Simple Logics for Basic Algebras

• Autorzy: Cı̅rulis, Ja̅nis

Abstrakty

EN

An MV-algebra is an algebra (A, ⊕, ¬, 0), where (A, ⊕, 0) is a commutative monoid and ¬ is an idempotent operation on A satisfying also some additional axioms. Basic algebras are similar algebras that can roughly be characterised as nonassociative (hence, also non-commutative) generalizations of MV-algebras. Basic algebras and commutative basic algebras provide an equivalent algebraic semantics in the sense of Blok and Pigozzi for two recent logical systems. Both are Hilbert-style systems, with implication and negation as the primitive connectives. We present a considerably simpler logic, LB, for basic algebras, where implication and falsum are taken as primitives. We also consider some subvarieties of basic algebras known in the literature, discuss classes of implicational algebras term-equivalent to each of these varieties, and construct axiomatic extensions of LB for which these classes serve as equivalent algebraic semantics.

• Wydawca: Wydawnictwo Uniwersytetu Łódzkiego
• Czasopismo: Bulletin of the Section of Logic
• Rocznik: 2015
• Tom: 44
• Numer: 3-4

Daty

wydano

2015

Twórcy

autor

Cı̅rulis, Ja̅nis

other

Institute of Mathematics and Computer Science, University of Latvia, Raina b., 29, Riga LV-1459, Latvia

other

[e-mail]

Identyfikatory

URI

http://hdl.handle.net/11089/17903

DOI

10.18778/0138-0680.44.3.4.01