By Edward L. Keenan, Leonard M. Faltz (auth.)
In the spring of 1978, one of many authors of this booklet was once sitting in on a direction in good judgment for linguists given through the opposite writer. In trying to current a few of Montague's insights in an effortless approach (hopefully stay away from ing the notation which many locate tough at first), the authors begun dis cussions aimed in the direction of the development of an easy model-theoretical semantic equipment that could be utilized on to a small English-like language and used to demonstrate the equipment of formal logical interpretation. In those discussions issues inspired themselves on us. First, our job should be simplified through the use of boolean algebras and boolean homomorphisms within the versions; and moment, the boolean process we have been constructing had even more common relevance to the logical constitution of English than we first notion. throughout the summer time and fall of 1978 we persevered paintings at the process, proving the extra primary theorems (including what we've got come to name the Justification Theorem) and outlining the best way an intensional interpretation scheme should be constructed which made use of the boolean technique (which was once initially strictly extensional). We offered our findings in a monograph (Keenan and Faltz, 1978) which the UCLA Linguistics division kindly released as a part of their sequence known as Occa sional Papers in Linguistics; one of many authors additionally provided the method at a colloquium held on the iciness assembly of the Linguistic Society of the United States in December 1978.
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Additional info for Boolean Semantics for Natural Language
In our notation then we may assign be directly to the category (P I, PI> /
For example, the -ly function in English (slow ~ slowly) basically expresses the isomorphism between restrictive AP's and restrictive Adverb Phrases. A third and yet more general correspondence between SF and LF in our BOOLEAN SEMANTICS: AN OVERVIEW 27 system concerns the regularity in surface coding properties agreement and word order in particular - of the function-argument relation defined at the level of LF. As regards word order, not having marked it at LF allows us to state generalizations concerning the regularities in the ways in functionargument structures are linearized in the world's languages.
A category then is a set of expressions, and L is defined to be the union of these sets. Defining CAT The elements of CAT are built up recursively from two primitive category names 'N' and 'P', which we may think of as nominals and predicates respectively. 'N' for example will turn out to name the category of (zero place) common noun phrases. It will include expressions like man, woman, etc. 'P' will name the category of formulas, which we regard as zero-place predicates. Complex category names are formed from simpler ones by the use of slashes (J), bars C), and sub categorization features.