CHAPTER Addenda to Pure Combinatory Logic This chapter will treat various additions to, and modifications of, the subject matter of Chapters-7. ...

This paper proposes that the meanings of some natural language expressions should be thought of as functions on their own continuations. Continuations are a well-established analytic tool in the theory of programming language semantics; in brief, a continuation is the entire default future of a computation. I show how a continuation-based grammar can unify several aspects of natural language quantification in a new way: merely stating the truth conditions for quantificational expressions in terms of continuations automatically accounts for scope displacement (...) and scope ambiguity. To prove this claim, I exhibit a simple finite context-free grammar with a strictly compositional semantics in which quantificational NPs are interpreted in situ but take semantic scope over larger constituents. There is no Quantifier Raising (nor any use of a level of Logical Form distinct from overt syntax), no Cooper Storage (or similar mechanisms used in many recent HPSG, Categorial, or Type-logical treatments), and no need for type-shifting (as in Hendriks' Flexible Types account). Continuations also provide a natural account of generalized coordination that does not require either type-shifting or type polymorphism. Compositionality issues are discussed in some detail. (shrink)

There is no doubt that the model presented here is incomplete. Many important categories, particularly negation and the adverbials, have been entirely ignored, and the treatment of Tense and the affixes is certainly inadequate. It also remains to be seen how the many constructions that have been ignored here are to be accommodated within the framework that has been outlined. However, the fact that a standard categorial lexicon, plus the four rule schemata, seems to come close to exhaustively specifying the (...) main clause constructions of English, and also seems to explain a number of major constraints on transformations, encourages us to compare the theory with certain alternatives, and to examine its broader implications. (shrink)

This book is a major attempt to reconcile the empirical basis of linguistic science with the a priori nature of philosophical reasoning. Its purpose is to show how the methods and findings of linguistic science, especially of transformational grammar, can be used to cast light upon central problems of analytic philosophy. After dealing with recent objections to the use of linguistic techniques in philosophy, the author shows, with great force and clarity, how these techniques can be applied to such problems (...) as the analysis of singular terms, the concepts of fact, event, and causality, and the meaning of the word "good.". (shrink)

In this witty and fascinating book, Premack examines arguments over whether humans are unique because we can talk.

We introduce a logic BI in which a multiplicative (or linear) and an additive (or intuitionistic) implication live side-by-side. The propositional version of BI arises from an analysis of the proof-theoretic relationship between conjunction and implication; it can be viewed as a merging of intuitionistic logic and multiplicative intuitionistic linear logic. The naturality of BI can be seen categorically: models of propositional BI's proofs are given by bicartesian doubly closed categories, i.e., categories which freely combine the semantics of propositional intuitionistic (...) logic and propositional multiplicative intuitionistic linear logic. The predicate version of BI includes, in addition to standard additive quantifiers, multiplicative (or intensional) quantifiers ∀ new and ∃ new which arise from observing restrictions on structural rules on the level of terms as well as propositions. We discuss computational interpretations, based on sharing, at both the propositional and predicate levels. (shrink)

Investigates the application of logic to problem solving and computer programming. Requires no previous knowledge in this field, and therefore can be used as an introduction to logic, the theory of problem-solving and computer programming. Annotation copyrighted by Book News, Inc., Portland, OR.

During the first two years of human life a common neural substrate underlies the hierarchical organization of elements in the development of speech as well as the capacity to combine objects manually, including tool use. Subsequent cortical differentiation, beginning at age two, creates distinct, relatively modularized capacities for linguistic grammar and more complex combination of objects. An evolutionary homologue of the neural substrate for language production and manual action is hypothesized to have provided a foundation for the evolution of language (...) before the divergence of the hominids and the great apes. Support comes from the discovery of a Broca's area homologue and related neural circuits in contemporary primates. In addition, chimpanzees have an identical constraint on hierarchical complexity in both tool use and symbol combination. Their performance matches that of the two-year-old child who has not yet developed the neural circuits for complex grammar and complex manual combination of objects. (shrink)

This is a book about how we see: the environment around us (its surfaces, their layout, and their colors and textures); where we are in the environment; whether or not we are moving and, if we are, where we are going; what things are good for; how to do things (to thread a needle or drive an automobile); or why things look as they do.The basic assumption is that vision depends on the eye which is connected to the brain. The (...) author suggests that natural vision depends on the eyes in the head on a body supported by the ground, the brain being only the central organ of a complete visual system. When no constraints are put on the visual system, people look around, walk up to something interesting and move around it so as to see it from all sides, and go from one vista to another. That is natural vision—and what this book is about. (shrink)

First Published in 1999. Routledge is an imprint of Taylor & Francis, an informa company.

This text is written as a critical assessment of categorial grammars. It outlines their evolution, discusses their formal basis and explores their use for a number of linguistic phenomena. It also examines their treatment of such general issues as word-order, plausibility, logic and parsing.

This book is a thesis submitted to the Faculty of Arts of the University of Utrecht. It was prepared under the supervision of Prof. Dr. H. Schultink. I would like to express my gratitude to him for his criticisms of earlier versions which led to many improvements, in particular with respect to the exposition of the argument. To my co-referent Dirk van Dalen, reader in the Department of Philo sophy (,Centrale Interfaculteit') of the University of Utrecht, I am greatly indebted (...) for his valuable and fruitful suggestions about problems relevant to both linguistics and logic. Several ideas developed in this study owe their present concrete form to our many discussions. This thesis originates in syntactic research into the Aspects carried out in 1967 under the supervision of Albert Kraak, professor at the University of Nijmegen, who ever since gave much attention to my work in progress. I am very grateful to him for his careful and stimulating criticism as well as for the continuous support he gave me during these years. The present study closely relates to the work of my colleague Wim Klooster with regard to both its theoretical framework and its subject matter. Our joint work on the measurement of duration in Dutch is an integral part of the argument. I have greatly profited from the numerous discussions we have had. (shrink)

In 1969, John McCarthy and Pat Hayes uncovered a problem that has haunted the field of artificial intelligence ever since--the frame problem. The problem arises when logic is used to describe the effects of actions and events. Put simply, it is the problem of representing what remains unchanged as a result of an action or event. Many researchers in artificial intelligence believe that its solution is vital to the realization of the field's goals. Solving the Frame Problem presents the various (...) approaches to the frame problem that have been proposed over the years. The author presents the material chronologically--as an unfolding story rather than as a body of theory to be learned by rote. There are lessons to be learned even from the dead ends researchers have pursued, for they deepen our understanding of the issues surrounding the frame problem. In the book's concluding chapters, the author offers his own work on event calculus, which he claims comes very close to a complete solution to the frame problem. Artificial Intelligence series. (shrink)

In this entertaining and challenging collection of logic puzzles, Raymond Smullyan-author of Forever Undecided-continues to delight and astonish us with his gift for making available, in the thoroughly pleasurable form of puzzles, some of the most important mathematical thinking of our time.

Ambitious and elegant, this book builds a bridge between evolutionary theory and cultural psychology. Michael Tomasello is one of the very few people to have done systematic research on the cognitive capacities of both nonhuman primates and human children. The Cultural Origins of Human Cognition identifies what the differences are, and suggests where they might have come from. -/- Tomasello argues that the roots of the human capacity for symbol-based culture, and the kind of psychological development that takes place within (...) it, are based in a cluster of uniquely human cognitive capacities that emerge early in human ontogeny. These include capacities for sharing attention with other persons; for understanding that others have intentions of their own; and for imitating, not just what someone else does, but what someone else has intended to do. In his discussions of language, symbolic representation, and cognitive development, Tomasello describes with authority and ingenuity the "ratchet effect" of these capacities working over evolutionary and historical time to create the kind of cultural artifacts and settings within which each new generation of children develops. He also proposes a novel hypothesis, based on processes of social cognition and cultural evolution, about what makes the cognitive representations of humans different from those of other primates. -/- Lucid, erudite, and passionate, The Cultural Origins of Human Cognition will be essential reading for developmental psychology, animal behavior, and cultural psychology. (from the HUP website). (shrink)

relations between events both require a more complex structure on the domain underlying the meaning representations than is commonly assumed. This paper proposes an ontology based on such notions as causation and consequence, rather than on purely temporal primitives. A central notion in the ontology..

Ambiguities in natural language can multiply so fast that no person or machine can be expected to process a text of even moderate length by enumerating all possible disambiguations. A sentence containing $n$ scope bearing elements which are freely permutable will have $n!$ readings, if there are no other, say lexical or syntactic, sources of ambiguity. A series of $m$ such sentences would lead to $(n!)^m$ possibilities. All in all the growth of possibilities will be so fast that generating readings (...) first and testing their acceptability afterwards will not be feasible. -/- This insight has led a series of researchers to adopt a level of representation at which ambiguities remain unresolved. The idea here is not to generate and test many possible interpretations but to first generate one `underspecified' representation which in a sense represents all its complete specifications and then use whatever information is available to further specify the result. -/- One central hypothesis in the paper will be that the relation between an underspecified representation and its full representations is not so much the relation between one structure and a set of other structures but is in fact the relation between a description (a set of logical sentences) and its models. (shrink)