Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

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.

Logics --- Algebra

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Mathematical logic --- Many-valued logic --- Congresses. --- -Logic, Many-valued --- Logic, Multivalued --- Logic, Variable-valued --- Multivalued logic --- Variable-valued logic --- Nonclassical mathematical logic --- Values --- Congresses --- -Congresses --- Logic, Many-valued --- Many-valued logic - Congresses.

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

The essays in this collection are written by students, colleagues, and friends of Nuel Belnap to honor him on his sixtieth birthday. Our original plan was to include pieces from fonner students only, but we have deviated from this ever so slightly for a variety of personal and practical reasons. Belnap's research accomplishments are numerous and well known: He has founded (together with Alan Ross Anderson) a whole branch of logic known as "relevance logic." He has made contributions of fundamental importance to the logic of questions. His work in modal logic, fonnal pragmatics, and the theory of truth has been highly influential. And the list goes on. Belnap's accomplishments as a teacher are also distinguished and well known but, by virtue of the essential privacy of the teaching relationship, not so well understood. We would like to reflect a little on what makes him such an outstanding teacher.

Logic --- Mathematics --- Probabilities --- Truth --- Linguistics --- Philosophy --- Probabiliteit--Theorie --- Probabiliteitstheorie --- Probabilité [Théorie de la ] --- Waarschijnlijkheid--Theorie --- Waarschijnlijkheidstheorie --- Logic. --- Probabilities. --- Truth. --- Philosophy. --- Conviction --- Probability --- Statistical inference --- Argumentation --- Deduction (Logic) --- Deductive logic --- Dialectic (Logic) --- Logic, Deductive --- Logic of mathematics --- Mathematics, Logic of --- Belnap, Nuel D., --- Belief and doubt --- Skepticism --- Certainty --- Necessity (Philosophy) --- Pragmatism --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Intellect --- Psychology --- Science --- Reasoning --- Thought and thinking --- Methodology --- Mathematics - Philosophy --- Linguistics - Philosophy --- Belnap, Nuel D., - 1930 --- -Logic --- -Logic.

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Philosophy