 Many other expressions and phrases besides determiners show fixed monotonicity patterns. Beginning with van Benthem (1986) this has led to algorithms for how polarity markers are assigned to the nodes of analysis trees of sentences (relative to a given grammar), or how to incorporate such markers directly in the type notation; see Icard and Moss (2014) for an overview and further references. Besides their role in inference, such marking can also explain, and sometimes even predict, the distribution of negative polarity items in languages (end of  section 13).  Moreover, in many cases no syntactic analysis is necessary: inferences can be made directly on surface form, and would in this sense be available “on the fly” to speakers; compare  (43).  The paper just mentioned also presents a complete axiomatization of a formal Monotonicity Calculus, in which many varieties of reasoning with monotonicity can be  expressed.[41]