The inconsistency predicate on De Morgan lattices
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...
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| Format: | Article |
| Language: | ces |
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Karolinum Press
2017-11-01
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| Series: | Acta Universitatis Carolinae: Philosophica et Historica |
| Subjects: | |
| Online Access: | http://www.karolinum.cz/doi/10.14712/24647055.2017.15 |
| _version_ | 1819054477182763008 |
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| author | Adam Přenosil |
| author_facet | Adam Přenosil |
| author_sort | Adam Přenosil |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-21T12:52:15Z |
| format | Article |
| id | doaj.art-7ec751138d2b44ad91d2c49636ab9985 |
| institution | Directory Open Access Journal |
| issn | 0567-8293 2464-7055 |
| language | ces |
| last_indexed | 2024-12-21T12:52:15Z |
| publishDate | 2017-11-01 |
| publisher | Karolinum Press |
| record_format | Article |
| series | Acta Universitatis Carolinae: Philosophica et Historica |
| spelling | doaj.art-7ec751138d2b44ad91d2c49636ab99852022-12-21T19:03:27ZcesKarolinum PressActa Universitatis Carolinae: Philosophica et Historica0567-82932464-70552017-11-0120172456110.14712/24647055.2017.155364The inconsistency predicate on De Morgan latticesAdam PřenosilWe 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.http://www.karolinum.cz/doi/10.14712/24647055.2017.15De Morgan latticeinconsistencyBelnap–Dunn logicquasivarietyuniversal Horn class |
| spellingShingle | Adam Přenosil The inconsistency predicate on De Morgan lattices Acta Universitatis Carolinae: Philosophica et Historica De Morgan lattice inconsistency Belnap–Dunn logic quasivariety universal Horn class |
| title | The inconsistency predicate on De Morgan lattices |
| title_full | The inconsistency predicate on De Morgan lattices |
| title_fullStr | The inconsistency predicate on De Morgan lattices |
| title_full_unstemmed | The inconsistency predicate on De Morgan lattices |
| title_short | The inconsistency predicate on De Morgan lattices |
| title_sort | inconsistency predicate on de morgan lattices |
| topic | De Morgan lattice inconsistency Belnap–Dunn logic quasivariety universal Horn class |
| url | http://www.karolinum.cz/doi/10.14712/24647055.2017.15 |
| work_keys_str_mv | AT adamprenosil theinconsistencypredicateondemorganlattices AT adamprenosil inconsistencypredicateondemorganlattices |