Treatise on Intuitionistic Type Theory
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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. This book expounds several aspects of intuitionistic type theory, such as the notion of set, reference vs. computation, assumption, and substitution. Moreover, the book includes philosophically relevant sections on the principle of compositionality, lingua characteristica, epistemology, propositional logic, intuitionism, and the law of excluded middle. Ample historical references are given throughout the book.
Intuitionistic type theory can be described, somewhat boldly, as a partial fulfillment of the dream of a universal language for science. This book expounds several aspects of intuitionistic type theory, such as the notion of set, reference vs. computation, assumption, and substitution. Moreover, the book includes philosophically relevant sections on the principle of compositionality, lingua characteristica, epistemology, propositional logic, intuitionism, and the law of excluded middle. Ample historical references are given throughout the book.
The author was a PhD student of Per Martin-Löf, the inventor of intuitionistic type theory, and has unique insights in the field. There are many interesting connections between philosophy, logic, and computer science. A new and pedagogical treatment of the double negation interpretation is included.
Autor*in
Johan Georg Granström
Themen in »Treatise on Intuitionistic Type Theory«
intuitionism intuitionistic type theory lingua characteristica notion of knowledge notion of truth