Strong negation in intuitionistic style sequent systems for residuated lattices

2014 ◽  
Vol 60 (4-5) ◽  
pp. 319-334 ◽  
Author(s):  
Michał Kozak
Keyword(s):  
Residuated Lattices ◽  
Strong Negation ◽  
Sequent Systems

scholarly journals Residuated Structures and Orthomodular Lattices

Studia Logica ◽  
2021 ◽  
Author(s):  
D. Fazio ◽  
A. Ledda ◽  
F. Paoli
Keyword(s):  
Algebraic Logic ◽  
Residuated Lattices ◽  
Quantum Structures ◽  
Heyting Algebras ◽  
Quantum Algebras ◽  
Orthomodular Lattices ◽  
Lattice Of Subvarieties ◽  
Residuated Structures ◽  
Common Framework ◽  
Mv Algebras

AbstractThe variety of (pointed) residuated lattices includes a vast proportion of the classes of algebras that are relevant for algebraic logic, e.g., $$\ell $$ ℓ -groups, Heyting algebras, MV-algebras, or De Morgan monoids. Among the outliers, one counts orthomodular lattices and other varieties of quantum algebras. We suggest a common framework—pointed left-residuated $$\ell $$ ℓ -groupoids—where residuated structures and quantum structures can all be accommodated. We investigate the lattice of subvarieties of pointed left-residuated $$\ell $$ ℓ -groupoids, their ideals, and develop a theory of left nuclei. Finally, we extend some parts of the theory of join-completions of residuated $$\ell $$ ℓ -groupoids to the left-residuated case, giving a new proof of MacLaren’s theorem for orthomodular lattices.

Evaluation software for effects produced by MOOC in mediums with different linguistically levels

2018 ◽  
Vol 34 (3) ◽  
pp. 633-645
Author(s):  
Cornel Samoilă ◽  
Doru Ursuţiu ◽  
Vlad Jinga
Keyword(s):  
Statistical Analysis ◽  
Statistical Methods ◽  
Rapid Assessment ◽  
Assessment Method ◽  
Behavioral Changes ◽  
Strong Negation ◽  
Face To Face ◽  
Made In ◽  
The Way

Abstract MOOC appearance has produced, in a first phase, more discussions than contributions. Despite pessimistic opinions or those catastrophic foreseeing the end of the classic education by accepting MOOC, the authors consider that, as it is happening in all situations when a field is reformed, instead of criticism or catastrophic predictions, an assessment should be simply made. MOOC will not be better or worse if it is discussed and dissected but can be tested in action, perfected by results, or abandoned if it has no prospects. Without testing, no decision is valid. A similarity between the MOOC appearance and the appearance of the idea of flying machines heavier than air can be made. In the flight case, the first reaction was a strong negation (including at Academies level) and only performing the first independent flight with an apparatus heavier than air has shifted orientation from denial to contributions. So, practical tests clarified the battle between ideas. The authors of this article encourage the idea of testing–assessment and, therefore, imagined and proposed one software for quickly assess whether MOOC produces changes in knowledge, by simply transferring courses from ‘face-to-face’ environment into the virtual one. Among the methods of statistical analysis for student behavioral changes was chosen the Keppel method. It underpins the assessment method of this work being approached using both the version with one variable and also with three variables. It is intended that this attempts to pave the way for other series of rapid assessment regarding MOOC effects (using other statistical methods). We believe, that this is the only approach that can lead either to improve the system or to renunciation.

The subvariety of commutative residuated lattices represented by twist-products

2014 ◽  
Vol 71 (1) ◽  
pp. 5-22 ◽  
Author(s):  
Manuela Busaniche ◽  
Roberto Cignoli
Keyword(s):  
Residuated Lattices

Compatible Operations on Residuated Lattices

Studia Logica ◽  
2011 ◽  
Vol 98 (1-2) ◽  
pp. 203-222 ◽  
Author(s):  
J. L. Castiglioni ◽  
H. J. San Martín
Keyword(s):  
Residuated Lattices

Splittings in varieties of logic

2021 ◽  
pp. 1-48
Author(s):  
Brian A. Davey ◽  
Tomasz Kowalski ◽  
Christopher J. Taylor
Keyword(s):  
Residuated Lattices ◽  
Heyting Algebras ◽  
General Lemma ◽  
Negative Results ◽  
Splitting Algebras

We study splittings or lack of them, in lattices of subvarieties of some logic-related varieties. We present a general lemma, the non-splitting lemma, which when combined with some variety-specific constructions, yields each of our negative results: the variety of commutative integral residuated lattices contains no splitting algebras, and in the varieties of double Heyting algebras, dually pseudocomplemented Heyting algebras and regular double [Formula: see text]-algebras the only splitting algebras are the two-element and three-element chains.

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