Algorithmic correspondence and analytic rules

Abstract

We introduce the algorithm MASSA which takes classical modal formulas in input, and, when successful, effectively generates: (a) (analytic) geometric rules of the labelled calculus G3K, and (b) cut-free derivations (of a certain `canonical' shape) of each given input formula in the geometric labelled calculus obtained by adding the rule in output to G3K. We show that MASSA successfully terminates whenever its input formula is a (definite) analytic inductive formula, in which case, the geometric axiom corresponding to the output rule is, modulo logical equivalence, the first-order correspondent of the input formula.