An Automata-Theoretic Completeness Proof for Interval Temporal Logic

@inproceedings{Moszkowski2000AnAC,
  title={An Automata-Theoretic Completeness Proof for Interval Temporal Logic},
  author={Ben C. Moszkowski},
  booktitle={ICALP},
  year={2000}
}
Interval Temporal Logic (ITL) is a formalism for reasoning about time periods. To date no one has proved completeness of a relatively simple ITL deductive system supporting infinite time and permitting infinite sequential iteration comparable to ω-regular expressions. We have developed a complete axiomatization for such a version of quantified ITL over finite domains and can show completeness by representing finite-state automata in ITL and then translating ITL formulas into them. Here we limit… 
A complete axiomatization of interval temporal logic with infinite time
  • B. Moszkowski
  • Mathematics
    Proceedings Fifteenth Annual IEEE Symposium on Logic in Computer Science (Cat. No.99CB36332)
  • 2000
TLDR
A complete axiomatization is given for such a version of quantified ITL over finite domains and completeness can be shown by representing finite-state automata in ITL and then translating ITL formulas into them.
A Hierarchical Completeness Proof for Propositional Temporal Logic
  • B. Moszkowski
  • Philosophy, Mathematics
    Verification: Theory and Practice
  • 2003
We present a new proof of axiomatic completeness for Proposition Temporal Logic (PTL) for discrete, linear time for both finite and infinite time (without past-time). This makes use of a natural
A Hierarchical Completeness Proof for Propositional Interval Temporal Logic with Finite Time
TLDR
A completeness proof for Propositional Interval Temporal Logic (PITL) with finite time which avoids certain difficulties of conventional methods and is able to invoke certain theorems about regular languages over finite words without the need to explicitly describe the associated intricate proofs.
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TLDR
This work presents a completeness proof for Interval Temporal Logic with finite-time which avoids certain difficulties of conventional methods and is more gradated than previous efforts since it progressively reduce reasoning within the original logic to simpler reasoning in sublogics.
Using Temporal Logic to Analyse Temporal Logic: A Hierarchical Approach Based on Intervals
TLDR
This work further develops and perfects the hierarchical interval-oriented methods for analysing conventional propositional linear-time temporal logic (PTL) contained in earlier Outputs 1 and 3, including natural reductions to a normal form in PTL closely resembling Buechi automata.
A MONA-based Decision Procedure for Propositional Interval Temporal Logic
TLDR
A new semantics for PITL based on WS1S formulas is developed, which led to an easy translation to MONA programs, and one of the very few implementations of a decision procedure for Propositional ITL with projection, and the first one based on automata.
Compositional reasoning using intervals and time reversal
  • B. Moszkowski
  • Computer Science
    2011 Eighteenth International Symposium on Temporal Representation and Reasoning
  • 2011
TLDR
This work investigates some simple kinds of ITL formulas which have application to compositional reasoning and furthermore are closed under conjunction and the conventional temporal operator known both as “box” and “always”, and uses a natural form of time symmetry with 2-to-1 formulas.
Model Checking Propositional Projection Temporal Logic Based on SPIN
TLDR
This paper investigates a model checking algorithm for Propositional Projection Temporal Logic with finite models by transforming a PPTL formula to a Normal Form Graph, and then a Nondeterministic Finite Automaton (NFA).
PITL2MONA: Implementing a Decision Procedure for Propositional Interval Temporal Logic
TLDR
The application of PITL and its MONA-based decision procedure in solutions to the dining-philosophers and a multimedia synchronisation problem is shown, together with some experimental results on these and some other examples.
RGITL: A temporal logic framework for compositional reasoning about interleaved programs
TLDR
This paper gives a self-contained presentation of the temporal logic Rely-Guarantee Interval Temporal Logic (RGITL), which extends ITL with explicit interleaved programs and recursive procedures and includes an interleaving operator with compositional semantics.
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    Proceedings Fifteenth Annual IEEE Symposium on Logic in Computer Science (Cat. No.99CB36332)
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