reals
AiML 2014, Groningen
3 / 24
Outline
1
Introduction
2
RTL
3
Mosaics
4
Tableaux
5
Conclusion and Future Work
uwacrest
Reynolds (UWA)
Tableau over the reals
AiML 2014, Groningen
4 / 24
What we want and why Consider a collection of boolean signals switching between off and on over time. They might represent an abstraction of some combination of hardware, software, or wetware: eg a communication protocol, workflow, a multi-agent system, a physical system, or a distributed system. For many applications time is the real numbers: dense and continuous. Is a candidate description of behaviour even possible? Useful for sanity checks, synthesis of synchronisation skeletons, counter-examples, ... The RTLSAT problem answers these questions. uwacrest
Reynolds (UWA)
Tableau over the reals
AiML 2014, Groningen
5 / 24
RTL Fix a countable set L of propositional atoms.
Definition A real frame (R,
