An unlabeled bracketing solution to the problem of conjoined phrases in Montague's PTQ

In The proper treatment of quantification in ordimny Englim tk rQ) (Montague, 1973), Richard Montague presents the syntax and semantics of a fragment of English. His objective is to support the contention that “there is . . . no important theoretical difference between natural languages and the artificial languages of logicians” and that it is “possible to comprehend the syntax given in PTQ consists of an inductive defmition for each nonempty mathematically precise theory” [Montague, 1970, p. 3731. The formal syntax given in PTQ consisti of an inductive defmition for each nonempty grammatical category, in particular, the category of sentences. Parallel rules give a translation into an intensional logic for which semantics are provided. The semantic aspects of PTQ, particularly the elegance of the syntax/ semantics relation, are impressive. The range of English expressions generated by the syntax of PTQ is limited, but the fragment was selected for inclusion of philosophically difflcuh sentences. The standard logical operators have English representatives in Montague’s syntax; and by the translation rules for the fragment, these English words are explicitly correlated with the corresponding logical operators. The propositional operators are represented by and’s of sentences and of verb phrases, and or’s of sentences, verb phrases, and term phrases, and by negation of verb phrases; quantifiers are represented by every, the, and a; the modal operator for necessity by necessar@; and tense operators by the future and present perfect tenses of verbs. In addition, the syntax includes pronouns and allows relative clauses (formed with such that). Although the syntax of PTQ is weak, especially by current transformational standards, the work is important enough to justify investigating how far the fragment can be extended toward English. In this paper we approach this task by asking whether the system of PTQ can be modified so that the fragment which it claims to handle is actually handled correctly. The system as presented by Montague allows conjunction and disjunction of intransitive verb phrases and disjunction of term phrases.