Syncategorematic Conjunction and Structured Meanings
نویسنده
چکیده
One elegant and linguistically powerful guideline for a semantic theory of coordination will be referred to here as the Boolean assumption. According to this assumption conjunctive coordinators like and are described using the cross-categorial Boolean operator of Generalized Conjunction (GC). Symmetrically, disjunctive coordinators like or are modeled by Generalized Disjunction (GD). A common type theoretical definition of the operators GC and GD goes as follows: Definition: An extensional type is called t-reducible iff = t or = 1 2, where 1 is any type and 2 is a t-reducible type. For every t-reducible type : u ( ) def = ( Xt: Yt:X ^ Y = t X : Y : Z 1 :X(Z) u Y (Z) = 1 2 (GC) t ( ) def = ( Xt: Yt:X _ Y = t X : Y : Z 1 :X(Z) t Y (Z) = 1 2 (GD) Modeltheoretically the operators u and t can be shown to be indirectly representing the simple operations of set intersection and set union. The Boolean assumption is then a linguistic assumption about the lexical meanings [[and ]] and [[or ]] of the coordinator morphemes:
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