The Proper Treatment of Quantification in Ordinary English

Language, Lambdas, and Logic

“…In Montague's pivotal work ( (Montague 1973)) it was already implicit that semantic values of certain expressions were 'shifted' to values in higher types in order to get the combinatorics of the system right. For example, since quantifying noun phrases (in an extensional version of the theory) are treated as expressions of type (et)t, proper names are also treated as being of this type and the translation of John (say) is λP.P (john), not simply the constant john of type e. In a similar vein, since transitive verbs need to be combinable with noun phrases (type (et)t) in object position, they get type ((et)t)(et), not simply e(et).…”

“…We will take a straightforward possible worlds approach in the semantics dimension, essentially that of (Montague 1973), but streamlined in the way of (Muskens 1995). The function sending categories to types in PTQ is not strictly in agreement with our previous requirement that c 2 (AB) = c 2 (A)c 2 (B), and this brings with it certain complications (but see (Hendriks 1993)).…”

New Waves in Truth

“…See, e.g., Keenan & Stavi (1986), Keenan & Westerståhl (1997), and Peters & Westerståhl (2006) for overviews of recent work in the field. The fundamental idea of employing the earlier logical work to natural language perhaps goes as far back as Lewis (1970), although the idea was first sketched by Montague (1973) via λ-abstraction. Thus, we can 'translate' every boy swims as…”

Porting natural language interfaces between domains

“…Our natural language interface implements a compositional semantics approach (see [18,4]) to construct the logical formula corresponding to the input question. Compositional means here that the query to the database or knowledge base -i.e.…”