Duality and Anaphora

The four constraints on sentential anaphoric binding, known as binding principles, are observed to form a square of oppositions. With the formal tools of phase quantification, these constraints are analysed as the effect of phase quantifiers over reference markers in grammatical obliqueness hierarchies. The four quantifiers are shown to be organized in a square of duality. The impact of this result on the distinction quantificational vs. non quantificational NPs and on the semantics of nominals in general is discussed. 1 Quantification and Duality Logical duality has been a key issue in natural language semantics. It is a pattern noticed in many phenomena, ranging from the realm of determiners to the realm of temporality and modality, including topics such as the adverbials still/already or the conjunctions because/although, etc. ([6], [7], [5], [9] i.a.). While noting that the ubiquity of the square of duality may be the sign of a semantic universal, [1],p.23 highlighted its heuristic value for research on quantification inasmuch as "it suggests a systematic point of view from which to search for comparative facts"— a hint we explore in this paper. 2 Anaphoric Binding Constraints Given our purpose here, it is of note that the square of duality in (2) is different from the classical square of oppositions in (1). The difference lies in the fact that duality, inner negation and outer negation are third order concepts, while compatibility, contrariness and implication are second order concepts. There are instantiations of the square of oppositions without corresponding squares of duality, and vice-versa ([6],p.56 for discussion). Although the two squares are logically independent, the empirical emergence of a square of oppositions naturally raises the question about the possible existence of an associated square of duality. This is where we get focussed into our research topic, given the emergence of a square of oppositions with the four constraints on sentential anaphoric binding, also outer negation inner negation ¬Q~ Q~