Polynomial-time Equational Theory for Lattices with Unary Operators - Van Alten, C.J. (Order (Dordrecht), 2025)
The equational theory of the class of lattices with a pair of unary residuated operations is shown to be decidable in O ( n 5 ) time. The same complexity holds in the bounded case. The equational theory of the class of lattices, as well as the class of bounded lattices, with a unary operator is shown to be decidable in O ( n 3 ) time. Explicit algorithms are given for deciding the above equational theories. These algorithms use a dynamic programming approach and are based on a sequent calculus that extends Whitman’s sequent calculus for lattices.