By Edward L. Keenan, Leonard M. Faltz (auth.)
In the spring of 1978, one of many authors of this e-book used to be sitting in on a path in good judgment for linguists given via the opposite writer. In trying to current a few of Montague's insights in an trouble-free approach (hopefully keep away from ing the notation which many locate tough at first), the authors started dis cussions aimed in the direction of the development of an easy model-theoretical semantic equipment which may be utilized on to a small English-like language and used to demonstrate the tools of formal logical interpretation. In those discussions issues inspired themselves on us. First, our activity may be simplified through the use of boolean algebras and boolean homomorphisms within the versions; and moment, the boolean procedure we have been constructing had even more common relevance to the logical constitution of English than we first idea. throughout the summer season and fall of 1978 we persevered paintings at the approach, proving the extra basic theorems (including what we've come to name the Justification Theorem) and outlining the way an intensional interpretation scheme might be constructed which made use of the boolean strategy (which was once initially strictly extensional). We awarded our findings in a monograph (Keenan and Faltz, 1978) which the UCLA Linguistics division kindly released as a part of their sequence referred to as Occa sional Papers in Linguistics; one of many authors additionally awarded the approach at a colloquium held on the iciness assembly of the Linguistic Society of the USA in December 1978.
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Additional info for Boolean Semantics for Natural Language
For example it follows from the first 46 PART I: THE EXTENSIONAL LOGIC distributive law that the interpretation of (John and (Bill or Harry)) is the same element of TN as the interpretation of «John and BilT) or (John and Harry)). This is empirically correct; for example, because these two expressions must have identical interpretations, it will follow that the formulas «John and (Bill or Harry)) (read the book)) and «(John and BilT) or (John and Harry)) (read the book)) must have the same truth value.
Extensionally, both are functions of a very similar sort, namely homomorphisms, with the same domain, TN. They differ only with regard to their range algebras. Consequently, we are able to formulate several of the processes mentioned above in a fully general way, that is, for Pn's in general, regardless of whether n has value 1 or value 2. g. ) Note that the uniform semantic treatment of Pn's is in marked distinction to the treatment in PTQ. More generally, the classification of the sorts of algebras needed for natural language given earlier determine somewhat farther reaching correspondences between SF and LF.
This we have done in semantic, in fact boolean, terms. We refer the reader here to Keenan (1979) for more detailed discussion. Here we only stress that there are regularities in the way our function-argument structures are expressed in the SF's of the world's languages. So, to the extent that apprehending these function-argument relations is important to understanding the meaning of expressions we can say that languages do provide fairly regular observable means in surface for expressing these relations.
Boolean Semantics for Natural Language by Edward L. Keenan, Leonard M. Faltz (auth.)