By Ronnie Cann
This available advent to formal, and particularly Montague, semantics inside of a linguistic framework, presupposes no prior historical past in good judgment, yet takes scholars step by step from uncomplicated predicate/argument constructions and their interpretation to Montague's intentional good judgment.
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Extra resources for Formal Semantics: An Introduction
Npr Vf+FIN] the N. Ethel poisoned the cat. 2G, 6G, 7G, Lex Translating English into a logical language (9) Ethel poisoned cat The notion of derivation and the use of phrase structure trees are important, because, as we will see in the next section, translation from English into LPis not done on the strings of words that make up sentences, but on the syntactic structures of those sentences. Before going on to translation, however, let us first add another two rules to the grammar, both of which introduce the third person singular past tense form of the copular verb be.
Q(c,d). P(b). c. f. R(b,a,d). Q(b,b). (3) a. d. Q(c). a(P). b. e. R(b,a,b,b). Rabc. f. c. P(e). 2 A grammar fragment for English P(a,a) Having defined the (very simple) syntax of Lp, we are in a position to translate sentences of English into it. To show how translation works, we shall provide a grammar for a small fragment of English and then develop a translation procedure that associates every sentence generated by the grammar with at least one logical expression. As discussed at the end of Chapter 1, grammars for parts of a language are called grammar fragments and are often used in formal semantics to develop specific and precise theories about the meanings of the expressions they analyse.
Unlike verbs in natural languages, however, there is no upper limit on the number of arguments a predicate in LP can take; thus the language may contain an infinite number of subcategories of predicates, Pred«, where n is any number between zero 27 2 Predicates and arguments and infinity. For the purposes of translating from English into LP, however, we can safely ignore all predicates that have a valency higher than 3. Thus, only four of the possible subcategories of Pred are used below: Pred0, Predi, Pred2 and Pred3.