No Vacuous Quantification Constraints In Syntax

Much recent work appeals to a ban on vacuous quantification (NO VACUOUS QUANTIFICATION, henceforth NVQ) that operates not merely as a criterion of non-redundancy in an informal semantic sense but is actually assumed to constrain syntactic well-formedness. Enforcing NVQ is excessively expensive in computational terms, provably beyond the power of a context-free grammar (CFG) and probably requiring something more powerful than an indexed grammar for its statement (see section 3). There are syntactic phenomena that cannot be modeled in context-free terms, but, as Gazdar and Pullum (1985: §2.2.5) write, “no phenomena are known which would lead one to believe that the NLs fell outside their [the indexed grammars’] purview.” Therefore, we should subject arguments for the syntactic use of NVQ to unusually close scrutiny. I undertake that task here, concluding that NVQ has not been shown to be a necessary constraint on syntactic structures. The strategy is simple: reanalyze past appeals to NVQ using only a basic version of GPSG (as in Gazdar et al. 1985), which is known to define only context-free tree sets (Rogers 1996, 1997). In general, let P be a phenomenon that has been analyzed in terms of NVQ. Successful reanalysis of P using only statements in GPSG is a demonstration that P does not demand the formal complexity of NVQ, or any logic that could enforce it. It is in principle possible for reanalysis to fail for some choice of P ; the Swiss-German crossing dependencies described by Shieber 1985 are provably beyond the power of context-free grammars, and so would not yield to this reanalysis. But, as we will see, no phenomena with this status have been found to motivate NVQ, and it seems unlikely that such are forthcoming. The choice of GPSG is non-essential. Rogers (1998) provides an interpretation of GB theory in strictly context-free terms. And categorial grammars (CGs) with only directional application are context-free (Bar-Hillel et al. 1960). Hence, reanalysis within those theories would do equally well. But couching the discussion in GPSG terms is appropriate. Gazdar et al. 1985 is a paradigm case of the benefits of adopting a restrictive formalism and pushing it as far as possible. This generally leads to innovative analyses, and reveals areas in which additional power is required: a useful, abstract insight into language. But the primary motivation for this project centers around the issue of decidability of the satisfaction question. All of GPSG can be defined using a decidable logic. But it is possible that the extension of