Epsilon terms indexed by contexts were used by K. von Heusinger to represent definite and indefinite noun phrases as well as some other constructs of natural language. We provide a language and a complete first order system allowing to formalize basic aspects of this representation. The main axiom says that for any finite collection S 1,…,S k of distinct definable sets and elements a 1,…,a k of these sets there exists a choice function assigning a i to S i for (...) all i≤k. We prove soundness and completeness theorems for this system S ε i fin. (shrink)

Intuitionistic logic is presented here as part of familiar classical logic which allows mechanical extraction of programs from proofs. to make the material more accessible, basic techniques are presented first for propositional logic; Part II contains extensions to predicate logic. This material provides an introduction and a safe background for reading research literature in logic and computer science as well as advanced monographs. Readers are assumed to be familiar with basic notions of first order logic. One device for making this (...) book short was inventing new proofs of several theorems. The presentation is based on natural deduction. The topics include programming interpretation of intuitionistic logic by simply typed lambda-calculus (Curry-Howard isomorphism), negative translation of classical into intuitionistic logic, normalization of natural deductions, applications to category theory, Kripke models, algebraic and topological semantics, proof-search methods, interpolation theorem. The text developed from materal for several courses taught at Stanford University in 1992-1999. (shrink)

A survey of works on automatic theorem-proving in the ussr 1964-1970. the philosophical problems are not touched.

The 1996 European Summer Meeting of the Association of Symbolic Logic was held held the University of the Basque Country, at Donostia (San Se bastian) Spain, on July 9-15, 1996. It was organised by the Institute for Logic, Cognition, Language and Information (ILCLI) and the Department of Logic and Philosophy of Sciences of the University of the Basque Coun try. It was supported by: the University of Pais Vasco/Euskal Herriko Unib ertsitatea, the Ministerio de Education y Ciencia (DGCYT), Hezkuntza Saila (...) (Eusko Jaurlaritza), Gipuzkoako Foru Aldundia, and Kuxta Fun dazioa. The main topics of the meeting were Model Theory, Proof Theory, Re cursion and Complexity Theory, Models of Arithmetic, Logic for Artifi cial Intelligence, Formal Semantics of Natural Language and Philosophy of Contemporary Logic. The Program Committee consisted of K. Ambos Spies (Heidelberg), J.L. Balcazar (Barcelona), J.E. Fenstad (Oslo), D. Israel (Stanford), H. Kamp (Stuttgart), R. Kaye (Birmingham), J.M. Larrazabal (San Sebastian), D. Lascar (Paris, chairman), A. Marcja (Firenze), G. Mints (Stanford), M. Otero (Madrid), S. Ronchi della Rocca (Torino), K. Segerberg (Uppsala) and L. Vega (Madrid). The organizing Committee consisted of X. Arrazola (San Sebastian), A. Arrieta (San Sebastian), R. Beneyeto (Valencia), B. Carrascal (San Se bastian), K. Korta (San Sebastian), J.M. Larrazabal (San Sebastian, chair man), J.C. Martinez (Barcelona), J.M. Mendez (Salamanca), F. Migura (Victoria) and J. Perez (Victoria). (shrink)

Did science and philosophy develop differently in ancient Greece and ancient China? If so, can we say why? This book consists of a series of detailed studies of cosmology, natural philosophy, mathematics and medicine that suggest the answer to the first question is yes. To answer the second, the author relates the science produced in each ancient civilization first to the values of the society in question and then to the institutions within which the scientists and philosophers worked.

This inaugural lecture considers three main aspects of the relationship between science and morality in Greco-Roman antiquity: first some of the ancient debates on the morality of particular scientific research programmes, especially in connection with the practice of human and animal dissection and vivisection; secondly ancient attempts to secure the autonomy and objectivity of natural scientific inquiry; and thirdly the continuing influence - in certain areas of ancient science - of values, including moral and political values, and of the assumption (...) of the privileged position occupied by human beings in the animal kingdom and the cosmos. (shrink)

The distinction between students diagnosed with a learning disability and those considered merely slow learners is based on conceptually flawed assumptions that: 1) LD represents a brain dysfunction while SL does not; 2) LD is a well-defined disorder; 3) valid measurement instruments distinguish LD and SL; 4) special education for students with LD is fundamentally different from that for SL students. These erroneous beliefs are maintained because governmental legislation transformed a diagnosis of LD into an admission ticket to a variety (...) of government entitlements thereby subjecting it to political, legal, social and ideological forces. (shrink)

First published in 2002. Routledge is an imprint of Taylor & Francis, an informa company.