MSO with tests and reducts

Abstract

Tests added to Kleene algebra (by Kozen and others) are considered within Monadic Second Order logic over strings, where they are likened to statives in natural language. Reducts are formed over tests and non-tests alike, specifying what is observable. Notions of temporal granularity are based on observable change, under the assumption that a finite set bounds what is observable (with the possibility of stretching such bounds by moving to a larger finite set). String projections at different granularities are conjoined by superpositions that provide another variant of concatenation for Booleans.