The complexity of propositional linear temporal logics
Journal of the ACM (JACM)
Reasoning about infinite computations
Information and Computation
A Tableau System for Linear-TIME Temporal Logic
TACAS '97 Proceedings of the Third International Workshop on Tools and Algorithms for Construction and Analysis of Systems
A New One-Pass Tableau Calculus for PLTL
TABLEAUX '98 Proceedings of the International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
A Decision Algorithm for Full Propositional Temporal Logic
CAV '93 Proceedings of the 5th International Conference on Computer Aided Verification
Complete Sequent Calculi for Induction and Infinite Descent
LICS '07 Proceedings of the 22nd Annual IEEE Symposium on Logic in Computer Science
Countermodels from Sequent Calculi in Multi-Modal Logics
LICS '12 Proceedings of the 2012 27th Annual IEEE/ACM Symposium on Logic in Computer Science
| Hi-index | 0.00 |
A labelled sequent calculus is proposed for Priorean linear time logic, the rules of which reflect a natural closure algorithm derived from the fixed-point properties of the temporal operators. All the rules of the system are finitary, but proofs may contain infinite branches. Soundness and completeness of the calculus are stated with respect to a notion of provability based on a condition on derivation trees: A sequent is provable if and only if no branch leads to a `fulfilling sequent,' the syntactical counterpart of a countermodel for an invalid sequent. Decidability is proved through a terminating proof search procedure, with an exponential bound to the branches of derivation trees for valid sequents, calculated on the length of the characteristic temporal formula of the endsequent.