The Free Distributive Semilattice Extension of a Distributive Poset

González, Luciano J.

doi:10.1007/s11083-018-9471-6

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The Logic Preserving Degrees Of Truth1

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2018

2024

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Cited by 4 publications

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“…Since the logic S ≤ K is an extension of the logic S K , we have Fi S ≤ K (A) ⊆ Fi SK (A) for every algebra A. Let now A ∈ K. Since the lattice Fi F (A) is distributive, it follows that Fi F (A) = Fi(A) (see [29,Proposition 4.3]). Then, by Proposition 3.9 and Lemma 5.7, it follows that…”

Section: The Logic Preserving Degrees Of Truthmentioning

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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Section: The Logic Preserving Degrees Of Truthmentioning

confidence: 99%