ON CONTRA-CLASSICAL VARIANTS OF NELSON LOGIC N4 AND ITS CLASSICAL EXTENSION

2018 ◽  
Vol 11 (4) ◽  
pp. 805-820 ◽  
Author(s):  
HITOSHI OMORI ◽  
HEINRICH WANSING
Keyword(s):  
Paraconsistent Logic ◽  
Axiom System ◽  
Kripke Semantics ◽  
Classical Extension ◽  
Nelson Logic ◽  
General Method ◽  
Truth Tables

AbstractIn two recent articles, Norihiro Kamide introduces unusual variants of Nelson’s paraconsistent logic and its classical extension. Kamide’s systems, IP and CP, are unusual insofar as double negations in these logics behave as intuitionistic and classical negations, respectively. In this article we present Hilbert-style axiomatizations of both IP and CP. The axiom system for IP is shown to be sound and complete with respect to a four-valued Kripke semantics, and the axiom system for CP is characterized by four-valued truth tables. Moreover, we note some properties of IP and CP, and emphasize that these logics are unusual also because they are contra-classical and inconsistent but nontrivial. We point out that Kamide’s approach exemplifies a general method for obtaining contra-classical logics, and we briefly speculate about a linguistic application of Kamide’s logics.

A test for the equality of truth-tables

1952 ◽  
Vol 17 (3) ◽  
pp. 161-163 ◽  
Author(s):  
Jan Kalicki
Keyword(s):  
Finite Number ◽  
General Method ◽  
Truth Tables

In this paper the symbolism, definitions and results of my two papers, namely A test for the existence of tautologies according to many-valued truth-tables (hereafter referred to as ET) and Note on truth-tables (hereafter referred to as TT) will be presupposed.The problem whether two arbitrary truth-tables with finite number of elements are equal or not was reduced in TT to the question of equality of two identical tables in which different elements have been designated. However, no general method for testing the equality of truth-tables was given there, although some cases were discussed for which such a method is available. In the present paper we shall describe a general method using the considerations of ET and TT.

scholarly journals Quasi-N4-Lattices

2021 ◽  
Author(s):  
Umberto Rivieccio
Keyword(s):  
Paraconsistent Logic ◽  
General Setting ◽  
Extension Property ◽  
Double Negation ◽  
Structure Representation ◽  
Nelson Algebras ◽  
Nelson Logic ◽  
Double Negation Law ◽  
Logical Calculi ◽  
Twist Structure

Abstract Within the Nelson family, two mutually incomparable generalizations of Nelson constructive logic with strong negation have been proposed so far. The first and more well-known, Nelson paraconsistent logic , results from dropping the explosion axiom of Nelson logic; a more recent series of papers considers the logic (dubbed quasi-Nelson logic ) obtained by rejecting the double negation law, which is thus also weaker than intuitionistic logic. The algebraic counterparts of these logical calculi are the varieties of N4-lattices and quasi-Nelson algebras . In the present paper we propose the class of quasi- N4-lattices as a common generalization of both. We show that a number of key results, including the twist-structure representation of N4-lattices and quasi-Nelson algebras, can be uniformly established in this more general setting; our new representation employs twist-structures defined over Brouwerian algebras enriched with a nucleus operator. We further show that quasi-N4-lattices form a variety that is arithmetical, possesses a ternary as well as a quaternary deductive term, and enjoys EDPC and the strong congruence extension property.

Proof Systems for 3-valued Logics Based on Gödel’s Implication

2021 ◽  
Author(s):  
Arnon Avron
Keyword(s):  
Paraconsistent Logic ◽  
Type System ◽  
Type Systems ◽  
Cut Elimination ◽  
Proof Systems ◽  
Hilbert Type ◽  
Truth Tables

Abstract The logic $G3^{<}_{{{}^{\scriptsize{-}}}\!\!\textrm{L}}$ was introduced in Robles and Mendéz (2014, Logic Journal of the IGPL, 22, 515–538) as a paraconsistent logic which is based on Gödel’s 3-valued matrix, except that Kleene–Łukasiewicz’s negation is added to the language and is used as the main negation connective. We show that $G3^{<}_{{{}^{\scriptsize{-}}}\!\!\textrm{L}}$ is exactly the intersection of $G3^{\{1\}}_{{{}^{\scriptsize{-}}}\!\!\textrm{L}}$ and $G3^{\{1,0.5\}}_{{{}^{\scriptsize{-}}}\!\!\textrm{L}}$, the two truth-preserving 3-valued logics which are based on the same truth tables. (In $G3^{\{1\}}_{{{}^{\scriptsize{-}}}\!\!\textrm{L}}$ the set ${\cal D}$ of designated elements is $\{1\}$, while in $G3^{\{1,0.5\}}_{{{}^{\scriptsize{-}}}\!\!\textrm{L}}$  ${\cal D}=\{1,0.5\}$.) We then construct a Hilbert-type system which has (MP) for $\to $ as its sole rule of inference, and is strongly sound and complete for $G3^{<}_{{{}^{\scriptsize{-}}}\!\!\textrm{L}}$. Then we show how, by adding one axiom (in the case of $G3^{\{1\}}_{{{}^{\scriptsize{-}}}\!\!\textrm{L}}$) or one new rule of inference (in the case of $G3^{\{1,0.5\}}_{{{}^{\scriptsize{-}}}\!\!\textrm{L}}$), we get strongly sound and complete systems for $G3^{\{1\}}_{{{}^{\scriptsize{-}}}\!\!\textrm{L}}$ and $G3^{\{1,0.5\}}_{{{}^{\scriptsize{-}}}\!\!\textrm{L}}$. Finally, we provide quasi-canonical Gentzen-type systems which are sound and complete for those logics and show that they are all analytic, by proving the cut-elimination theorem for them.

A General Method for Spectrometer Design in the Scoff Approximation

1976 ◽  
Vol 34 ◽  
pp. 538-539
Author(s):  
J. R. Fields
Keyword(s):  
Electron Microscope ◽  
Transmission Electron Microscope ◽  
Energy Analysis ◽  
Incident Beam ◽  
Scanning Transmission Electron Microscope ◽  
Chemical Identification ◽  
Scanning Transmission Electron ◽  
Transmission Electron ◽  
Scanning Transmission ◽  
General Method

The energy analysis of electrons scattered by a specimen in a scanning transmission electron microscope can improve contrast as well as aid in chemical identification. In so far as energy analysis is useful, one would like to be able to design a spectrometer which is tailored to his particular needs. In our own case, we require a spectrometer which will accept a parallel incident beam and which will focus the electrons in both the median and perpendicular planes. In addition, since we intend to follow the spectrometer by a detector array rather than a single energy selecting slit, we need as great a dispersion as possible. Therefore, we would like to follow our spectrometer by a magnifying lens. Consequently, the line along which electrons of varying energy are dispersed must be normal to the direction of the central ray at the spectrometer exit.

Phase behavior of cationic and anionic surfactants at low concentrations

1992 ◽  
Vol 50 (1) ◽  
pp. 694-695
Author(s):  
E. Naranjo
Keyword(s):  
Phase Behavior ◽  
Structural Characterization ◽  
Dynamic Systems ◽  
Anionic Surfactants ◽  
Intermolecular Forces ◽  
Stable Form ◽  
Surfactant Mixtures ◽  
Low Concentrations ◽  
Cationic And Anionic Surfactants ◽  
General Method

Equilibrium vesicles, those which are the stable form of aggregation and form spontaneously on mixing surfactant with water, have never been demonstrated in single component bilayers and only rarely in lipid or surfactant mixtures. Designing a simple and general method for producing spontaneous and stable vesicles depends on a better understanding of the thermodynamics of aggregation, the interplay of intermolecular forces in surfactants, and an efficient way of doing structural characterization in dynamic systems.

Caricaturing as a general method to improve poor face recognition: Evidence from low-resolution images, other-race faces, and older adults.

2019 ◽  
Vol 25 (2) ◽  
pp. 256-279 ◽  
Author(s):  
Amy Dawel ◽  
Tsz Ying Wong ◽  
Jodie McMorrow ◽  
Callin Ivanovici ◽  
Xuming He ◽  
...  
Keyword(s):  
Older Adults ◽  
Face Recognition ◽  
Low Resolution ◽  
General Method ◽  
Low Resolution Images

Morphosemantic Analysis and Translation of Medical Compound Terms

1991 ◽  
Vol 30 (01) ◽  
pp. 30-35 ◽  
Author(s):  
P. Dujols ◽  
P. Aubas ◽  
C. Baylon ◽  
F. Grémy
Keyword(s):  
Medical Terms ◽  
General Method

This paper describes an automatic procedure for morphosemantic analysis and translation of compound medical terms. This analysis is of interest for the automatic indexation of medical discharge reports and summaries. Since words with the suffix -osis may have many different semantic interpretations, such -osis forms are taken as examples for a general method that avoids the difficulties in interpreting medical terms as reported in other studies.

Security of Cyber-Physical Systems: A Generalized Algorithm for Intrusion Detection and Determining Security Robustness of Cyber Physical Systems using Logical Truth Tables

2013 ◽  
Vol 9 ◽  
Author(s):  
Curtis G. Northcutt
Keyword(s):  
Intrusion Detection ◽  
Cyber Security ◽  
Logical Truth ◽  
Cyber Physical Systems ◽  
Security Model ◽  
Security Measures ◽  
Physical Systems ◽  
Multiple Signal ◽  
Security Attack ◽  
Truth Tables

The recent proliferation of embedded cyber components in modern physical systems [1] has generated a variety of new security risks which threaten not only cyberspace, but our physical environment as well. Whereas earlier security threats resided primarily in cyberspace, the increasing marriage of digital technology with mechanical systems in cyber-physical systems (CPS), suggests the need for more advanced generalized CPS security measures. To address this problem, in this paper we consider the first step toward an improved security model: detecting the security attack. Using logical truth tables, we have developed a generalized algorithm for intrusion detection in CPS for systems which can be defined over discrete set of valued states. Additionally, a robustness algorithm is given which determines the level of security of a discrete-valued CPS against varying combinations of multiple signal alterations. These algorithms, when coupled with encryption keys which disallow multiple signal alteration, provide for a generalized security methodology for both cyber-security and cyber-physical systems.

Gold Catalyzed Hydroamination of Propargylic Alcohols: Controlling Divergent Reaction Pathways to Access 1,3-Aminoalcohols, 3-Hydroxyketones or 3-Aminoketones

2018 ◽  
Author(s):  
Victor Laserna ◽  
Tom Sheppard
Keyword(s):  
Gold Catalysis ◽  
Reaction Pathways ◽  
High Yield ◽  
Reaction Conditions ◽  
Propargylic Alcohols ◽  
Catalytic Quantity ◽  
Selective Formation ◽  
General Method

A versatile approach to the valorization of propargylic alcohols is reported, enabling controlled access to three different products from the same starting materials. Firstly, a general method for the hydroamination of propargylic alcohols with anilines is described using gold catalysis to give 3-hydroxy imines with complete regioselectivity. These 3-hydroxyimines can be reduced to give 1,3-aminoalcohols with high syn seletivity. Alternatively, by using a catalytic quantity of aniline, 3-hydroxyketones can be obtained in high yield directly from propargylic alcohols. Further manipulation of the reaction conditions enables the selective formation of 3-aminoketones via a rearrangement/hydroamination pathway.<br>

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