Introduction to mathematical logic (3rd ed.)
Introduction to mathematical logic (3rd ed.)
A propositional modal logic of time intervals
Journal of the ACM (JACM)
Interval logics and their decision procedures: part I: an interval logic
Theoretical Computer Science
Maintaining knowledge about temporal intervals
Communications of the ACM
A Hardware Semantics Based on Temporal Intervals
Proceedings of the 10th Colloquium on Automata, Languages and Programming
An Adequate First Order Interval Logic
COMPOS'97 Revised Lectures from the International Symposium on Compositionality: The Significant Difference
Some Very Compositional Temporal Properties
PROCOMET '94 Proceedings of the IFIP TC2/WG2.1/WG2.2/WG2.3 Working Conference on Programming Concepts, Methods and Calculi
Complete Proof Systems for First Order Interval Temporal Logic
LICS '95 Proceedings of the 10th Annual IEEE Symposium on Logic in Computer Science
Labelled Natural Deduction for Interval Logics
CSL '01 Proceedings of the 15th International Workshop on Computer Science Logic
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Signed Interval Logic (SIL) is an extension of Interval Temporal Logic (ITL) with the introduction of the notion of a direction of an interval. We develop syntax, semantics, and proof system of SIL, and show that this proof system is sound and complete. The proof system of SIL is not more complicated than that of ITL but SIL is (contrary to ITL) capable of specifying liveness properties. Other interval logics capable of this (such as Neighbourhood Logic) have more complicated proof systems. We discuss how to define future intervals in SIL for the specification of liveness properties. To characterize the expressive power of SIL we relate SIL to arrow logic and relational algebra.