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THE ALGEBRA OF INTENSIONAL LOGICS IBD

J MICHAEL DUNN / JMICHAEL DUNN
COLLEGE PUBLICATIONS
10 / 2019
9781848903180
Inglés

Sinopsis

J. Michael Dunn',s PhD dissertation occupies a unique place in theádevelopment of the algebraic approach to logic. áIn The Algebra ofáIntensional Logics, Dunn introduced De Morgan monoids, a class ofáalgebras in which the algebra of Rá(the logic of relevant implication)áis free. áThis is an example where a logic',s algebra is neitheráa Boolean algebra with further operations, nor a residuated distributiveálattice. áDe Morgan monoids served as a paradigm example for theáalgebraization of other relevance logics, including E, the logicááof entailment and R-Mingle (RM), the extension ofááRáwith the mingle axiom.De Morgan monoids extend De Morgan lattices, which algebraize theáálogic of first-degree entailments that is a common fragment of RáandáE. áDunn studied the role of the four-element De Morgan algebra Dáin the representation of De Morgan lattices, and from this he derived aácompleteness theorem for first-degree entailments. áHe also showed thatáevery De Morgan lattice can be embedded into a 2-product of Booleanáalgebras, and proved related results about De Morgan lattices in whichánegation has no fixed point. áDunn also developed an informal interpretationáfor first-degree entailments utilizing the notion of aboutness, which wasámotivated by the representation of De Morgan lattices by sets.Dunn made preeminent contributions to several areas of relevanceálogic in his career spanning more than half a century. áIn proofátheory, he developed sequent calculuses for positive relevanceálogics and a tableaux system for first-degree entailments, inásemantics, he developed a binary relational semantics for the logicáRM. áThe use of algebras remained a central theme in Dunn',sáwork from the proof of the admissibility of the rule called &gamma,átoáhis theory of generalized Galois logics (or ``gaggles',',), in which theáresiduals of arbitrary operations are considered. áThe representation ofágaggles---utilizing relational structures---gave a new framework for relationalásemantics for relevance and for so-called substructural logics,áand led to an information-based interpretation of them.á

PVP
20,12€