Treatise on Intuitionistic Type Theory

Granstrom, Johan Georg

ISBN 10: 9400717350 / ISBN 13: 9789400717350

Verlag: Springer, 2011

Beschreibung

Intuitionistic type theory can be described, somewhat boldly, as a fulfillment of the dream of a universal language for science. In particular, intuitionistic type theory is a foundation for mathematics and a programming language. Series: Logic, Epistemology, and the Unity of Science. Num Pages: 212 pages, 8 black & white tables, biography. BIC Classification: HPC; HPK; HPL; PBC; PBKS; UM. Category: (P) Professional & Vocational. Dimension: 234 x 156 x 12. Weight in Grams: 485. . 2011. Hardback. . . . . Books ship from the US and Ireland.

Bestandsnummer des Verkäufers V9789400717350

Bibliografische Details

• Titel: Treatise on Intuitionistic Type Theory
• Verlag: Springer
• Erscheinungsjahr: 2011
• Sprache: Englisch
• ISBN-10: 9400717350
• ISBN-13: 9789400717350
• Einband: Hardcover
• Zustand: New

Über diesen Titel

Inhaltsangabe

Contents.- List of Figures.- List of Tables.- Introduction.- Chapter I. Prolegomena. 1. A treefold correspondence.- 2. The acts of the mind.- 3. The principle of compositionality.- 4. Lingua characteristica.- Chapter II. Truth of Knowledge. 1. The meaning of meaning.- 2. A division of being.- 3. Mathematical entities.- 4. Judgement and assertion.- 5. Reasoning and demonstration.- 6. The proposition.- 7. The laws of logic.- 8. Variables and generality.- 9. Division of definitions.- Chapter III. The Notion of Set. 1. A History of set-like notions.- 2. Set-theoretical notation.- 3. Making universal concepts ito objects of thought.- 4. Canonical sets and elements.- 5. How to define a canonical set.- 6. More canonical sets.- Chapter IV. Reference and Computation. 1. Functions, algorithms, and programs.- 2. The concept of function.- 3. A formalization of computation.- 4. Noncanonical sets and elements.- 5. Nominal definitions.- 6. Functions as objects.- 7. Families of sets.- Chapter V. Assumption and Substitution. 1. The concept of function revisited.- 2. Hypothetical assertions.- 3. The calculus of substitutions.- 4. Sets and elements in hypothetical assertions.- 5. Closures and λ -calculas.- 6. The disjoint union of a family of sets.- 7. Elimination rukes.- 8. Propositions as sets.- Chapter VI. Intuitionism. 1. The intuitionistic interpretation of apagoge.- 2. the law of excluded middle.- 3. The philosophy of mathematics.- Bibliography.- Index of Proper Names.- Index of Subjects.-

Über die Autorin bzw. den Autor

Johan G. Granström (1977) holds an Uppsala doctorate in mathematical logic (2009). He had the privilege of having Em.Prof. Per Martin-Löf, the father of dependent types, as doctoral supervisor (2003-2009), along with Prof. Erik Palmgren, a renowned expert in constructive mathematics.

Dr. Granström has been a short-term research fellow at Ludwig-Maximilians-Universität München (2006-2007) and a research associate in formal methods for MDA at King’s College London (2009). Before entering into doctoral studies he was employed in the computer industry as systems developer, consultant, and software architect (1998-2003).  He worked as Systems and Solutions Architect at Svea Ekonomi (2009-2011) and is currently employed by Google, Zürich (2011- ).