Download Boolean Semantics for Natural Language by Edward L. Keenan, Leonard M. Faltz (auth.) PDF

By Edward L. Keenan, Leonard M. Faltz (auth.)

In the spring of 1978, one of many authors of this ebook was once 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 straight forward manner (hopefully stay away from­ ing the notation which many locate tricky at first), the authors begun dis­ cussions aimed in the direction of the development of an easy model-theoretical semantic equipment which can 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 types; and moment, the boolean method we have been constructing had even more common relevance to the logical constitution of English than we first proposal. through the summer time and fall of 1978 we persisted paintings at the process, proving the extra primary theorems (including what we've come to name the Justification Theorem) and outlining the best way an intensional interpretation scheme might be constructed which made use of the boolean process (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 process at a colloquium held on the iciness assembly of the Linguistic Society of the United States in December 1978.

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Thus we shall write man EN rather than nwn En(N). (ii) Note that and, or, and not are not members of any category. Such expressions will be called syncategorematic. The only syncategorematic elements of Vare and, or, and not. (iii) It follows from Definition 6 that the only non-empty categories of L are N, R, Nprop , N/N, Po, PI, and P 2 . Of these, all but Po have lexical members, that is elements which are also in the basic vocabulary V. In the extensions of L we propose other categories will become non-empty in either 38 PART I: THE EXTENSIONAL LOGIC of two ways: one, we shall add new items to V and new lexical conditions (rules) assigning them to categories currently empty, and two, a few new types of rules (conditions) will be added allowing us to form derived expressions in Pn for all finite n, as well as N n for all finite n.

Fully specifying that function, however, would require that we enter many details of agreement and word order phenomena which are irrelevant to our principle goal of representing English meanings. g. PTQ, and that characterizing the corresponding SF's of English is considerably more difficult than in that work. A second reason for a disparity between SF and LF here lies with the nature of English ambiguity. Semantically ambiguous forms, as judged pre theoretically , can not be directly interpreted.

Below we give a formal definition of CAT. We use f/J to denote the empty set, and for any set W, W* denotes the power set of W, that is, W* =df {K: K ~ W}. And standardly, for any ordinal n ~ 1, wn will denote the set of all sequences of n elements of W. We note that the full generality of the notation given below will not be utilized in the syntax of the core language itself, but it will be used in various of the extensions of that language to be proposed later. DEFINITION l. SFL, or the set of subcategorization features of L, is {{proper}} .

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