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Tarskian model theory is almost universally understood as a formal counterpart of the preformal notion of semantics, of the “linkage between words and things”. The wide-spread opinion is that to account for the semantics of natural language is to furnish its settheoretic interpretation in a suitable model structure; as exemplified by Montague 1974.

An essential part of natural language understanding, and hence of formal semantics, is the interpretation of temporal expressions. But the very variety of temporal phenomena---such as tense, aspect, aktionsart, temporal adverbials, and the temporal structure of extended text---has tended to result in formal semantic analyses using a wide variety of formal tools, often of a complex nature. It seems important to try and find unifying perspectives on this work, and above all, to try and gain some insight into the logical resources needed to deal with natural language temporal phenomena.

Formal pragmatics plays an important, though secondary, role in modern analytical philosophy of language: its aim is to explain how context can affect the meaning of certain special kinds of utterances. During recent years, the adequacy of formal tools has come under attack, often leading to one or another form of relativism or antirealism. Our aim will be to extend the critique to formal pragmatics while showing that sceptical conclusions can be avoided by developing a different approach to the issues. In particular, we will show that formal pragmatics cannot provide a complete account of how context affects the meaning of utterances, both on its own terms and when faced with evidence of important aspects of natural languages. The focal issue is the relevant kind of context in which pragmatics should examine utterances. Our contention will be that the relevant context of an utterance is determined by the function of that utterance, this function being dependent upon the primary function of language – to convey information. We will argue that the functions of utterances and of language are too broad to be caught by the tools of formal pragmatics of the sort advocated by Montague (1968, 1974), which are an extension the methods of traditional model-theoretic semantics. The particular formal approach we will use as the main example is David Kaplan’s position (1979, 1989), an extension of Montague’s program.

Formal pragmatics plays an important, though secondary, role in modern analytical philosophy of language: its aim is to explain how context can affect the meaning of certain special kinds of utterances. During recent years, the adequacy of formal tools has come under attack, often leading to one or another form of relativism or antirealism.1 Our aim will be to extend the critique to formal pragmatics while showing that sceptical conclusions can be avoided by developing a different approach to the issues. In particular, we will show that formal pragmatics cannot provide a complete account of how context affects the meaning of utterances, both on its own terms and when faced with evidence of important aspects of natural languages. The focal issue is the relevant kind of context in which pragmatics should examine utterances. Our contention will be that the relevant context of an utterance is determined by the function of that utterance, this function being dependent upon the primary function of language – to convey information. We will argue that the functions of utterances and of language are too broad to be caught by the tools of formal pragmatics of the sort advocated by Montague (1968, 1974), which are an extension the methods of traditional model-theoretic semantics.2 The particular formal approach we will use as the main example is David Kaplan’s position (1979, 1989),3 an extension of Montague’s program.

This book provides a systematic study of three foundational issues in the semantics of natural language that have been relatively neglected in the past few decades. focuses on the formal characterization of intensions, the nature of an adequate type system for natural language semantics, and the formal power of the semantic representation language proposes a theory that offers a promising framework for developing a computational semantic system sufficiently expressive to capture the properties of natural language meaning while remaining computationally tractable written by two leading researchers and of interest to students and researchers in formal semantics, computational linguistics, logic, artificial intelligence, and the philosophy of language.

Semantics is concerned with meaning: what meanings are, how meanings are assigned to words, phrases and sentences of natural and formal languages, and how meanings can be combined and used for inference and reasoning. The goal of this chapter is to introduce computational linguists and computer scientists to the tools, methods, and concepts required to work on natural language semantics. Semantics, while often paired with pragmatics, is nominally distinct. On a traditional view, semantics concerns itself with the compositional buildup of meaning from the lexicon to the sentence level whereas pragmatics concerns the way in which contextual factors and speaker intentions affect meaning and inference (see, e.g., Potts to appear in this volume). Although the semantics-pragmatics distinction is historically important, and continues to be widely adopted, in practice it is not clearcut. Work in semantics inevitably involves pragmatics and vice versa. Furthermore, it is not a distinction which is of much relevance for applications in computational linguistics. This chapter is organized as follows. In sections 2 and 3 we introduce foundational concepts and discuss ways of representing the meaning of sentences, and of combining the meaning of smaller expressions to produce those sentential meanings. In section 4 we discuss the representation of meaning for larger units, especially with respect to anaphora, and introduce two formal theories that go beyond sentence meaning: Discourse Representation Theory and Dynamic Semantics. Then, in section 5 we discuss temporality, introducing event semantics, and describing standard approaches to the semantics of tense and aspect. Section 6 concerns the tension between the surface-oriented statistical methods characteristic of much of computational linguistics and the more abstract methods typical of formal semantics and includes discussion of a range of phenomena for which it seems particularly important to utilize insights from formal semantics..

Formal semantics is an approach to SEMANTICS1, the study of meaning, with roots in logic, the philosophy of language, and linguistics, and since the 1980’s a core area of linguistic theory. Characteristics of formal semantics to be treated in this article include the following: Formal semanticists treat meaning as mind-independent (though abstract), contrasting with the view of meanings as concepts “in the head” (see I-LANGUAGE AND E-LANGUAGE and MEANING EXTERNALISM AND INTERNALISM); formal semanticists distinguish semantics from knowledge of semantics (Lewis 1975, Cresswell 1978), which has consequences for the notion of semantic COMPETENCE. A central part of the meaning of a sentence on this approach is its TRUTH CONDITIONS, and most although not all formal semantics is model-theoretic, relating linguistic expressions to model-theoretically constructed semantic values cast in terms of truth, REFERENCE, and possible worlds. This sets formal semantics apart from approaches which view semantics as relating a sentence just to a representation on another linguistic “level” (LOGICAL FORM) or a representation in an innate LANGUAGE OF THOUGHT. The formal semanticist could accept such representations as an aspect of semantics but would insist on asking what the model-theoretic semantic interpretation of the given representationlanguage is (Lewis 1970). Formal semantics is centrally concerned with COMPOSITIONALITY at the SYNTAX-SEMANTICS INTERFACE, how the meanings of larger constituents are built up from the meanings of their parts on the basis of their syntactic structure, and with the relation between compositional SENTENCE MEANING and meaning in discourse.

The relationships between logic and natural language are multiverse. On the one hand, logic is a theory of argumentation, proving and giving reasons, and such activities are primarily carried out in natural language. This means that logic is, in a certain loose sense, about natural language. On the other hand, logic has found it useful to develop its own linguistic means which sometimes in a sense compete with those of natural language. This has led to the situation where the systems of logic can be taken as interesting "models" of various aspects of natural language. Â Â Â Â Â Â Â The alliance of logic and linguistics has flowered especially from the beginning of the seventies, when scholars like Montague, Lewis, Cresswell, Partee and others showed how semantics of natural language can be explicated with the help certain suitable logical calculi and the corresponding model theory. (Montague went so far as to claim that in view of this, there is no principal difference between natural and formal languages - but this is, as far as I can see, rather misguiding.) Since that time, the interdisciplinary movement of formal semantics (associating not only linguists and logicians, but also philosophers, computer scientists, cognitive psychologists and others) has yielded a rich repertoire of formal theories of natural language, some of them (like Hintikka's game-theoretical semantics or the dynamic logic of Groenendijk and Stokhof) being based directly on logic, others (like the situation semantics of Barwise and Perry or DRT of Kamp) exploiting different formal strategies. Â Â Â Â Â Â Â Moreover, although the enterprise of formal semantics (i.e. of modeling natural language semantics by means of certain formal structures) seems to be the principal point of contact between linguistics and logic, there are also other cooperative enterprises. One of the most fruitful ones seems to be the logical analysis of syntax, which has resulted from elaboration of what was originally called categorial grammar. (However, even this enterprise can be seen as importantly stimulated by Montague.) Â Â Â Â Â Â Â All in all, the region in which logic and theoretical linguistics overlap has grown both in size and fertility..

Formal semantics is an enterprise which accounts for meaning in formal, mathematical terms, in the expectation of providing a helpful explication1 of the concept of the meaning of specific word kinds (such as logical ones), or of words and expressions generally. Its roots go back to Frege, who proposed exempting concepts, meanings of predicative expressions, from the legislation of psychology and relocating them under that of mathematics. This started a spectacular enterprise, fostered at first within formal logic and later moving into the realm of natural languages, and featuring a series of eminent scholars, from Tarski and Carnap to Montague and David Lewis. Partly independently of this, Frege set the agenda for a long-term discussion of the question of what a natural language is, his own contribution being that language should be seen not as a matter of subjective psychology, but rather as a reality objective in the sense in which mathematics is objective. His formal semantics, then, was just an expression of this conception of language. And many theoreticians now take it for granted that formal semantics is inseparably connected with a Platonist conception of language. Moreover, the more recent champions of formal semantics, Montague and David Lewis, took for granted that natural language is nothing else than a structure of the very kind envisaged by the theories of formal logicians. While Montague claims quite plainly that there is no substantial difference between formal and natural languages ("I reject the contention," he says, 1974, p. 188, "that an important theoretical difference exists between formal and natural languages"), Lewis states that it is fully correct to say that a linguistic community entertains a language in the form of a mathematical structure ("we can say", states Lewis, 1975, p..

One way of describing the enterprise of natural language semantics is by analogy with interpreted formal languages, e.g. the language of arithmetic interpreted on the natural numbers. English is then the formal language consisting of the well-formed sentences of English interpreted on the structure we happen to nd around us. The business of the natural language semanticist is to describe the correlation of the formal expressions with that structure. This paper is directed against this particular interpretation 1 of the enterprise of logical natural language semantics.