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ErgSemantics_Quantification

DanFlickinger edited this page May 9, 2016 · 5 revisions

Overview of Quantification

The ERG assumes that all instance variables (of type x) are bound by a generalized quantifier, i.e. a predication whose ARG0 (or BV in some derived MRS views) is the instance variable, and whose RSTR and BODY arguments can be resolved in a fully-scoped MRS such that all instances of that variable are included within them. The representations output by the ERG are not fully scoped, but in fact underspecified, providing partial constraints on scope only as motivated by the syntax of the language. In particular, as Copestake et al (2005) argue, the syntax of English leaves the body of quantifiers unconstrained and provides a partial constraint on the restriction, where the semantic contribution of the nominal constituent that a quantifier-predicate-introducing element attaches to in the syntax is required to be within the restriction of the quantifier. Thus in the ERG, the BODY of quantifier predications is left unconstrained, while the RSTR is linked to the semantic contribution of the nominal constituent, via a qeq constraint:

  h0:*[ARG0 x]
  [ARG0 x, RSTR h1]
  { h1 =q h0 }

Predicate hierarchy

Quantifier predicates in the ERG are organized as a hierarchy rooted in the type abstract_q, with subtypes universal_q, existential_q, and thirdtype. The universal quantifiers include the surface predicates _all_q, _each_q, _every_q, and _each+and+every_q, as well as the additionally constrained _both_q and _either_q. The existential quantifiers include the surface predicates _a_q and _some_q, as well as a variety of abstract and surface predicates which currently encode in the predicates themselves some distinctions which might be better expressed as properities of the bound variable, including deixis (proximal and distal) and definiteness. Also included as subtypes of existential_q are distinct but possibly superfluous abstract predicates that bind variables for proper names (proper_q) and pronouns (pron_q). Quantifiers which are neither existential nor universal include _most_q, which_q, and _no_q, as well as a special predicate idiom_q_i used in the ERG's treatment of idioms, and a variety of other surface predicates introduced lexically. The full hierarchy of quantifier predicates is shown here:

[add graphic of quantifier hierarchy here]

Abstract quantifier predicates

The interpretations of the abstract quantifier predicates are grouped by the three most general subtypes:

existential_q

  • def_explicit_q - Lexical entries of several types with decomposed semantics introduce a definite quantifier predication: (1) determiners with decomposed semantics, including possessive pronouns such as his, the possessive clitic s, and names of months of the year, treated in the ERG as determiners for e.g. July 10; (2) some nominal adverbials such as awhile where the orthography still reflects an overt determiner, as well as some adverbials such as earlier that should be corrected to def_implicit_q since the determiner is not overt.

  • def_implicit_q - Several kinds of lexical entries with decomposed semantics introduce a definite quantifier predication, though the word is not itself a determiner. These include nominal adverbials such as here and now, nominal possessives such as hers and mine, and adjectives such as next and last which can also satisfy the determiner requirement for temporal nouns, as in next week will be convenient.

  • free_relative_q and free_relative_ever_q - Free relatives such as whoever and whenever have a decomposed semantics in the ERG, introducing an implicit quantifier binding the variable of the relevant entity.

  • number_q

  • pronoun_q

  • proper_q

  • some_q

  • udef_q

universal_q

  • every_q - This predicate subsumes the two surface predicates _every_q and _each+and+every_q.

Additional Information