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.