Convergent Grammar Overview

Convergent Grammar (CVG) is a framework for linguistic analysis, under development at the Ohio State University and INRIA-Lorraine, which traces its origins to Extended Montague Grammar (EMG, the categorial grammar (CG) and phrase structure grammar (PSG) of the 1970s and early 1980s). CVG has a parallel architecture which combines the pure derivationality of recent categorial frameworks (especially ACG) with the weak syntactocentrism of HPSG.

Parallel means that candidate phonological, syntactic, and semantic derivations are generated by independent components of the grammar. This distinguishes CVG (and ACG and HPSG) from the cascaded architecture of TG, where semantics and phonology (or the components LF and PF which respectively determine them) are fed by, or transformationally derived from, syntax.

Each component has its own logic, in the format of sequent-style natural deduction (ND) with (Curry-Howard) proof terms. Pure derivationality means that linguistic derivations are proofs, or, more precisely, typing judgments for proof terms. They are not trees in the sense of structures whose geometric configurations are linguistically significant.

Thus derivations do not consist of sequences of structural operations (such as merging, copying, deleting, or moving) on arboreal representations.

The syntax-semantics interface recursively specifies which pairs of a syntactic derivation with a semantic one belong to the language in question.

The syntax-phonology interface recursively specifies which pairs of a syntactic derivation and a phonological one belong to the language in question.

Thus CVG's architecture is syntactocentric (there is no direct relation between phonology and semantics), but only weakly so (the relations defined by the interfaces are not functions).

The syntactic proof terms bear an uncanny resemblance to mid-1970s transformational grammar (TG) representations: labelled bracketings with syntactic variables (traces) bound by (often inaudible) operators. But unlike TG, there is no movement (of binding operators, or of anything else).

The semantic proof terms are reminiscent of TG logical forms (LFs), but differ from LFs in the following respects:

  1. They are completely formalized (as proof terms of a logic called RC).
  2. They are not in any sense derived from syntax.
  3. They are not in any sense "after syntax"; rather, the syntactic and semantic (and phonological) components of a linguistic expression are constructed in parallel.
  4. There are simple and fully explicit transforms of RC into both standard and hyperintensional versions of possible-worlds semantics.

The semantic logic RC is similar to lambda calculus, but instead of the usual hypothetical proof schema, it has a schema that generalizes the semantics of Gazdar's's linking rules for unbounded dependencies.

In addition, it has two schemata corresponding to introduction and elimination rules for Moortgat's q-connective, but unlike TLG, this is in the semantic logic, not the syntactic one. These schemata are straightforward ND embodiments of Cooper storage and retrieval respectively.