and properties of mosaics. Fix the dimension, n ? 2. The letters p; q denote numbers ! n. The qth element of a sequence s is written as s q . All mosaics are coherent unless otherwise stated. A map is (by definition) a certain set of ordered pairs (a binary relation), and we will use its form here. Many maps will act on the right. The identity map on a set X is denoted by IdX . DEFINITION 1 A linked system of mosaics (LSM) is an object of the form (I; (X i ; ` i ); ij : i; j 2 I); Marx and Mikul'as are supported by UK EPSRC grant no. GR/K54946. 1 April 1, 1996 2 where I is a non-empty set, for each i 2 I, (X<F9

This is a review of those aspects of the theory of varieties of Boolean algebras with operators (BAO's) that emphasise connections with modal logic and structural properties that are related to natural properties of logical systems.

Local search techniques have widespread use for solving propositional satisfiability problems. We investigate the use of adaptive local search techniques for model generation problems for modal logics; we focus on the modal logic S5. A local search algorithm extended with an adaptive heuristic is presented and tested on an ensemble of randomly generated problem instances. We briefly discuss the limitations of using local search for other NP-complete modal logics.