Difference functions of dependence spaces

Abstract

Here the reduction problem is studied in an algebraic structure called dependence space. We characterize the reducts by the means of dense families of dependence spaces. Dependence spaces defined by indiscernibility relations are also considered. We show how we can determine dense families of dependence spaces induced by indiscernibility relations by applying indiscernibility matrices. We also study difference functions which connect the reduction problem to the general problem of identifying the set of all minimal Boolean vectors satisfying an isotone Boolean function.