This book is dedicated to Dov Gabbay, one of the most outstanding and most productive researchers in the area of logic, language and reasoning. He has exerted a profound influence in the major fields of logic, linguistics and computer science. Most of the chapters included, therefore, build on his work and present results or summarize areas where Dov has made major contributions. In particular his work on Labelled Deductive Systems is addressed in most of the contributions. The chapters on computational linguistics address logical and deductive aspects of linguistic problems. The papers by van Benthem Lambek and Moortgat investigate categorial considerations and the use of labels within the "parsing as deduction" approach. Analyses of particular linguistic problems are given in the remaining papers by Kamp, Kempson, Moravcsik, Konig and Reyle. They address the logic of generalized quantifiers, the treatment of cross-over phenomena and temporal/aspectual interpretation, as well as applicability of underspecified deduction in linguistic formalisms. The more logic-oriented chapters address philosophical and proof-theoretic problems and give algorithmic solutions for most of them. The spectrum ranges from K. Segerberg's contribution which brings together the two traditions of epistemic and doxastic logics of belief, to M. Finger and M. Reynold's chapter on two-dimensional executable logics with applications to temporal databases. The book demonstrates that a relatively small number of basic techniques and ideas, in particular the idea of labelled deductive systems, can be successfully applied in many different areas.

This is the first textbook that approaches natural language semantics and logic from the perspective of Discourse Representation Theory, an approach which emphasizes the dynamic and incremental aspects of meaning and inference. The book has been carefully designed for the classroom. It is aimed at students with varying degrees of preparation, including those without prior exposure to semantics or formal logic. Moreover, it should make DRT easily accessible to those who want to learn about the theory on their own. Exercises are available to test understanding as well as to encourage independent theoretical thought. The book serves a double purpose. Besides a textbook, it is also the first comprehensive and fully explicit statement of DRT available in the form of a book. The first part of the book develops the basic principles of DRT for a small fragment of English (but which has nevertheless the power of standard predicate logic). The second part extends this fragment by adding plurals; it discusses a wide variety of problems connected with plural nouns and verbs. The third part applies the theory to the analysis of tense and aspect. Many of the problems raised in Parts Two and Three are novel, as are the solutions proposed. For undergraduate and graduate students interested in linguistics, theoretical linguistics, computational linguistics, artificial intelligence and cognitive science. Suitable for students with no previous exposure to formal semantics or logic.

th This volume is dedicated to Dov Gabbay who celebrated his 50 birthday in October 1995. Dov is one of the most outstanding and most productive researchers we have ever met. He has exerted a profound influence in major fields of logic, linguistics and computer science. His contributions in the areas of logic, language and reasoning are so numerous that a comprehensive survey would already fill half of this book. Instead of summarizing his work we decided to let him speak for himself. Sitting in a car on the way to Amsterdam airport he gave an interview to Jelle Gerbrandy and Anne-Marie Mineur. This recorded conversation with him, which is included gives a deep insight into his motivations and into his view of the world, the Almighty and, of course, the role of logic. In addition, this volume contains a partially annotated bibliography of his main papers and books. The length of the bibliography and the broadness of the topics covered there speaks for itself.

Preface This book is about semantics and logic. More specifically, it is about the semantics and logic of natural language; and, even more specifically than that, it is about a particular way of dealing with those subjects, known as Discourse Representation Theory, or DRT. DRT is an approach towards natural language semantics which, some thirteen years ago, arose out of attempts to deal with two distinct problems. The first of those was the semantic puzzle that had been brought to contempo rary attention by Geach's notorious "donkey sentences" - sentences like If Pedro owns some donkey, he beats it, in which the anaphoric connection we perceive between the indefinite noun phrase some donkey and the pronoun it may seem to conflict with the existential meaning of the word some. The second problem had to do with tense and aspect. Some languages, for instance French and the other Romance languages, have two morphologically distinct past tenses, a simple past (the French Passe Simple) and a continuous past (the French Imparfait). To articulate precisely what the difference between these tenses is has turned out to be surprisingly difficult."

This is the first textbook that approaches natural language semantics and logic from the perspective of Discourse Representation Theory, an approach which emphasizes the dynamic and incremental aspects of meaning and inference. The book has been carefully designed for the classroom. It is aimed at students with varying degrees of preparation, including those without prior exposure to semantics or formal logic. Moreover, it should make DRT easily accessible to those who want to learn about the theory on their own. Exercises are available to test understanding as well as to encourage independent theoretical thought. The book serves a double purpose. Besides a textbook, it is also the first comprehensive and fully explicit statement of DRT available in the form of a book. The first part of the book develops the basic principles of DRT for a small fragment of English (but which has nevertheless the power of standard predicate logic). The second part extends this fragment by adding plurals; it discusses a wide variety of problems connected with plural nouns and verbs. The third part applies the theory to the analysis of tense and aspect. Many of the problems raised in Parts Two and Three are novel, as are the solutions proposed. For undergraduate and graduate students interested in linguistics, theoretical linguistics, computational linguistics, artificial intelligence and cognitive science. Suitable for students with no previous exposure to formal semantics or logic.

presupposition fails, we now give a short introduction into Unification Grammar. Since all implementations discussed in this volume use PROLOG (with the exception of BlockjHaugeneder), we felt that it would also be useful to explain the difference between unification in PROLOG and in UG. After the introduction to UG we briefly summarize the main arguments for using linguistic theories in natural language processing. We conclude with a short summary of the contributions to this volume. UNIFICATION GRAMMAR 3 Feature Structures or Complex Categories. Unification Grammar was developed by Martin Kay (Kay 1979). Martin Kay wanted to give a precise defmition (and implementation) of the notion of 'feature'. Linguists use features at nearly all levels of linguistic description. In phonetics, for instance, the phoneme b is usually described with the features 'bilabial', 'voiced' and 'nasal'. In the case of b the first two features get the value +, the third (nasal) gets the value -. Feature value pairs in phonology are normally represented as a matrix. bilabial: + voiced: + I nasal: - Feature matrix for b.] In syntax features are used, for example, to distinguish different noun classes. The Latin noun 'murus' would be characterized by the following feature-value pairs: gender: masculin, number: singular, case: nominative, pred: murus. Besides a matrix representation one frequently fmds a graph representation for feature value pairs. The edges of the graph are labelled by features. The leaves denote the value of a feature."