Unificational Glue

draft; comments welcome In this paper I will describe a tentative proposal for using unification rather than lambda-calculus to effect semantic assembly in LFG glue logic. Some motivations for trying this out are: (1) a. The resulting relationship between f-structures and 'logical forms' is more in accordance with the general form of correspondence-based grammatical architectures. b. The system is inherently more restrictive (in effect, it requires (the equivalents of) higher order lambdas to be linear). c. The system permits the formulation of some plausible monotonicity constraints which aren't straightforwardly formulable in the standard lambda-based system. None of this constitutes anything like an argument that the idea is right, but I think it does show that it is worth a bit of exploration. A side-effect is that it highlights some subtle unclarities in the interpretation of glue-logic, as I'll discuss shortly. The technique I will employ is to have the meaning-constructors consist of a unifiable structure as their meaning-side, and, on the glue-side, a conventional glue-term supplemented with indexes to substructures of the meaning-side. When constructors combine, indexes will be identified, forcing unifications of the meaning-side structures to produce the assembled result. This is similar to the standard technique for faking beta-reduction with unification in Prolog, and suffers from the same limitations. Whether this is an empirical drawback or virtue is presently unclear, but it does constitute a difference from the standard lambda-based technique. I will present the approach using both proof-nets (Fry 1999, Andrews 2004) and natural deduction (Asudeh 2004), and will assume a basic familiarity with the workings of both approaches. A significant issue is that unifi-cational glue makes no sense at all unless one accepts a level of 'logical form', a level at which quantifier and related scope ambiguities are structurally represented. Standard lambda-based glue does not require such a commitment: