|
Universal logic is the field of logic that studies the common features of all logical systems, aiming to be to logic what universal algebra is to algebra. A number of approaches to universal logic have been proposed since the twentieth century, using model theoretic, and categorical approaches. == Development == The roots of universal logic may go as far back as some work of Alfred Tarski in the early twentieth century, but the modern notion was first presented in the 1990s by Swiss logician Jean-Yves Béziau.〔The Road to Universal Logic: Festschrift for 50th Birthday of Jean-Yves Béziau Volume I, edited by Arnold Koslow and Arthur Buchsbaum 2014 Birkhäuser ISBN 978-3319101927 pp 2-10〕 The term 'universal logic' has also been separately used by logicians such as Richard Sylvan and Ross Brady to refer to a new type of (weak) relevant logic.〔Brady, R. 2006. ''Universal Logic''. Stanford: CSLI Publications. ISBN 1-57586-255-7.〕 In the context defined by Béziau, three main approaches to universal logic have been explored in depth: * An abstract model theory system axiomatized by Jon Barwise,〔Jon Barwise. Axioms for abstract model theory. Annals of Mathematical Logic,7:221–265, 1974〕 * a topological / categorical approach based on sketches (sometimes called categorical model theory),〔Steffen Lewitzka "A Topological Approach to Universal Logic" Logica Universalis 2007 Birkhauser pp 35-61〕 * a categorical approach originating in Computer Science based on Goguen and Burstall's notion of institution.〔Razvan Diaconescu, "Three decades of institution theory" in Universal Logic: An Anthology edited by Jean-Yves Béziau 2012 Springer ISBN 978-3-0346-0144-3 pp 309-322〕 While logic has been studied for centuries, Mossakowski et al commented in 2007 that "it is embarrassing that there is no widely acceptable formal definition of “a logic”.〔T. Mossakowski, J. A. Goguen, R. Diaconescu, A. Tarlecki, "What is a Logic?", Logica Universalis 2007 Birkhauser, pp. 113–133.〕 These approaches to universal logic thus aim to address and formalize the nature of what may be called 'logic' as a form of "sound reasoning".〔 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Universal logic」の詳細全文を読む スポンサード リンク
|