Applications to Monadic Definability
Stanley Peters · 2008
Abstract This chapter applies the Ehrenfeucht-Fraïssé (EF) technique to present a variety of results about the expressive power of certain monadic quantifiers. After repeating the general method, (un)definability relative to first-order logic and then relative to stronger logics is considered. The chapter also discusses issues of expressivity and monotonicity, and gives a number of exercises for applying the EF-tools. The direct applications of the method concern logical languages, but results about such languages may transfer to natural languages under certain conditions. The possible consequences for expressibility issues within natural languages are examined. In particular, the prospects of finding a universal statement that would somehow describe or even explain the role of monotonicity in the context of expressive power in natural languages is analysed, in view of certain rather striking technical results about definability in terms of monotone quantifiers.