The logic of distributive nearlattices

González, Luciano J.

doi:10.1007/s00500-017-2750-0

Cited by 11 publications

(8 citation statements)

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“…Let A be a nearlattice. Following the results developed in [15], we introduce the next notation. For each natural number n we define inductively for every a 1 , .…”

Section: α-Filtersmentioning

confidence: 99%

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Note on $\alpha$-filters in distributive nearlattices

Calomino¹

2018

Math.Boh.

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“…Let A be a nearlattice. Following the results developed in [15], we introduce the next notation. For each natural number n we define inductively for every a 1 , .…”

Section: α-Filtersmentioning

confidence: 99%

“…A particular class of nearlattices are the distributive nearlattices. In [6] and [7], a full duality is developed for distributive nearlattices and some applications are given, and recently in [15], the author proposes a sentential logic associated with the class of distributive nearlattices.…”

Section: Introductionmentioning

confidence: 99%

Note on $\alpha$-filters in distributive nearlattices

Calomino¹

2018

Math.Boh.

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“…Nearlattices and distributive nearlattices were studied by several authors [32,13,10,3,11,12,8,9,30,31]. Definition 2.5 ([3]).…”

Section: Distributive Nearlatticesmentioning

confidence: 99%

Selfextensional logics with a distributive nearlattice term

González

2018

Arch. Math. Logic

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We define when a ternary term m of an algebraic language L is called a distributive nearlattice term (DN-term) of a sentential logic S. Distributive nearlattices are ternary algebras generalising Tarski algebras and distributive lattices. We characterise the selfextensional logics with a DN-term through the interpretation of the DN-term in the algebras of the algebraic counterpart of the logics. We prove that the canonical class of algebras (under the point of view of Abstract Algebraic Logic) associated with a selfextensional logic with a DN-term is a variety, and we obtain that the logic is in fact fully selfextensional.Mathematics Subject Classification. 03G27, 03B22, 03G25, 06A12.Keywords. Selfextensional logics, distributive nearlattices, logics based on partial orders, abstract algebraic logic.

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“…A natural generalization of implication algebras is the class of nearlattices: join-semilattices with greatest element in which every principal filter is a bounded lattice. These structures were studied by different authors in [17,21,20,12,14,15,8,9,18,19]. A particular class of nearlattices is the class of distributive nearlattices, i.e., join-semilattices with greatest element in which every principal filter is a bounded distributive lattice.…”

Section: Introductionmentioning

confidence: 99%

“…Recently, distributive nearlattices were studied from the point of view of algebraic logic. In [18,19] a sentential logic was defined and studied in such a way that its algebraic counterpart is the class of distributive nearlattices.…”

Section: Introductionmentioning

confidence: 99%