Reductio ad Contradictionem: An Algebraic Perspective

0454996 - ÚI 2017 RIV NL eng J - Článek v odborném periodiku
Přenosil, Adam
Reductio ad Contradictionem: An Algebraic Perspective.
Studia Logica. Roč. 104, č. 3 (2016), s. 389-415. ISSN 0039-3215. E-ISSN 1572-8730
Grant CEP: GA ČR GAP202/10/1826
Institucionální podpora: RVO:67985807
Klíčová slova: de Morgan algebras * contradiction * reductio ad contradictionem * reductio ad absurdum * four-valued logic * paraconsistent logic * inconsistency * completeness
Kód oboru RIV: BA - Obecná matematika
Impakt faktor: 0.589, rok: 2016

We introduce a novel expansion of the four-valued Belnap–Dunn logic by a unary operator representing reductio ad contradictionem and study its algebraic semantics. This expansion thus contains both the direct, non-inferential negation of the Belnap–Dunn logic and an inferential negation akin to the negation of Johansson’s minimal logic. We formulate a sequent calculus for this logic and introduce the variety of reductio algebras as an algebraic semantics for this calculus. We then investigate some basic algebraic properties of this variety, in particular we show that it is locally finite and has EDPC. We identify the subdirectly irreducible algebras in this variety and describe the lattice of varieties of reductio algebras. In particular, we prove that this lattice contains an interval isomorphic to the lattice of classes of finite non-empty graphs with loops closed under surjective graph homomorphisms.
Trvalý link: http://hdl.handle.net/11104/0255654