Decidability w.r.t. logical consecutions of linear temporal logic extended by since and previous
This paper aims to prove that the linear temporal logic LTLn,n-1u,s (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 LTLn,n-1u,s (N). As a consequence this algorithm solves satisfiability problem and shows that LTLn,n-1u,s (N) itself is decidable, despite LTLn,n-1u,s (N) does not have the finite model property.
decidability linear temporal logic temporal logic inference rules algorithms admissible inference rules