scholarly journals Priestley duality for (modal) N4-lattices

10.29007/p4ch ◽  
2018 ◽  
Author(s):  
Ramon Jansana ◽  
Umberto Rivieccio
Keyword(s):  
Recent Work ◽  
Substructural Logics ◽  
Priestley Duality ◽  
Algebraic Semantics ◽  
Nelson Logic ◽  
Wide Family ◽  
Algebraic Counterpart

N4-lattices are the algebraic semantics of paraconsistent Nelson logic, which was introduced as an inconsistency-tolerant counterpart of the better-known logic of Nelson. Paraconsistent Nelson logic combines interesting features of intuitionistic, classical and many-valued logics (e.g., Belnap-Dunn four-valued logic); recent work has shown that it can also be seen as one member of the wide family of substructural logics.The work we present here is a contribution towards a better topological understanding of the algebraic counterpart of paraconsistent Nelson logic, namely a variety of involutive lattices called N4-lattices.

scholarly journals Basic Core Fuzzy Logics and Algebraic Routley–Meyer-Style Semantics

Axioms ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 273
Author(s):  
Eunsuk Yang
Keyword(s):  
Fuzzy Logic ◽  
Substructural Logics ◽  
Algebraic Semantics ◽  
Relational Semantics ◽  
Fuzzy Logics

Recently, algebraic Routley–Meyer-style semantics was introduced for basic substructural logics. This paper extends it to fuzzy logics. First, we recall the basic substructural core fuzzy logic MIAL (Mianorm logic) and its axiomatic extensions, together with their algebraic semantics. Next, we introduce two kinds of ternary relational semantics, called here linear Urquhart-style and Fine-style Routley–Meyer semantics, for them as algebraic Routley–Meyer-style semantics.

Quasi-Nelson algebras and fragments

2021 ◽  
pp. 1-29
Author(s):  
Umberto Rivieccio ◽  
Ramon Jansana
Keyword(s):  
Residuated Lattices ◽  
Substructural Logic ◽  
Lambek Calculus ◽  
Nelson Algebras ◽  
Algebraic Language ◽  
Nelson Logic ◽  
Algebraic Counterpart

Abstract The variety of quasi-Nelson algebras (QNAs) has been recently introduced and characterised in several equivalent ways: among others, as (1) the class of bounded commutative integral (but non-necessarily involutive) residuated lattices satisfying the Nelson identity, as well as (2) the class of (0, 1)-congruence orderable commutative integral residuated lattices. Logically, QNAs are the algebraic counterpart of quasi-Nelson logic, which is the (algebraisable) extension of the substructural logic ℱℒ ew (Full Lambek calculus with Exchange and Weakening) by the Nelson axiom. In the present paper, we collect virtually all the results that are currently known on QNAs, including solutions to certain questions left open in earlier publications. Furthermore, we extend our study to some subreducts of QNAs, that is, classes of algebras corresponding to fragments of the algebraic language obtained by eliding either the implication or the lattice operations.

Substructural fuzzy logics

2007 ◽  
Vol 72 (3) ◽  
pp. 834-864 ◽  
Author(s):  
George Metcalfe ◽  
Franco Montagna
Keyword(s):  
Linear Logic ◽  
Substructural Logics ◽  
Unit Interval ◽  
Residuated Lattices ◽  
Cut Elimination ◽  
Algebraic Semantics ◽  
Fuzzy Logics ◽  
The Real ◽  
Gentzen Systems ◽  
Intuitionistic Linear Logic

AbstractSubstructural fuzzy logics are substructural logics that are complete with respect to algebras whose lattice reduct is the real unit interval [0, 1]. In this paper, we introduce Uninorm logic UL as Multiplicative additive intuitionistic linear logic MAILL extended with the prelinearity axiom ((A → B) ∧ t) V ((B → A)∧ t). Axiomatic extensions of UL include known fuzzy logics such as Monoidal t-norm logic MIX and Gödel logic G, and new weakening-free logics. Algebraic semantics for these logics are provided by subvarieties of (representable) pointed bounded commutative residuated lattices. Gentzen systems admitting cut-elimination are given in the framework of hypersequents. Completeness with respect to algebras with lattice reduct [0, 1] is established for UL and several extensions using a two-part strategy. First, completeness is proved for the logic extended with Takeuti and Titani's density rule. A syntactic elimination of the rule is then given using a hypersequent calculus. As an algebraic corollary, it follows that certain varieties of residuated lattices are generated by their members with lattice reduct [0, 1].

Nelson’s logic 𝒮

2020 ◽  
Author(s):  
Thiago Nascimento ◽  
Umberto Rivieccio ◽  
João Marcos ◽  
Matthew Spinks
Keyword(s):  
Residuated Lattices ◽  
The Other ◽  
Algebraic Semantics ◽  
Intended Interpretation ◽  
Nelson Logic

Abstract Besides the better-known Nelson logic ($\mathcal{N}3$) and paraconsistent Nelson logic ($\mathcal{N}4$), in 1959 David Nelson introduced, with motivations of realizability and constructibility, a logic called $\mathcal{S}$. The logic $\mathcal{S}$ was originally presented by means of a calculus (crucially lacking the contraction rule) with infinitely many rule schemata and no semantics (other than the intended interpretation into Arithmetic). We look here at the propositional fragment of $\mathcal{S}$, showing that it is algebraizable (in fact, implicative), in the sense of Blok and Pigozzi, with respect to a variety of three-potent involutive residuated lattices. We thus introduce the first known algebraic semantics for $\mathcal{S}$ as well as a finite Hilbert-style calculus equivalent to Nelson’s presentation; this also allows us to clarify the relation between $\mathcal{S}$ and the other two Nelson logics $\mathcal{N}3$ and $\mathcal{N}4$.

What sentimentalists should say about emotion

2019 ◽  
Vol 42 ◽  
Author(s):  
Charlie Kurth
Keyword(s):  
Moral Judgment ◽  
Recent Work ◽  
Relevant Information ◽  
Moral Cognition ◽  
Multilevel Structure

Abstract Recent work by emotion researchers indicates that emotions have a multilevel structure. Sophisticated sentimentalists should take note of this work – for it better enables them to defend a substantive role for emotion in moral cognition. Contra May's rationalist criticisms, emotions are not only able to carry morally relevant information, but can also substantially influence moral judgment and reasoning.

The Sun as a Magnetic Star

1976 ◽  
Vol 32 ◽  
pp. 457-463
Author(s):  
John M. Wilcox ◽  
Leif Svalgaard
Keyword(s):  
Recent Work ◽  
Rotation Axis ◽  
Polar Field ◽  
Magnetic Star ◽  
Rotational Axis ◽  
Field Variation ◽  
The Sun ◽  
Arbitrary Angle ◽  
Solar Magnetism ◽  
Oblique Rotator

SummaryThe sun as a magnetic star is described on the basis of recent work on solar magnetism. Observations at an arbitrary angle to the rotation axis would show a 22-year polar field variation and a 25-day equatorial sector variation. The sector variation would be similar to an oblique rotator with an angle of 90° between the magnetic and rotational axis.

Microstructural comparison of synthetic bioceramics with natural bioceramics

1991 ◽  
Vol 49 ◽  
pp. 38-39
Author(s):  
Shulin Wen ◽  
Jingwei Feng ◽  
A. Krajewski ◽  
A. Ravaglioli
Keyword(s):  
Recent Work ◽  
Human Body ◽  
Human Tissues ◽  
Main Constituent ◽  
Laboratory Furnace ◽  
Chinese Adult ◽  
Human Enamel ◽  
Biological Compatibility ◽  
Synthetic Hydroxyapatite ◽  
Synthetic Work

Hydroxyapatite bioceramics has attracted many material scientists as it is the main constituent of the bone and the teeth in human body. The synthesis of the bioceramics has been performed for years. Nowadays, the synthetic work is not only focused on the hydroapatite but also on the fluorapatite and chlorapatite bioceramics since later materials have also biological compatibility with human tissues; and they may also be very promising for clinic purpose. However, in comparison of the synthetic bioceramics with natural one on microstructure, a great differences were observed according to our previous results. We have investigated these differences further in this work since they are very important to appraise the synthetic bioceramics for their clinic application.The synthetic hydroxyapatite and chlorapatite were prepared according to A. Krajewski and A. Ravaglioli and their recent work. The briquettes from different hydroxyapatite or chlorapatite powders were fired in a laboratory furnace at the temperature of 900-1300°C. The samples of human enamel selected for the comparison with synthetic bioceramics were from Chinese adult teeth.

Substrate specificity and inducibility of TACE (tumour necrosis factor α-converting enzyme) revisited: the Ala-Val preference, and induced intrinsic activity

2003 ◽  
Vol 70 ◽  
pp. 39-52 ◽  
Author(s):  
Roy A. Black ◽  
John R. Doedens ◽  
Rajeev Mahimkar ◽  
Richard Johnson ◽  
Lin Guo ◽  
...  
Keyword(s):  
Substrate Specificity ◽  
Recent Work ◽  
Tumour Necrosis Factor ◽  
Tumour Necrosis ◽  
Transforming Growth Factor ◽  
Intrinsic Activity ◽  
Converting Enzyme ◽  
Tumour Necrosis Factor Α ◽  
Factor Α ◽  
Necrosis Factor

Tumour necrosis factor α (TNFα)-converting enzyme (TACE/ADAM-17, where ADAM stands for a disintegrin and metalloproteinase) releases from the cell surface the extracellular domains of TNF and several other proteins. Previous studies have found that, while purified TACE preferentially cleaves peptides representing the processing sites in TNF and transforming growth factor α, the cellular enzyme nonetheless also sheds proteins with divergent cleavage sites very efficiently. More recent work, identifying the cleavage site in the p75 TNF receptor, quantifying the susceptibility of additional peptides to cleavage by TACE and identifying additional protein substrates, underlines the complexity of TACE-substrate interactions. In addition to substrate specificity, the mechanism underlying the increased rate of shedding caused by agents that activate cells remains poorly understood. Recent work in this area, utilizing a peptide substrate as a probe for cellular TACE activity, indicates that the intrinsic activity of the enzyme is somehow increased.

Recent work on group III antimonides and arsenides

Physica ◽  
1954 ◽  
Vol 3 (7-12) ◽  
pp. 1065-1067
Author(s):  
H HROSTOWSKI ◽  
M TANENBAUM
Keyword(s):  
Recent Work ◽  
Group Iii
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