A study of the contribution semantics makes to the syntactic patterns of English: an intepretive theory of grammar.

In the opening sections of this paper, we defined ambiguity in terms of distinct sentences (for a single sentence-string) with, in particular, distinct sets of truth conditions for the corresponding negative sentence-string. Lexical vagueness was defined as equivalent to disjunction, for under conditions of the negation of a sentence-string containing such an expression, all the relevant more specific interpretations of the string had also to be negated. Yet in the case of mixed quantification sentences, the strengthened, more specific, interpretations of (...) some such positive string are not all of them necessarily implied to be false if the corresponding negative sentence-string is asserted. On the contrary, as we saw in section 6, a negative sentence-string can be used to deny one of the more specific interpretations of the corresponding positive string without also denying other weaker interpretations of that same string. One might therefore argue that the only empirical evidence availble for assessing quantified sentences suggests clearly that these sentence-strings are ambiguous. Indeed logicians, many of whom restrict their attention to propositions, MUST recognise logical ambiguity at this point. For the contextualisation of the negative sentences in section 6 showed that it was possible to assert the falsity of some proposition P expressed by the sentence S while asserting a further proposition which was compatible with the truth of S. However the corresponding conclusion that such sentence-strings are sententially ambiguous is not a necessary conclusion for the linguist: for the alternative account of postulating a single semantic representation plus a set of semantic procedures is also compatible with the negation evidence. Moreover we have seen independent reasons for thinking that if sentential ambiguity is assumed to be in one-to-one correspondence with what we should now call logical ambiguity, a considerable body of generalisations is lost. For the maximal ambiguity account, it should be recalled, is committed to assigning at least thirteen distinct propositions and hence thirteen distinct sentence outputs for every sentence-string containing no more than two quantifiers, for three out of the four interpretations originally outlined in this paper can be understood with each numeral taken either in an ’exactly’ sense or in an ’at least’ sense. Moreover there is no explanation of why just these interpretations are available-they are merely an arbitrary list, no more connected than are the two interpretations of John saw her duck, with no reason to predict that the ambiguity would carry over from language to language. If then it is granted that an ambiguity account fails to capture appropriate generalisations, only two alternative accounts of mixed quantification sentence-strings remain viable-an analysis proposing an initial co-ordinate logical form like the logical form III, which is the strongest form compatible with each of the propositional interpretations of sentence-string Two examiners marked six scripts, and the radically weak form in which only existential quantification (both over sets and over members of those sets) is invoked. Since there are strong arguments to suggest that the procedures which both analyses require are semantic, there seems no reason not to adopt the radical vagueness account, with its considerably greater simplicity. (shrink)

The formal semantics that we have proposed for definite and indefinite descriptions analyzes them both as variable-binding operators and as referring terms. It is the referential analysis which makes it possible to account for the facts outlined in Section 2, e.g. for the purely ‘instrumental’ role of the descriptive content; for the appearance of unusually wide scope readings relative to other quantifiers, higher predicates, and island boundaries; for the fact that the island-escaping readings are always equivalent to maximally wide scope (...) quantifiers; and for the appearance of violations of the identity conditions on variables in deleted constituents. We would emphasize that this is not a random collection of observations. They cohere naturally with each other, and with facts about other phrases that are unambigously referential.We conceded at the outset of this paper that the referential use of an indefinite noun phrase does not, by itself, motivate the postulation of a referential interpretation. Our argument has been that the behavior of indefinites in complex sentences cannot be economically described, and certainly cannot be explained, unless a referential interpretation is assumed. It could be accounted for in pragmatic terms only if the whole theory of scope relations and of conditions on deletion could be eliminated from the semantics and incorporated into a purely pragmatic theory. But this seems unlikely. (shrink)

'Mass terms', words like water, rice and traffic, have proved very difficult to accommodate in any theory of meaning since, unlike count nouns such as house or dog, they cannot be viewed as part of a logical set and differ in their grammatical properties. In this study, motivated by the need to design a computer program for understanding natural language utterances incorporating mass terms, Harry Bunt provides a thorough analysis of the problem and offers an original and detailed solution. An (...) extension of classical set theory, Ensemble Theory, is defined, and this provides the conceptual basis of a framework for the analysis of natural language meaning which Dr Bunt calls Two-level model-theoretic semantics. The validity of the framework is convincingly demonstrated by the formal analysis of a fragment of English including sentences with quantified and modified mass terms. Separate chapters of the book are devoted to an axiomatic definition of Ensemble Theory and a detailed discussion of its status as a mathematical formalism. (shrink)

The format of this book is unusual, especially for a book about linguistics. The book is meant primarily as a research monograph aimed at linguists who have some background in formal semantics, e. g. Montague Grammar. However, I have two other audiences in mind. Linguists who have little or no experience of formal semantics, but who have worked through a basic mathematics for linguists course (e. g. using Wall, 1972, or Partee, 1978), should, perhaps with the help of a sympathetic (...) Montague gramma rian, be able to discover enough of how I have adapted some of the basic ideas in formal semantics to make the developments that I undertake in the rest of the book accessible. Logicians and computer scientists who know about model theoretic semantics and formal systems should be able to glean enough from Chapters I and II about linguistic concerns and techniques to be able to read the remainder of the book, again possibly with the help of a sympathetic Montague grammarian. However, readers should beware. Chapter II is not meant as a general introduction either to formal semantics or to linguistics and while much of the presentation there is going over ground that is already well covered in the literature, the particular formulation and the emphases are very much oriented to the developments to be undertaken later in the book. (shrink)