Johan van Benthem and Alice ter Meulen, eds.
Handbook of Logic and Language

Elsevier Science B.V. / The MIT Press 1997, 
Oxford/Shannon/Tokio / Cambridge (Massachusetts).
xxiii + 1247 pp.

Reviewed by 
Jaroslav Peregrin

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.
        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.
        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.)
        All in all, the region in which logic and theoretical linguistics overlap has grown both in size and fertility. And so the task set out by the book under review, namely a comprehensive survey of this field, is far from simple; and the authors of the volume had to produce not less than some twelve hundreds pages of text to carry it out. Fortunately, the book has such a distinguished cast that the guide through the realms of logicolinguistics which the reader gets is genuinely firsthand. In view of this, the book aspires to become a real Principia Semantica of our age.
        The book is divided into three parts: Frameworks, General Topics and Descriptive Topics, and into twenty chapters. The opening chapter of the book is devoted (what else?) to Montague Grammar; it is written jointly by Barbara Partee and Herman Hendriks. The ninety pages of this contribution offer an excellent and deep introduction into both the motives behind Montague's deed ("Montagovian revolution", as the authors term it), and the resulting theory; and add a comprehensive bibliography of Montagovian books and papers. The twenty five years which have elapsed since the publication of Montague's crucial articles enable the authors to assess the real import and impact of this revolution. 
        The next chapter, Michael Moortgart's
Categorial Type Logics, focuses on the relatively recent, but intensively flourishing, enterprise of applying the methods of logic to syntactic structure. The basic idea of this enterprise is that of treating syntactic combination as inference: we read the fact that expressions of the respective categories A1,...,An combine into an expression of the category A as, in effect, A1,...,An implies A. Given suitable ways of categorial indexings, what we gain are various kinds of interesting logical systems. Moortgart's exposition of the state of the art is detailed and exhaustive.
        The third chapter, written by Jan van Eijck and Hans Kamp, deals with the broad theme of Representing discourse in context; it is in fact largely devoted to the popular framework of Kamp's discourse representation theory. The underlying idea of this framework is that "each new sentence of a discourse is interpreted in the context provided by the sentences preceding it" (p. 181). This yields the theory which is well known for its illustrious box-based formalism (an aspect which is perhaps more attractive, for a working linguist, than it is usually assumed), but which has also solid formal backing - and this is what the authors demonstrate in this chapter.
        The next chapter is devoted to Situation Theory - the metaphysical, or model-theoretical part of the once famous, but now perhaps not so much popular, Situation Semantics. As Jerry Seligman and Lawrence S. Moss, the authors of this chapter, put it, Situation Theory investigates "foundational questions about the emerging [from Barwise and Perry's work] ontology, with the hope of providing a unified mathematical framework in which the linguists' work could be interpreted" and it "was intended to stand to Situation Semantics as Type Theory stands to Montague Grammar" (241). The task of the authors was a difficult one, for after the short heyday of Barwise's and Perry's
proposal the enterprise splintered into a couple of different enterprises which had to be reconstituted into a single framework. But I think they succeeded - they offered a rich gallery of metaphysical denizens borne by situation theory, and a rich mathematics to handle them.
        The penultimate chapter of the first part of the book presents an introduction to GB theory, the recent outgrowth of the Chomskian approach to language. The author of this chapter is James Higginbotam. This is a slightly different kind of semantic theory: neither a model-theoretic, nor a set-theoretic reconstruction of meanings or representations behind linguistic items, but rather a theory of semantics as one of the layers of human language faculty - as argued for by Chomsky and his followers. And it also does not rest on logic (with the exception of the usage of the term 'logical form', which was chosen by Chomsky, I think unhappily, for the semantic layer). However, although the Chomskian approach differs considerably from those inspired by logic, the latter would hardly be possible without the former
's prior 'mathematization' of linguistics. And besides this, the great majority of people involved with the theory of natural language are in this or another way significantly influenced by the Chomskian picture; so the elements of the picture often loom even in theories which are otherwise developed from different perspectives.
        The closing chapter of the foundational part of the book is devoted to the framework of Game-theoretical semantics, a dynamic semantic framework stalwartly championed and elaborated by Jaako Hintikka since the beginning of the seventies. The present contribution is written by Hintikka together with Gabriel Sandu. Hintikka originally considered the fact that standard logic allows for a game-theoretical interpretation (its formulas being construed as encodings of certain games between 'Me' and 'Nature') and concluded that there is no decisive reason to restrict oneself to precisely those kinds of games which happened to be catered for by this very logic. Hintikka's and Sandu's current result is what they call independence-friendly logic: a logico-semantical system superficially close to standard predicate calculus, but possessing a number of remarkable logical properties (the most shocking of them being the ability to express its own truth predicate).
        I think that the six chapters of the first part of the Handbook, which are to cover the basic logicolinguistic frameworks, have been chosen with real ingenuity - they encompass the most substantial and the most self-contained systems of 'formal' and 'logical' approaches to natural language and especially its semantics. First, there are three paradigmatic frameworks which can be seen as representing the three most important stages of development which have occurred since the original marriage of linguistics and logic within Montague's writings: the first of them, which can be called intensional and which culminated in the seventies, is represented by Montague Grammar, the second, hyperintensional, one, whose heyday was roughly the following decade, can be seen as represented by Situation Semantics, whereas the third, dynamic, paradigm, whose culmination we are currently witnessing, is represented by DRT. Besides them, there is the current stage of the not to be neglected Chomskian approach to language, which has opened the door for formal methods in linguistics and in various ways deeply influenced many of the more logical approaches. And I also agree that the game-theoretical semantics is a framework worth being included: this approach, though perhaps less popular than the other, exploited the dynamic view of language long before it became common. 
        The second part of the book, General Topics, is opened by the chapter on Compositionality, written by Theo M. V. Janssen. Janssen explains what compositionality is (discussing various kinds of formulations of the principle of compositionality), gives examples and then outlines mathematical theories of compositionality. He concludes is that semantics can be either compositional or non-compositional, and that there are decisive reasons to prefer compositional theories - so that compositionality is a substantial desideratum of a good semantic theory. My impression is that despite the exhaustive discussions of many aspects of compositionality which Janssen presents, he fuses together, unhappily, two different problems: the philosophical problem of the status of compositionality (is compositionality constitutive to the very concept of meaning, or is compositionality only a contingent property of some meanings?) and a mathematical question about properties of compositional mappings (which may be construed, relatively noncontroversially, as homomorphisms of certain kinds of algebras). Janssen gives a thorough answer to the latter question, but his claim that compositionality is not essential is ambiguous and in both senses problematical: if it is to be interpreted as saying that there are not only homomorphic mappings, then it is a platitude not worth stating, and if it is to be interpreted as claiming that compositionality is not constitutive of meaning, then it would have to be supported by a discussion of what meaning is - a discussion which Janssen does not offer.
        Chapter VIII, written by William C. Rounds, describes the framework of Feature Logic. This logic was devised to deal with formal structures emerging from the formal analysis of natural language which can be seen as sets of attribute-value pairs. Rounds' contribution is a detailed overview of the corresponding formal apparatus.
        Raymond Turner, the author of Chapter IX called Types, addresses the general logical concept of type, as a semantic counterpart of the syntactic concept of category. (The concept was introduced into modern logic by Russell, whose name, curiously enough, is not mentioned in Turner's paper.) He introduces the basic logical formalism which can be taken as framing general theory of types, namely Church's typed lambda-calculus, and discusses its relationship to other logical formalisms, like categorial logic or higher order predicate calculus. Then he discusses a number of problems connected with the idea of a type: various kinds of type-polymorphism, constructivity etc.
        In Chapter X, Dynamics, Reinhard Muskens, Johan van Benthem and Albert Visser analyze the foundations of the current widespread tendencies toward "dynamization" of semantics. The common idea behind them is recognized to be that of context change: like a command of a computer program, a natural language utterance comes to be seen not as statically expressing a content, but as dynamically changing the current context or information state. The authors then discuss the ways in which this general idea is captured within various kinds of semantic theories: the most common way seems to be to see the change of context as the change of assignment of values to some variable elements of a representation (this is the way of Kamp's discourse representation theory, Heim's file-change semantics and Groenendijk and Stokhof's dynamic predicate logic), but it is also possible, as the authors point out, to construe it in terms of change of the attentional state, the change of assumptions, or the change of belief. (The last perspective then yields the intensively studied logical theory of belief-revision.) The formal aspects of dynamic logical frameworks are then discussed in detail. 
        Chapter XI, written by Jens Erik Fenstad, analyzes the concept of Partiality; on a very general level, perhaps too general. The range of phenomena which the author sees as instances of partiality is vast: truth-value gaps, elliptical utterances, presuppositions, incomplete knowledge, partial algorithms and many more. Unfortunately, this makes the concept of partiality so general that it becomes almost empty of content. The most interesting part of the chapter seems to be that which concentrates on the clearly graspable topic of truth-value gaps and partial logic.
        Chapter XII bears the title of Mathematical Linguistics and Proof Theory and is written by Wojciech Buszkowski; it partly overlaps with Mortgaart's exposition of categorial type logic from Part I of the book. The author sees mathematical linguistics, originally mostly the theory of syntax of formal languages based on generative grammars and automata, as now married with proof theory (in the way analyzed by Moortgart).  
        Chapter XIII slightly departs from the other topics of this part, it does not provide a theory of an aspect of language, but rather of language learning. The authors are Daniel Osherson, Dick de Jongh, Eric Martin and Scott Weinstein; and the title of the chapter is Formal Learning Theory. What is in focus are various models of knowledge acquisition and especially language learning, often built with the help of logical and model-theoretical tools.
        Richmond H. Thomason, the author of the last, fourteenth, chapter of this part, addresses the topic of Nonmonotonicity in Linguistics. His contribution consists of the discussions of various settings which may lead to nonmonotonic inference, of formal apparatuses which may be employed to account for it (especially feature structures), and of the case studies of nonmonotonicity within phonology, morphology, syntax and semantics.
        On the whole, I think that Part II is slightly less well-balanced than Part I. First, there seem to exist "categorical differences" between the topics of the individual contributions. The core of the contributions concentrate on particular general concepts (compositionality, types, dynamics, partiality, nonmonotonicity), while others rather discuss specific fields (mathematical linguistics, learning theory) or even specific frameworks (feature logics). Besides this, some place their emphasis on the analysis of the very concept they address, whereas others concentrate on the corresponding mathematics. However, this is not meant as a real criticism - it is only a matter of the ingenious layout of Part I having aroused expectations of the same ingeniousness of organization within subsequent parts.
        The third part of the book, Descriptive topics, contains contributions addressing various specific aspects of language and of those formal theories which have been developed to account for these aspects. The first of this part's chapters is devoted to Generalized Quantifiers; the authors are Edward L. Keenan and Dag
Westert?hl. The contribution gives the motivation for developing a theory of generalized quantifiers and summarizes the basics of the corresponding mathematics. However, some of the aspects of the authors' exposition should perhaps be more clearly explained: I doubt that I am alone in failing to see, e.g., why, if we abbreviate [P(E)->2] as <1>, we should abbreviate [P(E)->[P(E)->2]] as <1,1>; or what is the rationale behind seeing the sentence Most critics reviewed just three films as a single quantifier most ... just three applied to critics, films and reviewed.
        Mark Steedman's chapter Temporality accounts for its subject in an extraordinarily illuminating way. It divides the theme of temporality into three basic compartments: (i) temporal ontology, which addresses all kinds of entities which are being employed to account for temporality (such as activities, accomplishments, achievements); (ii) temporal relations, which accounts for the types of relationships which may be considered to obtain between entities of these kinds; and (iii) temporal reference, which deals with the reference points of utterances and with temporal anaphora.
        Also the next contribution, devoted to Presuppositions and written by David Ian Beaver, belongs to the best chapters of the book: it not only analyzes all relevant aspects of the phenomenon in question and all important ways to account for it, but presents the analysis in an extremely systematic and comprehensible way. Beaver first distinguishes between semantic presuppositions (A is presupposed by B if B cannot have a truth value unless A is true) and pragmatic presuppositions (A is a pragmatic presupposition of a speaker S if S simply takes A for granted), then overviews locutions which trigger presuppositions and then goes on to discuss, in detail, the formal means used to account for presuppositions. These means are basically of two kinds: static (multivalence and partiality) and dynamic (based on contexts and context-change potentials). 
        The next, shorter chapter, Plurals and collectivity by Jan
Tore L?nning, discusses semantic analysis of plural nouns. Within the framework of standard logic, the author discerns two basic kinds of approaches: either to take the denotations of plurals as some suitable higher-order objects, or to take them simply as members of the universe, in which case the universe is to be given a 'mereological' structure. Ways which bypass standard logic altogether are also mentioned.
        The penultimate chapter of the book concentrates on Questions and is written by Jeroen Groenendijk and Martin Stokhof. The authors consider two possible approaches to questions: the pragmatic approach (which amounts to accounting for questions on the level of speech acts, not on the level of semantic content) and the semantic one (which has it that questions have semantic content in the same way as assertions do and can be analyzed by analyzing the specific nature of this content). Groenendijk and Stokhof discuss various logical, computational and linguistic theories based on either of the two approaches.
        The closing chapter, by Francis Jeffry Pelletier and Nicholas Asher deals with the phenomena of Generics and Defaults. Its authors expose the peculiar status of generics (which are in a sense
'law-like' despite allowing for exceptions) and survey the usual ways to account for them (such as relevant quantification, approaches based on prototypes or stereotypes etc.). Of these, attend primarily to default logic. At the end of the paper they develop their own formal theory of generics.
        The handbook is an extremely successful attempt at a state of the art summary of the interdisciplinary field which centers around the intersection of logic and linguistics (and partly also philosophy of language, computer science etc.) All the contributions are written by competent authors; many of them probably by the most competent ones. Moreover, they are almost all written in the disciplined way which validates them as true encapsulations of the state of the art of the problematic they address, rather than as vehicles of popularization for their authors. This makes the book into an indispensable compendium for anyone working with language. 
        However, it seems to me that it is precisely such a representative survey of the whole field in question, and the possibility of seeing the whole field from a 'bird's eye view' it offers, which could (and perhaps should) also provoke some very general, foundational (and maybe sometimes heretical) questions about the nature of the whole enterprise. I myself am plagued by the obsessive thought that now, faced with such a vast amount of answers, it is time to pay more attention to understanding (and in some cases plainly finding out) the questions to which they belong.