Generalized Galois Logics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Generalized Galois Logics write by Katalin Bimbó. This book was released on 2008. Generalized Galois Logics available in PDF, EPUB and Kindle. Nonclassical logics have played an increasing role in recent years in disciplines ranging from mathematics and computer science to linguistics and philosophy. Generalized Galois Logics develops a uniform framework of relational semantics to mediate between logical calculi and their semantics through algebra. This volume addresses normal modal logics such as K and S5, and substructural logics, including relevance logics, linear logic, and Lambek calculi. The authors also treat less-familiar and new logical systems with equal deftness.
The Algebra of Intensional Logics
The Algebra of Intensional Logics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Algebra of Intensional Logics write by J. Michael Dunn. This book was released on 2019-10-30. The Algebra of Intensional Logics available in PDF, EPUB and Kindle. J. Michael Dunn's PhD dissertation occupies a unique place in the development of the algebraic approach to logic. In The Algebra of Intensional Logics, Dunn introduced De Morgan monoids, a class of algebras in which the algebra of R (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 E, the logic of entailment and R-Mingle (RM), the extension of R with the mingle axiom. De Morgan monoids extend De Morgan lattices, which algebraize the logic of first-degree entailments that is a common fragment of R and E. Dunn studied the role of the four-element De Morgan algebra D 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. 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 RM. 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.
Generalized Galois Connections
Generalized Galois Connections - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Generalized Galois Connections write by Eugene Leo Allgower. This book was released on 1959. Generalized Galois Connections available in PDF, EPUB and Kindle.
J. Michael Dunn on Information Based Logics
J. Michael Dunn on Information Based Logics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook J. Michael Dunn on Information Based Logics write by Katalin Bimbo. This book was released on 2016-04-02. J. Michael Dunn on Information Based Logics available in PDF, EPUB and Kindle. This book celebrates and expands on J. Michael Dunn’s work on informational interpretations of logic. Dunn, in his Ph.D. thesis (1966), introduced a semantics for first-degree entailments utilizing the idea that a sentence can provide positive or negative information about a topic, possibly supplying both or neither. He later published a related interpretation of the logic R-mingle, which turned out to be one of the first relational semantics for a relevance logic. An incompatibility relation between information states lends itself to a definition of negation and it has figured into Dunn's comprehensive investigations into representations of various negations. The informational view of semantics is also a prominent theme in Dunn’s research on other logics, such as quantum logic and linear logic, and led to the encompassing theory of generalized Galois logics (or "gaggles"). Dunn’s latest work addresses informational interpretations of the ternary accessibility relation and the very nature of information. The book opens with Dunn’s autobiography, followed by a list of his publications. It then presents a series of papers written by respected logicians working on different aspects of information-based logics. The topics covered include the logic R-mingle, which was introduced by Dunn, and its applications in mathematical reasoning as well as its importance in obtaining results for other relevance logics. There are also interpretations of the accessibility relation in the semantics of relevance and other non-classical logics using different notions of information. It also presents a collection of papers that develop semantics for various logics, including certain modal and many-valued logics. The publication of this book is well timed, since we are living in an "information age.” Providing new technical findings, intellectual history and careful expositions of intriguing ideas, it appeals to a wide audience of scholars and researchers.
Generalized Galois Theory
Generalized Galois Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Generalized Galois Theory write by Paul Ponomarenko. This book was released on 1965. Generalized Galois Theory available in PDF, EPUB and Kindle.
