A Hierarchical Completeness Proof for Propositional Interval Temporal Logic with Finite Time

@article{Moszkowski2004AHC,
  title={A Hierarchical Completeness Proof for Propositional Interval Temporal Logic with Finite Time},
  author={Ben C. Moszkowski},
  journal={Journal of Applied Non-Classical Logics},
  year={2004},
  volume={14},
  pages={104 - 55}
}
  • B. Moszkowski
  • Published 1 January 2004
  • Computer Science
  • Journal of Applied Non-Classical Logics
We present a completeness proof for Propositional Interval Temporal Logic (PITL) with finite time which avoids certain difficulties of conventional methods. It is more gradated than previous efforts since we progressively reduce reasoning within the original logic to simpler reasoning in sublogics. Furthermore, our approach benefits from being less constructive since it is able to invoke certain theorems about regular languages over finite words without the need to explicitly describe the… 
A Complete Axiom System for Propositional Interval Temporal Logic with Infinite Time
  • B. Moszkowski
  • Philosophy, Computer Science
    Log. Methods Comput. Sci.
  • 2012
TLDR
This work solves the longstanding open problem of finding a complete axiom system for basic quantifier-free propositional ITL (PITL) with infinite time for analysing nonterminating computational systems and provides evidence of the naturalness of interval-based reasoning.
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
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.
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.
Boolean Abstraction for Temporal Logic Satisfiability
TLDR
A new approach to the satisfiability of PSL formulae is proposed; it follows recent approaches to decision procedures for Satisfiability Modulo Theory, typically applied to fragments of First Order Logic.
Reasoning about history based access control policy using past time operators of interval temporal logic
Interval Temporal Logic (ITL) is a flexible notation for the propositional and firstorder logical reasoning about periods of time that exist in specifications of hardware and software systems. ITL is
Real-time and Probabilistic Temporal Logics: An Overview
TLDR
This paper analyzes real-time and probabilistic temporal logics which have been widely used in this field and extrapolate the notions of decidability, axiomatizability, expressiveness, model checking, etc. for each logic analysed.
Two-Variable Separation Logic and Its Inner Circle
TLDR
This work shows that first-order separation logic with a unique record field restricted to two quantified variables and no program variables is undecidable, and establishes insightful and concrete relationships between two-variable separation logic and propositional interval temporal logic (PITL), data logics, and modal logics.
...
...

References

SHOWING 1-10 OF 70 REFERENCES
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
An Automata-Theoretic Completeness Proof for Interval Temporal Logic
TLDR
A complete axiomatization is developed 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, limiting ourselves to finite time.
Dynamic Linear Time Temporal Logic
Compositional reasoning about projected and infinite time
  • B. Moszkowski
  • Computer Science
    Proceedings of First IEEE International Conference on Engineering of Complex Computer Systems. ICECCS'95
  • 1995
TLDR
It is demonstrated that the generalization of Jones' techniques for assumptions and commitments handles not only safety properties but also liveness ones, as well as how to compositionally reason in ITL about the absence of deadlock in systems running for infinite time.
Complete proof systems for first order interval temporal logic
  • B. Dutertre
  • Computer Science
    Proceedings of Tenth Annual IEEE Symposium on Logic in Computer Science
  • 1995
TLDR
This paper considers several classes of models for ITL which make different assumptions about time and constructs a complete and sound proof system for each class.
Complete Proof System for QPTL
TLDR
The paper presents an axiomatic system for quantified propositional temporal logic (QPTL), which is propositionalporal logic equipped with quantification over propositions (Boolean variables) and its expressive power is strictly higher than that of the unquantified version (PTL).
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.
Sequential method in propositional dynamic logic
TLDR
A Gentzen-type sequential formulation of this logic is presented to establish its semantical completeness with due regard to sequential formulation as such and to show that the sequential system of prepositional dynamic logic does not enjoy the so-called cut-elimination theorem.
Temporal and Modal Logic
  • E. Emerson
  • Philosophy
    Handbook of Theoretical Computer Science, Volume B: Formal Models and Sematics
  • 1990
...
...