AUC PHILOSOPHICA ET HISTORICA
AUC PHILOSOPHICA ET HISTORICA

AUC Philosophica et Historica (Acta Universitatis Carolinae Philosophica et Historica) is a multidisciplinary academic journal focused on the humanities with more than 50 years of tradition.

The journal is indexed in CEEOL, DOAJ, and EBSCO.

AUC PHILOSOPHICA ET HISTORICA, Vol 2017 No 2 (2017), 45–61

The inconsistency predicate on De Morgan lattices

Adam Přenosil

DOI: https://doi.org/10.14712/24647055.2017.15
published online: 14. 11. 2017

abstract

We consider expansions of De Morgan lattices by an additional unary predicate interpreted in each De Morgan lattice by the ideal generated by all elements of the form a ∧ −a, and describe the finite lattice of strict universal Horn classes of such structures, thereby extending the description of the lattice of quasivarieties of De Morgan lattices due to Pynko. We also consider the same problem for expansions of De Morgan lattices by a constant interpreted as the maximal element of this ideal whenever it exists.

keywords: De Morgan lattice; inconsistency; Belnap–Dunn logic; quasivariety; universal Horn class

references (7)

1. Michael E. Adams and Wiesław Dziobiak. Lattices of quasivarieties of 3-element algebras. Journal of Algebra, 166: 181–210, 1994. CrossRef

2. Nuel D. Belnap. A useful four-valued logic. In J. Michael Dunn and George Epstein, editors, Modern uses of multiple-valued logic, volume 2 of Episteme, pages 5–37. Springer Netherlands, 1977. CrossRef

3. Nuel D. Belnap and Joel Spencer. Intensionally complemented distributive lattices. Portugaliae Mathematica, 25: 99–104, 1966.

4. J. Michael Dunn. Intuitive semantics for first-degree entailments and 'coupled trees'. Philosophical Studies, 29(3): 149–168, 1976. CrossRef

5. Hernando Gaitán and Milton H. Perea. A non-finitely based quasi-variety of De Morgan algebras. Studia Logica, 78: 237–248, 2004. CrossRef

6. Viktor A. Gorbunov. Algebraic Theory of Quasivarieties. Siberian School of Algebra and Logic. Springer, 1998.

7. Alexej P. Pynko. Implicational classes of De Morgan lattices. Discrete Mathematics, 205(1-3): 171–181, 1999. CrossRef

Creative Commons License
The inconsistency predicate on De Morgan lattices is licensed under a Creative Commons Attribution 4.0 International License.


periodicity: 2 x per year
ISSN: 0567-8293
E-ISSN: 2464-7055

Download