The complexity of propositional linear temporal logics
Journal of the ACM (JACM)
Logics of time and computation
Logics of time and computation
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
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
Improved Automata Generation for Linear Temporal Logic
CAV '99 Proceedings of the 11th International Conference on Computer Aided Verification
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
Decidability of Hybrid Logic with Local Common Knowledge Based on Linear Temporal Logic LTL
CiE '08 Proceedings of the 4th conference on Computability in Europe: Logic and Theory of Algorithms
Multi-agent Logics with Interacting Agents Based on Linear Temporal Logic: Deciding Algorithms
ICAISC '08 Proceedings of the 9th international conference on Artificial Intelligence and Soft Computing
Logic of Plausibility for Discovery in Multi-agent Environment Deciding Algorithms
KES '08 Proceedings of the 12th international conference on Knowledge-Based Intelligent Information and Engineering Systems, Part III
Temporal Logic for Modeling Discovery and Logical Uncertainty
KES '09 Proceedings of the 13th International Conference on Knowledge-Based and Intelligent Information and Engineering Systems: Part II
Rules admissible in transitive temporal logic TS4, sufficient condition
Theoretical Computer Science
Interpretation of chance discovery in temporal logic, admissible inference rules
KES'10 Proceedings of the 14th international conference on Knowledge-based and intelligent information and engineering systems: Part III
A framework to compute inference rules valid in agents' temporal logics
KES'10 Proceedings of the 14th international conference on Knowledge-based and intelligent information and engineering systems: Part I
Inference rules in multi-agents' temporal logics
Transactions on computational collective intelligence IV
KES'11 Proceedings of the 15th international conference on Knowledge-based and intelligent information and engineering systems - Volume Part I
Chance discovery and unification in linear modal logic
KES'11 Proceedings of the 15th international conference on Knowledge-based and intelligent information and engineering systems - Volume Part II
International Journal of Intelligent Information Technologies
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We present a framework for constructing algorithms recognizing admissible inference rules (consecutions) in temporal logics with Until and Since based on Kripke/Hintikka structures modeling parallel time with common past. Logics $\mathcal{PTL}_\alpha$ with various branching factor $\alpha\in {\mathcal N} \cup \{\omega\}$ after common past are considered. The offered technique looks rather flexible, for instance, with similar approach we showed [33] that temporal logic based on sheafs of integer numbers with common origin is decidable by admissibility. In this paper we extend obtained algorithms to logics $\mathcal{PTL}_\alpha$. We prove that any logic $\mathcal{PTL}_\alpha$ is decidable w.r.t. admissible consecutions (inference rules), as a consequence, we solve satisfiability problem and show that any $\mathcal{PTL}_\alpha$ itself is decidable.