“Sometimes” and “not never” revisited: on branching versus linear time temporal logic
Journal of the ACM (JACM) - The MIT Press scientific computation series
The temporal logic of reactive and concurrent systems
The temporal logic of reactive and concurrent systems
Finite automata, formal logic, and circuit complexity
Finite automata, formal logic, and circuit complexity
Reasoning about knowledge
On concurrent programming
Model checking
An axiomatic basis for computer programming
Communications of the ACM
On the temporal analysis of fairness
POPL '80 Proceedings of the 7th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Process logic: preliminary report
POPL '79 Proceedings of the 6th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Using Finite-Linear Temporal Logic for Specifying Database Dynamics
CSL '88 Proceedings of the 2nd Workshop on Computer Science Logic
Proceedings of the Conference on Logic of Programs
Testing Linear Temporal Logic Formulae on Finite Execution Traces
Testing Linear Temporal Logic Formulae on Finite Execution Traces
Complete Axiomatizations for Reasoning about Knowledge and Time
SIAM Journal on Computing
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At the last TACAS in Barcelona, already almost a year ago, Alur, Etessami, and Madhusudan [2004] introduced CaRet, a temporal logic framework for reasoning about programs with nested procedure calls and returns. The details of the logic were themselves interesting (I will return to them later), but a thought struck me during the presentation, whether an axiomatization might help understand the new temporal operators present in CaRet. Thinking a bit more about this question quickly led to further questions about the notion of finiteness and infinity in temporal logic as it is used in Computer Science. This examination of the properties of temporal logic operators under finite and infinite interpretations is the topic that I would like to discuss here. I will relate the discussion back to CaRet towards the end of the article, and derive a sound and complete axiomatization for an important fragment of the logic.