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
Hereditarily structurally complete modal logics
Journal of Symbolic Logic
Temporal verification of reactive systems: safety
Temporal verification of reactive systems: safety
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
Verifying Temporal Properties of Reactive Systems: A STeP Tutorial
Formal Methods in System Design
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
Model Checking Knowledge and Time
Proceedings of the 9th International SPIN Workshop on Model Checking of Software
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
Ground Temporal Logic: A Logic for Hardware Verification
CAV '94 Proceedings of the 6th International Conference on Computer Aided Verification
Another Look at LTL Model Checking
CAV '94 Proceedings of the 6th 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
A Deductive Proof System for CTL
CONCUR '02 Proceedings of the 13th International Conference on Concurrency Theory
LICS '01 Proceedings of the 16th Annual IEEE Symposium on Logic in Computer Science
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
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 Discovery and Knowledge: Decision Algorithm
KES '08 Proceedings of the 12th international conference on Knowledge-Based Intelligent Information and Engineering Systems, Part II
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
Logic of Discovery in Uncertain Situations--- Deciding Algorithms
KES '07 Knowledge-Based Intelligent Information and Engineering Systems and the XVII Italian Workshop on Neural Networks on Proceedings of the 11th International Conference
Information Sciences: an International Journal
International Journal of Advanced Intelligence Paradigms
Logic of discovery and knowledge: decision algorithm
Intelligent Decision Technologies
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
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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As specifications and verifications of concurrent systems employ Linear Temporal Logic (LTL), it is increasingly likely that logical consequence in LTL will be used in description of computations and parallel reasoning. We consider the linear temporal logic $\mathcal{LTL^{U,B}_{N,N^{-1}} (Z)}$ extending the standard LTL by operations B (before) and N−1 (previous). Two sorts of problems are studied: (i) satisfiability and (ii) description of logical consequence in $\mathcal{LTL^{U,B}_{N,N^{-1}} (Z)}$ via admissible logical consecutions (inference rules). The model checking for LTL is a traditional way of studying such logics. Most popular technique based on automata was developed by M.Vardi (cf. [39, 6]). Our paper uses a reduction of logical consecutions and formulas of LTL to consecutions of a uniform form consisting of formulas of temporal degree 1. Based on technique of Kripke structures, we find necessary and sufficient conditions for a consecution to be not admissible in $\mathcal{LTL^{U,B}_{N,N^{-1}} (Z)}$. This provides an algorithm recognizing consecutions (rules) admissible in $\mathcal{LTL^{U,B}_{N,N^{-1}} (Z)}$ by Kripke structures of size linear in the reduced normal forms of the initial consecutions. As an application, this algorithm solves also the satisfiability problem for $\mathcal{LTL^{U,B}_{N,N^{-1}} (Z)}$.