# 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} }

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…

## 23 Citations

A Complete Axiom System for Propositional Interval Temporal Logic with Infinite Time

- Philosophy, Computer ScienceLog. Methods Comput. Sci.
- 2012

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

- Philosophy, MathematicsVerification: 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…

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- Computer Science, PhilosophyTheor. Comput. Sci.
- 2020

Compositional reasoning using intervals and time reversal

- Computer Science2011 Eighteenth International Symposium on Temporal Representation and Reasoning
- 2011

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.

A decision procedure and complete axiomatization for projection temporal logic

- Computer ScienceTheor. Comput. Sci.
- 2020

Using Temporal Logic to Analyse Temporal Logic: A Hierarchical Approach Based on Intervals

- Computer ScienceJ. Log. Comput.
- 2007

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

- Computer ScienceCAV
- 2007

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

- Computer Science
- 2014

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

- Computer Science, PhilosophyArXiv
- 2010

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

- PhilosophyACM Trans. Comput. Log.
- 2015

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.

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