📄 An Improper Treatment of Quantification in Ordinary English

Summary

Hobbs tackles quantifier scope ambiguity. A sentence with several quantified noun phrases, such as one about democratic countries, politicians, people, issues and times, gets 120 distinct scopings in standard logical form. Yet humans understand it without ever choosing one. He rejects three alternatives: a disjunction of all readings, Cooper/Woods-style quantifier stores, and Skolemization with later argument dropping. In their place he proposes a flat, scope-neutral logical form made of conjoined atomic predications. Determiners become relations between sets. Each quantified noun phrase introduces a set whose "typical element" is treated as a real entity, justified through a coarser grain size at which members are indistinguishable. Dependencies between sets are expressed with dependency functions. Resolving scope then becomes an ordinary inference task (coreference, coercion, predicate refinement) that only adds conjuncts instead of restructuring the formula. A nondeterministic algorithm recovers every conventional scoping consistent with the dependencies found so far. The treatment covers monotone increasing determiners only. Its value is that semantic representations can stay vague exactly where people stay vague.

Key points

• The motivating example sentence has 120 truly distinct scopings, each satisfiable by a model where the others fail.
• Monotone increasing determiners (every, some, most, many, several, any, a few) are modelled as relations between the noun-phrase set and a witness set (Barwise and Cooper). "No" and "few" fall outside the approach.
• "Any" is read as a random element of a set. This accounts for its need for modal or dispositional contexts and for contrasts with "every", but it does not explain existential "any" in questions.
• "Ontological promiscuity" extends Davidson's event individuals to all predications through primed predicates, e.g. see'(E,J,B).
• Embedded quantifiers ("Every representative of a company arrived") are resolved against small models via dependency functions. Donkey-sentence pronouns are handled by resolving "it" to the company variable. An algorithm built from TOPBVS and BRANCH enumerates the admissible scopings.

Interesting ideas

• I1. Keep scope underspecified and let later inference narrow it monotonically, by conjoining a dependency fact rather than rebuilding the formula.
• I2. Reify every predication as an entity (primed predicates), so that adverbs, times, causes, beliefs and pronouns can all point at it uniformly.
• I3. Treat the typical element of a set as a coarse-grained individual, so plural noun phrases behave like single referents that anaphors and generics can target.
• I4. Check scope readings by interpreting the formula against small concrete models: which identification makes the sentence true reveals the dependency.
• I5. Generate all conventional readings from the neutral form on demand, pruned by known dependency constraints.

For Mova

How these ideas could serve Mova, our small open language model — its files, stages and tests:

• I1 (frames): prag could emit quantified frames with open scope and attach dependency facts only when the world or the question forces a decision, which keeps every step explainable.
• I2 (world): the world model could give each state and event an ID that later facts, temporal order and anaphora reference, instead of nesting them.
• I3 (world): a set-of-entities node with a typical-element proxy would let "the farmers… he/they" and generic statements link to one entity while members inherit its properties.
• I4 (answer): readers for word problems could test candidate readings against the concrete world of the text and choose the one consistent with the stated numbers.
• I5 (learn): enumerating admissible scopings provides a controlled candidate set for evaluation, with impossible scopings serving as negative controls.