Categorematic unreducible polyadic quantifiers in Lexical Resource Semantics

Early work on quantification in natural languages showed that sentences like ˋEvery ape picked different berries', on the reading that the sets of berries picked by any two apes are not the same, can be logically represented with a single polyadic quantifier for the two nominal phrases. However, since that quantifier cannot be decomposed into two quantifiers for the two nominal phrases, a compositional semantic analysis of this reading is not possible under standard assumptions about syntax and semantics. This paper shows how a constraint-based semantics with Lexical Resource Semantics can define a systematic syntax-semantics interface which captures the reading in question with a polyadic quantifier.

A typology of negation in a constraint-based framework of syntax and semantics

Negation and negative indefinites raise problems for the principle of compositionality of meaning, because we find both double and single negation readings in natural languages. De Swart and Sag (2002) solve the compositionality problem in a polyadic quantifier framework. The syntax-semantics interface exploits an extension of the Cooper storage mechanism that HPSG uses to account for scope ambiguities. In de Swart and Sag (2002), all negative quantifiers are collected into an N-store, and are interpreted by means of iteration (double negation) or resumption (negative concord) upon retrieval. This puts the ambiguity between single and double negation readings in the grammar, rather than in the lexical items. This paper extends the earlier analysis with a typology of negation and negative indefinites using bi-directional optimality theory (OT). The constraints defined are universal, but their ranking varies from one language to the next. In negative concord languages, the functional motivation for the marking of 'negative variables' wins out, so we use n-words. Double negation languages value first-order iteration, so we use plain indefinites or negative polarity items within the scope of negation. The bi-directional set-up is essential, for syntactic and semantic variation go hand in hand.