Copyright © 1999 Massachusetts Institute of Technology
The logical form of a sentence (or utterance) is a formal representation of its logical structure -- that is, of the structure that is relevant to specifying its logical role and properties. There are a number of (interrelated) reasons for giving a rendering of a sentence's logical form. Among them is to obtain proper inferences (which otherwise would not follow; cf. Russell's theory of descriptions), to give the proper form for the determination of truth-conditions (e.g., Tarski's method of truth and satisfaction as applied to quantification), to show those aspects of a sentence's meaning that follow from the logical role of certain terms (and not from the lexical meaning of words; cf. the truth-functional account of conjunction), and to formalize or regiment the language in order to show that it is has certain metalogical properties (e.g., that it is free of paradox or that there is a sound proof procedure).
Logical analysis -- that is, the specification of logical forms for sentences of a language -- presumes that some distinction is to be made between the grammatical form of sentences and their logical form. In LOGIC, of course, there is no such distinction to be drawn. By design, the grammatical form of a sentence specified by the syntax of, for instance, first-order predicate logic simply is its logical form. In the case of natural language, however, the received wisdom of the tradition of FREGE, Russell, Wittgenstein, Tarski, Carnap, Quine, and others has been that on the whole, grammatical form and logical form cannot be identified; indeed, their nonidentity has often been given as the raison d'être for logical analysis. Natural languages have been held to be insufficiently specified in their grammatical form to reveal directly their logical form, and that no mere paraphrase within the language would be sufficient to do so. This led to the view that, as far as natural languages were concerned, logical analysis was a matter of rendering sentences of the language in some antecedently defined logical (or formal) language, where the relation between the sentences in the languages is to be specified by some sort of contextual definition or rules of translation.
In contemporary linguistic theory, there has been a continuation of this view in work inspired largely by Montague (especially, Montague 1974). In large part because of technical developments in both logic (primarily in the areas of type theories and POSSIBLE WORLDS SEMANTICS) and linguistics (with respect to categorial rule systems), this approach has substantially extended the range of phenomena that could be treated by translation into an interpreted logical language, shedding the pessimism of prior views as to how systematically techniques of logical analysis can be formally applied to natural language (see Partee 1975; Dowty, Wall, and Peters 1981; Cooper 1983). Within linguistic theory, however, the term "logical form" has been much more closely identified with a different view that takes natural language to be in an important sense logical, in that grammatical form can be identified with logical form. The hallmark of this view is that the derivation of logical forms is continuous with the derivation of other syntactic representations of a sentence. As this idea was developed initially by Chomsky and May (with precursors in generative semantics), the levels of syntactic representation included Deep Structure, Surface Structure, and Logical Form (LF), with LF -- the set of syntactic structures constituting the "logical forms" of the language -- derived from Surface Structure by the same sorts of transformational rules that derived Surface Structure from Deep Structure.
As with other approaches to logical form, quantification provides a central illustration. This is because, since Frege, it has been generally accepted that the treatment of quantification requires a "transformation" of a sentence's surface form. On the LF approach, it was hypothesized (originally in May 1977) that the syntax of natural languages contains a rule -- QR, for Quantifier Raising -- that derives representations at LF for sentences containing quantifier phrases, functioning syntactically essentially as does WH-MOVEMENT (the rule that derives the structure of "What did Max read?"). By QR, (1) is derived as the representation of "Every linguist has read Syntactic Structures" at LF, and because QR may iterate, the representations in (2) for "Every linguist has read some book by Chomsky".
With the aid of the syntactic notions of "trace of movement" (t1, t2) and "c-command" (both of which are independently necessary within syntactic theory), the logically significant distinctions of open and closed sentence, and of relative scope of quantifiers, can be easily defined with respect to the sort of representations in (1) and (2). Interpreting the trace in (1) as a variable, "t1 has read Syntactic Structures" stands as an open sentence, falling within the scope of the c-commanding quantifier phrase "every linguist1;" similar remarks hold for (2), except that (2a) and (2b) can be recognized as representing distinct scope orderings of the quantifiers (see Heim 1982; May 1985, 1989; Hornstein and Weinberg 1990; Fox 1995; Beghelli and Stowell 1997; and Reinhart 1997 for further discussion of the treatment of quantification within the LF approach). A wide range of arguments have been made for the LF approach to logical form. Illustrative of the sort of argument presented is the argument from antecedent-contained deletion (May 1985). A sentence such as "Dulles suspected everyone that Angleton did" has a verb phrase elided (its position is marked by the pro-form "did"). If, however, the ellipsis is to be "reconstructed" on the basis of the surface form, the result will be a structural regress, as the "antecedent" verb phrase, "suspected everyone that Angleton did" itself contains the ellipsis site. However, if the reconstruction is defined with respect to a structure derived by QR:
the antecedent is now the VP "suspected t," obtaining, properly, an LF-representation comparable in form to that which would result if there had been no deletion:
Among other well-known arguments for LF are weak crossover (Chomsky 1976), the interaction of quantifier scope and bound variable anaphora (Higginbotham 1980; Higginbotham and May 1981), superiority effects with multiple wh-constructions (Aoun, Hornstein, and Sportiche 1981) and wh-complementation in languages without overt wh-movement (Huang 1982). Over the past two decades, there has been active discussion in linguistic theory of the precise nature of representations at LF, in particular with respect to the representation of binding (see BINDING THEORY) as this pertains to quantification and ANAPHORA, and of the semantic interpretation of such representations (cf. Larson and Segal 1995). This has taken place within a milieu of evolving conceptions of SYNTAX and SEMANTICS and has led to considerable refinement in our conceptions of the structure of logical forms and the range of phenomena that can be analyzed. Constant in these discussions has been the assumption that logical form is integrated into syntactic description generally, and hence that the thesis that natural languages are logical is ultimately an empirical issue within the general theory of syntactic rules and principles.
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Copyright © 1999 Massachusetts Institute of Technology