L-algebras and three main non-classical logics |
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Institution: | Institute for Algebra and Number Theory, University of Stuttgart, Pfaffenwaldring 57, D-70550 Stuttgart, Germany |
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Abstract: | The semantics of three main branches of non-classical logic, intuitionistic, many-valued, and quantum logic, is unified by the concept of L-algebra. The corresponding three classes of algebras (Heyting algebras, MV-algebras, and orthomodular lattices) are associated to specializations of a bounded L-algebra, given by simple equations. Three basic specializations lead to three more classes of algebras, including quantized Heyting algebras which have not been considered before. All these algebras are obtained from a new class of L-algebras which simultaneously satisfy general versions of Glivenko's and Mundici's theorems. |
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Keywords: | Heyting algebra MV-algebra Orthomodular lattice |
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