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Logical Form in Linguistics




Entry for MIT Encyclopedia of Cognitive Sciences


The LOGICAL FORM of a sentence (or utterance) is a formal representation of its logical structure; that is, of the structure which 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 which 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 can not be identified; indeed, their non-identity has often been given as the raison d'etre 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-world semantics) and linguistics (with respect to categorial rule systems), this approach has substantially extended the range of phenomena which 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 which 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 structure constituting the "logical forms" of the language - derived from Surface Structure by the same sorts of transformational rules which 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 - 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 since QR may iterate, the representations in (2) for "Every linguist has read some book by Chomsky":

(1) [ every linguist1 [ t1 has read Syntactic Structures]]

(2)a [ every linguist1 [ some book by Chomsky2 [ t1 has read t2]]]

b [ some book by Chomsky2 [ every linguist1 [ t1 has read t2]]]

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 with 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:

(6) everyone that Angleton did [Dulles suspected t],

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:

(7) everyone that Angleton suspected t [Dulles suspected t]

Among other well-know 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, 1980).

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 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 range of phenomena which 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 an ultimately an empirical issue within the general theory of syntactic rules and principles.


Aoun, J., N. Hornstein and D. Sportiche (1981) Some Aspects of Wide Scope Quantification. Journal of Linguistic Research, 1, 69 - 95.

Beghelli, F. and T. Stowell (1997) Distributivity and Negation: The Syntax of Each and Every. In A. Szabolcsi, ed., Ways of Taking Scope Dordrecht: Kluwer.

Chomsky, N. (1976) Conditions on Rules of Grammar. Linguistic Analysis, 2, 303 - 351.

Cooper, R. (1983) Quantification and Syntactic Theory. Dordrecht: Reidel.

Dowty, D., Wall, R.E., and Peters, S. (1981) Introduction to Montague Semantics. Dordrecht: Reidel.

Fox, D. (1995) Economy and Scope. Natural Language Semantics, 3, 283 - 341.

Higginbotham, J, (1980) Pronouns and Bound Variables. Linguistic Inquiry, 11, 679 - 708.

Higginbotham, J. and R. May (1981) Questions, Quantifiers and Crossing. The Linguistic Review, 1, 41 - 79.

Heim, I. (1982) The Semantics of Definite and Indefinite Noun Phrases. Doctoral dissertation, University of Massachusetts, Amherst, Massachusetts.

Hornstein, N. and A. Weinberg (1990) The Necessity of LF. The Linguistic Review, 7, 129 - 168.

Huang, C.-T. J. (1982) Logical Relations in Chinese and the Theory of Grammar. Doctoral dissertation, MIT, Cambridge, Ma.

Larson, R. and G. Segal Knowledge of Meaning. Cambridge, MA: MIT Press.

May, R. (1977) The Grammar of Quantification. Doctoral dissertation, MIT, Cambridge, Ma. (Facsimile edition published by Garland Publishing, New York, 1991.)

May, R. (1985) Logical Form: Its Structure and Derivation. Cambridge, MA: MIT Press,

May, R. (1989) Interpreting Logical Form. Linguistics and Philosophy. 12, 387 - 435.

. Montague, R. (1974) The Proper Treatment of Quantification in Ordinary English. In R. Thomason (Ed.), Formal Philosophy: Selected Papers of Richard Montague. New Haven: Yale University Press.

Partee, B. (1975) Montague Grammar and Trasnformational grammar. Linguistic Inquiry, 6, 203-300.

Reinhart, T. (1997) Quantifier Scope: How Labor in Divided between QR and Choice Functions. Linguistics and Philosophy, 20, 399 - 467.


Chomsky, N. (1995) The Minimalist Program. Cambridge, MA: MIT Press.

Fiengo, R. and R. May (1994) Indices and Identity. Cambridge, MA: MIT Press.

Frege, G. (1892) On Sense and Reference. (Translated by M. Black.) In P. Geach and M. Black (Eds.), Translations from the Philosophical Writings of Gottlob Frege. Oxford: Basil Blackwell.

Hornstein, N. (1984) Logic as Grammar Cambridge, MA: MIT Press.

Hornstein, N. (1995) Logical Form. Oxford: Blackwell.

Jaeggli, O. (1980) On Some Phonologically-Null Elements of Syntax. Doctoral disserataion, MIT, Cambridge, Ma.

Koopman, H. and D. Sportiche (1982) Variables and the Bijection Principle.The Linguistic Review, 2, 139 - 161

Lakoff, G. (1972) On Generative Semantics. In D. Steinberg and L. Jakobovits (Eds.), Semantics. Cambridge: Cambridge University Press, 232 -296.

May, R. (1991a) Syntax, Semantics and Logical Form. In A. Kasher (Ed), The Chomskyan Turn Oxford: Basil Blackwell.

May, R. (1991b) Linguistic Theory and the Naturalist Approach to Semantics. In Donna Jo Napoli and Judy Kegl (Eds), Bridges Between Psychology and Linguistics: A Swarthmore Festschrift for Lila Gleitman. Hillsdale, NJ: Lawrence Erlbaum Associates.

Pesetsky, D. (1987) Wh-in-situ: Movement and Selective Binding. In E. Reuland and A. ter Meulen, eds., The Representation of (In)definiteness. Cambridge, MA: MIT Press.

Quine, W.V.O. (1960) Word and Object. Cambridge, MA: MIT Press.

Russell, B. (1905) On Denoting. Mind, 14, 479-493.

Wittgenstein, L. (1922) Tractatus Logico-Philosophicus. (Translated by D.F. Pears and B.F. McGuiness.). London: Routledge and Kegan Paul.

Robert May

Department of Linguistics

School of Social Sciences

University of California

Irvine, CA 92697

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