{"product_id":"the-algebra-of-intensional-logics-paperback","title":"The Algebra of Intensional Logics - Paperback","description":"\u003cdiv\u003e\u003cp style=\"text-align: right;\"\u003e\u003ca href=\"https:\/\/reportcopyrightinfringement.com\/\" target=\"_blank\" rel=\"nofollow\"\u003e\u003cb\u003eReport copyright infringement\u003c\/b\u003e\u003c\/a\u003e\u003c\/p\u003e\u003c\/div\u003e\u003cp\u003eby \u003cb\u003eJ. Michael Dunn\u003c\/b\u003e (Author), \u003cb\u003eKatalin Bimbó\u003c\/b\u003e (Introduction by)\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eJ. Michael Dunn's PhD dissertation occupies a unique place in the development of the algebraic approach to logic. In \u003cem\u003eThe Algebra of Intensional Logics\u003c\/em\u003e, Dunn introduced De Morgan monoids, a class of algebras in which the algebra of \u003cstrong\u003eR\u003c\/strong\u003e (the logic of relevant implication) is free. This is an example where a logic's algebra is neither a Boolean algebra with further operations, nor a residuated distributive lattice. De Morgan monoids served as a paradigm example for the algebraization of other relevance logics, including \u003cstrong\u003eE\u003c\/strong\u003e, the logic of entailment and \u003cstrong\u003eR-M\u003c\/strong\u003eingle (\u003cstrong\u003eRM\u003c\/strong\u003e), the extension of \u003cstrong\u003eR\u003c\/strong\u003e with the mingle axiom.\u003c\/p\u003e\u003cp\u003e\u003cbr\u003e De Morgan monoids extend De Morgan lattices, which algebraize the logic of first-degree entailments that is a common fragment of \u003cstrong\u003eR\u003c\/strong\u003e and \u003cstrong\u003eE\u003c\/strong\u003e. Dunn studied the role of the four-element De Morgan algebra \u003cem\u003eD\u003c\/em\u003e in the representation of De Morgan lattices, and from this he derived a completeness theorem for first-degree entailments. He also showed that every De Morgan lattice can be embedded into a 2-product of Boolean algebras, and proved related results about De Morgan lattices in which negation has no fixed point. Dunn also developed an informal interpretation for first-degree entailments utilizing the notion of aboutness, which was motivated by the representation of De Morgan lattices by sets.\u003c\/p\u003e\u003cp\u003e\u003cbr\u003e Dunn made preeminent contributions to several areas of relevance logic in his career spanning more than half a century. In proof theory, he developed sequent calculuses for positive relevance logics and a tableaux system for first-degree entailments; in semantics, he developed a binary relational semantics for the logic \u003cstrong\u003eRM\u003c\/strong\u003e. The use of algebras remained a central theme in Dunn's work from the proof of the admissibility of the rule called γ to his theory of generalized Galois logics (or   gaggles''), in which the residuals of arbitrary operations are considered. The representation of gaggles---utilizing relational structures---gave a new framework for relational semantics for relevance and for so-called substructural logics, and led to an information-based interpretation of them. \u003c\/p\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eNumber of Pages:\u003c\/strong\u003e 144\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eDimensions:\u003c\/strong\u003e 0.31 x 9.21 x 6.14 IN\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003ePublication Date:\u003c\/strong\u003e October 30, 2019\u003c\/div\u003e\n            ","brand":"BooksCloud","offers":[{"title":"Default Title","offer_id":47337398468857,"sku":"9781848903180","price":25.92,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0789\/2782\/3097\/files\/niCspzNHf99781848903180.webp?v=1769679198","url":"https:\/\/bookscloud.io\/products\/the-algebra-of-intensional-logics-paperback","provider":"BooksCloud Book Dropshipping","version":"1.0","type":"link"}