Any system used to carry information must be characterized syntactically, defining its grammatical expressions, and semantically, defining how they are used to express meaning. Its semantics is distinguished in addition from its phonology, the sound structure a system may have, and from its pragmatics, including the rules of social interaction between its users. The interface between the syntax, semantics, phonology and pragmatics of an information system is a core concern of theoretical research.
A very strict view of the relation between syntax and semantics is based on the principle of ‘compositionality’, stemming from Gottlob Frege’s (1960 [1892]) work, according to which the meaning of an expression is a function derived from the meaning of its parts and the way they are put together. Several logicians adopted it as a methodological principle in the late 1960s to characterize the syntax and semantics of a fragment of English in a logically precise way. Several other assumptions were inherited from Frege, including the idea that clauses refer to truth-values, that the substitution of logically equivalent expressions preserves truth-value in extensional contexts, but that intensional contexts require substitution of expressions with the same sense, not merely co-reference, to preserve truth-value. A flourishing research programme ensued on the logical semantics of natural language with a categorial syntax and a truth-conditional semantics. Interpretation was considered a structure preserving mapping from a syntactic tree of a clause to its truth-conditions in a settheoretic possible worlds model. The central notion of logical entailment was characterized by truth-preserving operations on the ‘logical form’ of the premises. Logical entailments disregard context, for no matter what additional information is obtained, they are always preserved. Core issues in this research programme were scope ambiguities, binding of pronouns, and generalized quantifiers.
First, scope ambiguities: quantificational expressions can be found in various linguistic categories. Noun phrases (NPs) contain ‘universal quantifiers’, every student or all books, and ‘existential quantifiers’, a student or three books. ‘Modal quantification’ is expressed in adverbials, possibly, necessarily, allegedly, hypothetically, and modal auxiliary verbs, may, must, can, might, or attitude verbs with clausal complements, doubt that, believe that, consider that and know that. Any clause that contains at least one universal and one existential quantificational expression exhibits a scope ambiguity, requiring disambiguation by systematically permuting their order in the logical form. To obtain different orders in a compositional semantics the technique of ‘quantifying in’ combines the quantifier Q1 to occur first with an expression containing the other quantifiers Q2,…, Qn and a free variable, to be bound by Q1. This proved to be widely applicable not only to linguistic quantification, but also to relative clauses and bound pronouns.
Second, binding of pronouns: a pronoun may refer to different referents, depending on the linguistic context in which it occurs. The inviting analogy between free variables in logic and pronouns in natural language constituted a very fruitful heuristic, despite its obvious shortcomings, e.g. a proper name binds a pronoun in John loves his mother, but an individual constant cannot bind a free variable in logical systems. If an NP is quantified in, it binds all free occurrences of the same variable, expressing co-reference. However, scope conflicts may arise, for instance, in the interpretation of Every student who read a book liked it. When a book is quantified into Every student who read it liked it to bind both occurrences of it, a book cannot refer to different books depending on which student is meant, but implies that all students who read a book, read the same one and liked it. Similar problems arise in expressing co-reference of individuals across intensional contexts, as in A student believed he read a novel, but John thought it was a short story. Furthermore, pronouns can be bound only by existential NPs or proper names across clauses, but in logic no quantifier can bind a variable in another formula. These three kinds of problems facing truthconditional semantics lead eventually to the dynamic semantic systems, defining interpretation as a process of incremental updates of information.
Third, generalized quantifiers: initiated by R. Montague, all NPs are interpreted by sets of sets of individuals. The universal quantifier every student requires a set containing all sets that include all students, the existential a student requires a set containing all sets that include at least one (possibly different) student, and a proper name John requires a set of all sets that have John as an element. All kinds of natural, non-logical determiners lend themselves to such set-theoretic interpretation, enriching our understanding of the variety of quantification in natural languages.
After two decades the truth-conditional approach proved to face insuperable technical difficulties in accounting for the linguistic principles binding pronouns within a clause as well as between clauses and for the meaning of any context-sensitive expressions. To remedy this, the concept of interpretation had to be changed fundamentally, argued some semanticists in the early 1980s, including J.Barwise, I.Heim, H.Kamp and B.Partee. Rather than consider it a static relation between a syntactic analysis of an isolated expression and its truth-conditions in a model, interpretation should be viewed as a dynamic process updating the information available at a certain stage, using connected discourse or texts. The reference of a pronoun and, in general, the content of an expression often depend on the current context, the information available, and the external situation in which it is used. Various logical systems, designed for dynamic interpretation, broadened the concerns of semantics beyond coreference of pronouns, scope ambiguities and logical entailments, to include new topics on how context is affected by interpretation. Core issues in this research programme of dynamic semantics are dynamic binding of pronouns, context shifts, and hybrid forms of reasoning.
First, dynamic binding of pronouns: co-reference of pronouns within a clause as well as between clauses in discourse motivated the development of dynamic semantics. Some systems require a pronoun to co-refer with a definite description in which the information about the intended referent is accumulated. Other systems design structured representations of the information available so that only some of the descriptive conditions determine the referent. This constitutes a very lively area of research, combining logical and computational techniques with linguistic data.
Second, context shifts: a dynamic semantics must determine how information is preserved while the interpretation proceeds, requiring a precise understanding of how the presuppositions of expressions (conditions which must be satisfied for the expression to be evaluated) are projected in a clause, and preserved or lost during the interpretation of discourse. This issue was raised originally in linguistic theory by L.Karttunen and S.Peters in the 1970s, as a pragmatic issue, but resurfaced in dynamic semantics. The interpretation of indefinites, and tense and aspect also gives rise to specific rules for shifting contexts when descriptive information is given about different individuals or events.
Third, hybrid forms of reasoning: reasoning may mix descriptive information with assumptions on what the words mean, how causal correlations are structured, what we see or hear and our private information. To design logical systems that model such hybrid forms of inference constitutes a major challenge for dynamic semantics. This concept of inference must be sensitive to various forms of context-change, for different conclusions are drawn at different times depending on what information is available. Though logical entailments are immune to changes in context, our reasoning is not, even if linguistic means exist to immunize information against context-sensitivity.
In dynamic semantics the old boundary disputes between syntax, phonology, semantics and pragmatics have turned into more fruitful collaborations on representational interfaces of the modular system. The information one expresses in using language may also depend on intonation, social status and power, on traditions and cultural values. Ultimately, a comprehensive semantic theory of meaning and interpretation should encompass all such issues and yet represent a precise system of inference.
Alice G.B.ter Meulen
Indiana University
Reference
Frege, G. (1960 [1892]) ‘On sense and reference’, in P.Geach and M.Black (eds) Translations from the Philosophical Writings of Gottlob Frege, Oxford.
Further reading
Barwise, J. and Perry, J. (1983) Situations and Attitudes, Cambridge, MA.
Benthem, J. van (1986) Essays in Logical Semantics, Dordrecht, The Netherlands.
Davidson, D. and Harman, G. (1972) Semantics of Natural Language, Dordrecht, The Netherlands.
Gårdenfors, P. (ed.) (1987) Generalized Quantifiers: Linguistic and Logical Approaches, Dordrecht, The Netherlands.
Kamp, H. and Reyle, U. (1993) From Discourse to Logic, Dordrecht, The Netherlands.
Keenan, E. and Faltz, L. (1985) Boolean Semantics of Natural Language, Dordrecht, The Netherlands.
Meulen, A. ter (1994) The Representation of Time in Natural Language: The Dynamic Interpretation of Tense and Aspect, Cambridge, MA.
Montague, R. (1972) Formal Philosophy, ed. R.Thomason, New Haven, CT.
Oehrle, D., Bach, E. and Wheeler, D. (eds) (1988) Categorial Grammars and Natural Language Structures, Dordrecht, The Netherlands.
Partee, B., Meulen, A. ter and Wall R. (1990) Mathematical Methods in linguistics, Dordrecht, The Netherlands.
