Iconic variables

We argue that some sign language loci (i.e. positions in signing space that realize discourse referents) are both formal variables and simplified representations of what they denote; in other words, they are simultaneously logical symbols and pictorial representations. We develop a 'formal semantics with iconicity' that accounts for their dual life; the key idea ('formal iconicity') is that some geometric properties of signs must be preserved by the interpretation function. We analyze in these terms three kinds of iconic effects in American and French Sign Language (ASL and LSF): (i) structural iconicity, where relations of inclusion and complementation among loci are directly reflected in their denotations; (ii) locus-external iconicity, where the high or low position of a locus in signing space has a direct semantic reflex, akin to the semantic contribution of gender features of pronouns; and (iii) locus-internal iconicity, where different parts of a structured locus are targeted by different directional verbs, as was argued by Liddell and Kegl. The resulting semantics combines insights of two traditions that have been sharply divided by recent debates. In line with the 'formalist camp' (e.g. Lillo-Martin and Klima, Neidle, and Sandler and Lillo-Martin), our theory treats loci as variables, and develops an explicit formal analysis of their behavior. But we also incorporate insights of the 'iconic camp', which emphasized the role of iconic constraints in sign language in general and in pronominals in particular (e.g. Cuxac, Taub, Liddell). However, this synthesis is only possible if formal semantics makes provisions for iconic requirements at the very core of its interpretive procedure. (An Appendix discusses relevant data from Italian Sign Language [LIS].).