The complexity of propositional linear temporal logics
Journal of the ACM (JACM)
Logics of time and computation
Logics of time and computation
Handbook of theoretical computer science (vol. B)
The temporal logic of reactive and concurrent systems
The temporal logic of reactive and concurrent systems
Temporal logic (vol. 1): mathematical foundations and computational aspects
Temporal logic (vol. 1): mathematical foundations and computational aspects
Hereditarily structurally complete modal logics
Journal of Symbolic Logic
An automata-theoretic approach to linear temporal logic
Proceedings of the VIII Banff Higher order workshop conference on Logics for concurrency : structure versus automata: structure versus automata
Quasi-Characteristic Inference Rules for Modal Logics
LFCS '97 Proceedings of the 4th International Symposium on Logical Foundations of Computer Science
Temporal Logic with Forgettable Past
LICS '02 Proceedings of the 17th Annual IEEE Symposium on Logic in Computer Science
Reasoning about The Past with Two-Way Automata
ICALP '98 Proceedings of the 25th International Colloquium on Automata, Languages and Programming
Alternating the Temporal Picture for Safety
ICALP '00 Proceedings of the 27th International Colloquium on Automata, Languages and Programming
Efficient Decision Procedures for Model Checking of Linear Time Logic Properties
CAV '99 Proceedings of the 11th International Conference on Computer Aided Verification
Improved Automata Generation for Linear Temporal Logic
CAV '99 Proceedings of the 11th International Conference on Computer Aided Verification
Modal Logics Preserving Admissible for S4 Inference Rules
CSL '94 Selected Papers from the 8th International Workshop on Computer Science Logic
The Declarative Past and Imperative Future: Executable Temporal Logic for Interactive Systems
Temporal Logic in Specification
Mathematical modal logic: a view of its evolution
Journal of Applied Logic
Admissible Rules of Modal Logics
Journal of Logic and Computation
Logical Consecutions in Intransitive Temporal Linear Logic of Finite Intervals
Journal of Logic and Computation
The temporal logic of programs
SFCS '77 Proceedings of the 18th Annual Symposium on Foundations of Computer Science
CIAA'03 Proceedings of the 8th international conference on Implementation and application of automata
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This paper aims to prove that the linear temporal logic LTL$^{u,s}_{n,n-1}$(N), which is an extension of the standard linear temporal logic LTL by operations Since and Previous (LTL itself, as standard, uses only Until and Next) and is based on the frame of all natural numbers N, as generating Kripke/Hintikka structure, is decidable w.r.t. admissible consecutions (inference rules). We find an algorithm recognizing consecutions admissible in LTL$^{u,s}_{n,n-1}$(N). As a consequence this algorithm solves satisfiability problem and shows that LTL$^{u,s}_{n,n-1}$(N) itself is decidable, despite LTL$^{u,s}_{n,n-1}$(N) does not have the finite model property.