Automated Proof Support for Interval Logics
LPAR '01 Proceedings of the Artificial Intelligence on Logic for Programming
An Automata-Theoretic Completeness Proof for Interval Temporal Logic
ICALP '00 Proceedings of the 27th International Colloquium on Automata, Languages and Programming
Compositional Reasoning Using Interval Temporal Logic and Tempura
COMPOS'97 Revised Lectures from the International Symposium on Compositionality: The Significant Difference
An Adequate First Order Interval Logic
COMPOS'97 Revised Lectures from the International Symposium on Compositionality: The Significant Difference
CSL '99 Proceedings of the 13th International Workshop and 8th Annual Conference of the EACSL on Computer Science Logic
Labelled Natural Deduction for Interval Logics
CSL '01 Proceedings of the 15th International Workshop on Computer Science Logic
A Complete Axiomatization of Interval Temporal Logic with Infinite Time
LICS '00 Proceedings of the 15th Annual IEEE Symposium on Logic in Computer Science
Completeness of temporal logics over infinite intervals
Discrete Applied Mathematics - Discrete mathematics and theoretical computer science (DMTCS)
On the completeness and decidability of duration calculus with iteration
Theoretical Computer Science
Axiomatisation and decidability of multi-dimensional Duration Calculus
Information and Computation
Semiring Neighbours: An Algebraic Embedding and Extension of Neighbourhood Logic
Electronic Notes in Theoretical Computer Science (ENTCS)
Complexity of propositional projection temporal logic with star†
Mathematical Structures in Computer Science
Sharpening the Incompleteness of the Duration Calculus
Electronic Notes in Theoretical Computer Science (ENTCS)
Formalising scheduling theories in duration calculus
Nordic Journal of Computing
Completeness of neighbourhood logic
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
Decidability of propositional projection temporal logic with infinite models
TAMC'07 Proceedings of the 4th international conference on Theory and applications of models of computation
A theory of duration calculus with application
Domain modeling and the duration calculus
Model checking propositional projection temporal logic based on SPIN
ICFEM'07 Proceedings of the formal engineering methods 9th international conference on Formal methods and software engineering
Connection between logical and algebraic approaches to concurrent systems†
Mathematical Structures in Computer Science
An improved decision procedure for propositional projection temporal logic
ICFEM'10 Proceedings of the 12th international conference on Formal engineering methods and software engineering
Stochastic differential dynamic logic for stochastic hybrid programs
CADE'11 Proceedings of the 23rd international conference on Automated deduction
Duration calculus: a real-time semantic for B
ICTAC'04 Proceedings of the First international conference on Theoretical Aspects of Computing
Compositionality of fixpoint logic with chop
ICTAC'05 Proceedings of the Second international conference on Theoretical Aspects of Computing
Lazy semiring neighbours and some applications
RelMiCS'06/AKA'06 Proceedings of the 9th international conference on Relational Methods in Computer Science, and 4th international conference on Applications of Kleene Algebra
FAC-RW'96 Proceedings of the BCS-FACS 7th conference on Refinement
LICS '12 Proceedings of the 2012 27th Annual IEEE/ACM Symposium on Logic in Computer Science
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Different interval modal logics have been proposed for reasoning about the temporal behavior of digital systems. Some of them are purely propositional and only enable the specification of qualitative time requirements. Others, such as ITL and the duration calculus, are first order logics which support the expression of quantitative, real-time requirements. These two logics have in common the presence of a binary modal operator `chop' interpreted as the action of splitting an interval into two parts. Proof systems for ITL or the duration calculus have been proposed but little is known about their power. This paper present completeness results for a variant of ITL where `chop' is the only modal operator. We consider several classes of models for ITL which make different assumptions about time and we construct a complete and sound proof system for each class.