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  1. The logic of partitions: Introduction to the dual of the logic of subsets: The logic of partitions.David Ellerman - 2010 - Review of Symbolic Logic 3 (2):287-350.
    Modern categorical logic as well as the Kripke and topological models of intuitionistic logic suggest that the interpretation of ordinary “propositional” logic should in general be the logic of subsets of a given universe set. Partitions on a set are dual to subsets of a set in the sense of the category-theoretic duality of epimorphisms and monomorphisms—which is reflected in the duality between quotient objects and subobjects throughout algebra. If “propositional” logic is thus seen as the logic of subsets of (...)
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  • Categories for the Working Mathematician.Saunders Maclane - 1971 - Springer.
    Category Theory has developed rapidly. This book aims to present those ideas and methods which can now be effectively used by Mathe­ maticians working in a variety of other fields of Mathematical research. This occurs at several levels. On the first level, categories provide a convenient conceptual language, based on the notions of category, functor, natural transformation, contravariance, and functor category. These notions are presented, with appropriate examples, in Chapters I and II. Next comes the fundamental idea of an adjoint (...)
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  • An Investigation of the Laws of Thought: On Which Are Founded the Mathematical Theories of Logic and Probabilities.George Boole - 2009 - [New York]: Cambridge University Press.
    Self-taught mathematician and father of Boolean algebra, George Boole (1815-1864) published An Investigation of the Laws of Thought in 1854. In this highly original investigation of the fundamental laws of human reasoning, a sequel to ideas he had explored in earlier writings, Boole uses the symbolic language of mathematics to establish a method to examine the nature of the human mind using logic and the theory of probabilities. Boole considers language not just as a mode of expression, but as a (...)
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  • A Mathematical Theory of Communication.Claude Elwood Shannon - 1948 - Bell System Technical Journal 27 (April 1924):379–423.
    The mathematical theory of communication.
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  • Counting distinctions: on the conceptual foundations of Shannon’s information theory.David Ellerman - 2009 - Synthese 168 (1):119-149.
    Categorical logic has shown that modern logic is essentially the logic of subsets (or "subobjects"). Partitions are dual to subsets so there is a dual logic of partitions where a "distinction" [an ordered pair of distinct elements (u,u′) from the universe U ] is dual to an "element". An element being in a subset is analogous to a partition π on U making a distinction, i.e., if u and u′ were in different blocks of π. Subset logic leads to finite (...)
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  • Category Theory.Steve Awodey - 2006 - Oxford, England: Oxford University Press.
    A comprehensive reference to category theory for students and researchers in mathematics, computer science, logic, cognitive science, linguistics, and philosophy. Useful for self-study and as a course text, the book includes all basic definitions and theorems, as well as numerous examples and exercises.
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  • Intuitionistic logic, model theory and forcing.Melvin Fitting - 1969 - Amsterdam,: North-Holland Pub. Co..
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  • (1 other version)An Investigation of the Laws of Thought, on Which are Founded the Mathematical Theories of Logic and Probabilities.Alonzo Church - 1951 - Journal of Symbolic Logic 16 (3):224-225.
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  • Introduction to mathematical logic..Alonzo Church - 1944 - Princeton,: Princeton university press: London, H. Milford, Oxford university press. Edited by C. Truesdell.
    This book is intended to be used as a textbook by students of mathematics, and also within limitations as a reference work.
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  • Theory of Equivalence Relations.Oystein Ore - 1943 - Journal of Symbolic Logic 8 (1):55-56.
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