Paraconsistency, self-extensionality, modality

2018 ◽  
Vol 28 (5) ◽  
pp. 851-880
Author(s):  
Arnon Avron ◽  
Anna Zamansky
Keyword(s):  
Intuitionistic Logic ◽  
Modal Logics ◽  
The Other ◽  
Paraconsistent Logics ◽  
Classical Negation ◽  
Inconsistent Theories ◽  
Replacement Property ◽  
General Method

Abstract Paraconsistent logics are logics that, in contrast to classical and intuitionistic logic, do not trivialize inconsistent theories. In this paper we take a paraconsistent view on two famous modal logics: B and S5. We use for this a well-known general method for turning modal logics to paraconsistent logics by defining a new (paraconsistent) negation as $\neg \varphi =_{Def} \sim \Box \varphi$ (where $\sim$ is the classical negation). We show that while that makes both B and S5 members of the well-studied family of paraconsistent C-systems, they differ from most other C-systems in having the important replacement property (which means that equivalence of formulas implies their congruence). We further show that B is a very robust C-system in the sense that almost any axiom which has been considered in the context of C-systems is either already a theorem of B or its addition to B leads to a logic that is no longer paraconsistent. There is exactly one notable exception, and the result of adding this exception to B leads to the other logic studied here, S5.

Mastication of Rubber. II. Interpolymerization of Natural Rubber and Neoprene on Cold Milling

1956 ◽  
Vol 29 (2) ◽  
pp. 427-437
Author(s):  
D. J. Angier ◽  
W. F. Watson
Keyword(s):  
Free Radicals ◽  
Natural Rubber ◽  
Small Molecules ◽  
The Other ◽  
Polymer Molecules ◽  
Commercially Important ◽  
The Individual ◽  
Cold Mill ◽  
General Method ◽  
Butadiene Styrene

Abstract The softening of elastomers on cold milling results from scission of the polymer molecules by the applied shearing forces. The ruptured chains are free radicals, which can undergo mutual combination, interaction with oxygen and various additives, and branching (grafting) on to other polymer molecules. A general method of producing graft and block interpolymers between elstomers is therefore indicated, namely, to cold-mill the polymers together in the absence of small molecules which can terminate the polymeric radicals in order that the radicals may cross-terminate or graft onto the polymer molecules of the other type. A survey of several pairs of the commercially important elastomers, natural rubber, butadiene-styrene, Neoprene, and butadiene-acrylonitrile, has shown that cold milling does effect interlinking. Detailed results for the rubber-Neoprene system are reported in this communication. Experimental verification of polymer interlinking was obtained from the solubility properties of the milled elastomers. Cold milling of Neoprene under nitrogen produces gel, whereas of natural rubber does not, but the milling of mixtures gives gels containing natural rubber. Also, the solubilities and precipitation of the milled mixtures cannot be accounted for by these properties of the individual polymers. Finally, Neoprene-natural rubber mixtures, after and not before cold-milling, can be cross-linked by magnesium oxide, with rubber bound into the vulcanizate.

An abstract algebraic logic approach to tetravalent modal logics

2000 ◽  
Vol 65 (2) ◽  
pp. 481-518 ◽  
Author(s):  
Josep Maria Font ◽  
Miquel Rius
Keyword(s):  
Algebraic Logic ◽  
Modal Logics ◽  
The Other ◽  
Abstract Algebraic Logic ◽  
Algebraic Semantics ◽  
Modal Algebras ◽  
Logic Approach ◽  
Abstract Logics ◽  
Joint Study

AbstractThis paper contains a joint study of two sentential logics that combine a many-valued character, namely tetravalence, with a modal character; one of them is normal and the other one quasinormal. The method is to study their algebraic counterparts and their abstract models with the tools of Abstract Algebraic Logic, and particularly with those of Brown and Suszko's theory of abstract logics as recently developed by Font and Jansana in their “A General Algebraic Semantics for Sentential Logics”. The logics studied here arise from the algebraic and lattice-theoretical properties we review of Tetravalent Modal Algebras, a class of algebras studied mainly by Loureiro, and also by Figallo. Landini and Ziliani, at the suggestion of the late Antonio Monteiro.

scholarly journals Canonical formulas via locally finite reducts and generalized dualities

10.29007/hgbj ◽  
2018 ◽  
Author(s):  
Nick Bezhanishvili
Keyword(s):  
Modal Logic ◽  
Intuitionistic Logic ◽  
Algebraic Approach ◽  
Modal Logics ◽  
Substructural Logic ◽  
Locally Finite ◽  
Canonical Formulas

The method of canonical formulas is a powerful tool for investigating intuitionistic and modal logics. In this talk I will discuss an algebraic approach to this method. I will mostly concentrate on the case of intuitionistic logic. But I will also review the case of modal logic and possible generalizations to substructural logic.

scholarly journals Quantum key distribution with correlated sources

2020 ◽  
Vol 6 (37) ◽  
pp. eaaz4487 ◽  
Author(s):  
Margarida Pereira ◽  
Go Kato ◽  
Akihiro Mizutani ◽  
Marcos Curty ◽  
Kiyoshi Tamaki
Keyword(s):  
Quantum Key Distribution ◽  
Key Distribution ◽  
The Other ◽  
Correlated Sources ◽  
Information Theoretic ◽  
Security Proofs ◽  
Information Theoretic Security ◽  
Special Cases ◽  
New Framework ◽  
General Method

In theory, quantum key distribution (QKD) offers information-theoretic security. In practice, however, it does not due to the discrepancies between the assumptions used in the security proofs and the behavior of the real apparatuses. Recent years have witnessed a tremendous effort to fill the gap, but the treatment of correlations among pulses has remained a major elusive problem. Here, we close this gap by introducing a simple yet general method to prove the security of QKD with arbitrarily long-range pulse correlations. Our method is compatible with those security proofs that accommodate all the other typical device imperfections, thus paving the way toward achieving implementation security in QKD with arbitrary flawed devices. Moreover, we introduce a new framework for security proofs, which we call the reference technique. This framework includes existing security proofs as special cases, and it can be widely applied to a number of QKD protocols.

A New General Method for the Determination of Optical Properties of Amorphous Silicon Films

1990 ◽  
Vol 192 ◽  
Author(s):  
G. Amato ◽  
L. Boarino ◽  
F. Fizzotti ◽  
C. Manfredotti
Keyword(s):  
Thin Films ◽  
Optical Properties ◽  
Amorphous Silicon ◽  
Optical Response ◽  
The Other ◽  
New Method ◽  
Silicon Thin Films ◽  
Physical Insight ◽  
General Method

ABSTRACTWe propose to apply a new method to model the optical response of amorphous silicon thin films. This method presents the advantage of having a good physical insight. On the other hand, although the model has been originally tested on different materials like a-Si, a-Ge and a-GaAs, we show that it is also sensitive to small differences like those that can exist between intrinsic and doped a-Si:H.

scholarly journals CONSTRUCTIVE GEOMETRY AND THE PARALLEL POSTULATE

2016 ◽  
Vol 22 (1) ◽  
pp. 1-104 ◽  
Author(s):  
MICHAEL BEESON
Keyword(s):  
Intuitionistic Logic ◽  
Euclidean Geometry ◽  
The Other ◽  
Field Theories ◽  
Kripke Models ◽  
Square Roots ◽  
The Third ◽  
Euclidean Field ◽  
Euclidean Field Theory ◽  
Independence Results

AbstractEuclidean geometry, as presented by Euclid, consists of straightedge-and-compass constructions and rigorous reasoning about the results of those constructions. We show that Euclidean geometry can be developed using only intuitionistic logic. This involves finding “uniform” constructions where normally a case distinction is used. For example, in finding a perpendicular to line L through point p, one usually uses two different constructions, “erecting” a perpendicular when p is on L, and “dropping” a perpendicular when p is not on L, but in constructive geometry, it must be done without a case distinction. Classically, the models of Euclidean (straightedge-and-compass) geometry are planes over Euclidean fields. We prove a similar theorem for constructive Euclidean geometry, by showing how to define addition and multiplication without a case distinction about the sign of the arguments. With intuitionistic logic, there are two possible definitions of Euclidean fields, which turn out to correspond to different versions of the parallel postulate.We consider three versions of Euclid’s parallel postulate. The two most important are Euclid’s own formulation in his Postulate 5, which says that under certain conditions two lines meet, and Playfair’s axiom (dating from 1795), which says there cannot be two distinct parallels to line L through the same point p. These differ in that Euclid 5 makes an existence assertion, while Playfair’s axiom does not. The third variant, which we call the strong parallel postulate, isolates the existence assertion from the geometry: it amounts to Playfair’s axiom plus the principle that two distinct lines that are not parallel do intersect. The first main result of this paper is that Euclid 5 suffices to define coordinates, addition, multiplication, and square roots geometrically.We completely settle the questions about implications between the three versions of the parallel postulate. The strong parallel postulate easily implies Euclid 5, and Euclid 5 also implies the strong parallel postulate, as a corollary of coordinatization and definability of arithmetic. We show that Playfair does not imply Euclid 5, and we also give some other independence results. Our independence proofs are given without discussing the exact choice of the other axioms of geometry; all we need is that one can interpret the geometric axioms in Euclidean field theory. The independence proofs use Kripke models of Euclidean field theories based on carefully constructed rings of real-valued functions. “Field elements” in these models are real-valued functions.

scholarly journals A general method of calculating the angles made by any planes of crystals, and the laws according to which they are formed

1833 ◽  
Vol 2 ◽  
pp. 227-229
Keyword(s):  
General Formula ◽  
Dihedral Angle ◽  
The Other ◽  
Plane Angle ◽  
General Process ◽  
Primitive Forms ◽  
Primary Form ◽  
General Method ◽  
Universal Application

The author, after stating the inconsistencies, inelegancies, and imperfections of the received notation for expressing the planes of a crystal, and the laws of decrement by which they arise, and of the usual methods of calculating their angles, explains the object of the present paper, which is to propose a system exempt from these inconveniencies, and adapted to reduce the mathematical portion of crystallography to a small number of simple formulae, of universal application. According to the method here followed, each plane of a crystal is represented by a symbol indicative of the laws from which it results, which, by varying only its indices, may be made to repre­sent any law whatever; and by means of these indices, and of the primary angles of the substance, we may derive a general formula expressing the dihedral angle contained between any one plane resulting from crystalline laws, and other . In the same manner we can find the angle contained between any two edges of the de­rived crystal. Conversely, having given the plane, or dihedral an­gles of any crystal, and its primary form, we can, by a direct and general process, deduce the laws of decrement according to which it is constituted. The purely mathematical part of this paper depends on two formulæ, demonstrated by the author elsewhere and here assumed as known; by means of one of which the dihedral angle included between any two planes can be calculated, when the equations of both planes are given; and by the other, the plane angle included between any two given right lines can in like manner be expressed by assigned functions of the coefficients of their equations, supposed given. These formulæ being taken for granted, nothing remains but to express by algebra­ical equations the planes which result from any assigned laws of decrement, for the different primitive forms which occur in crystallography.

scholarly journals Fund Management And the Liquidity of The Bank

2014 ◽  
Vol 16 (3) ◽  
pp. 231-258 ◽  
Author(s):  
Gantiah Wuryandani ◽  
Ramlan Ginting ◽  
Dudy Iskandar ◽  
Zulkarnain Sitompul
Keyword(s):  
Monetary Policy ◽  
Financial System ◽  
The Other ◽  
Fund Management ◽  
Panel Estimation ◽  
Dynamic Panel ◽  
Reserve Requirement ◽  
Bank Rate ◽  
Small Banks ◽  
General Method

This paper analyzes the liquidity of banks, both precautionary and involuntary liquidity. We apply dynamic panel estimation on individual bank data covering the period of Januari 2002 to November 2011.  The result shows that precautionary liquidity is more determined by the operation of the bank. On the other hand, the involuntary liquidity is more affected by the financial system condition. Related to the size, the  effect of the financial system condition and the macroeconomy is larger for the small banks. Moreover, the monetary policy in the form minimum reserve requirement affects the precautionary liquidity of the small banks; while the central bank rate is less influential to the bank liquidity.  Keywords: Banking, Liquidity, General Method of MomentJEL classification: G21, G11, C33

scholarly journals Metode Menentukan Kebutuhan Armada Penjualan: Studi Kasus Cabang Jakarta dari LIGI Perusahaan Asuransi Umum di Indonesia

2011 ◽  
Vol 2 (1) ◽  
pp. 399
Author(s):  
Brata Wibawa Djojo ◽  
Oey Charlie
Keyword(s):  
Sales Force ◽  
The Other ◽  
Structural Method ◽  
Insurance Company ◽  
Incremental Method ◽  
Classic Problem ◽  
Profitability Analysis ◽  
General Insurance ◽  
Turn Over ◽  
General Method

Many companies face a classic problem in sales people’s turn-over or under-target because of uncompeteny of sales people or highly unreasonable sales target. On the other side, management has a perception that the sales people they have are uncompetence and more recruitment for sales people is not reasonable with cost and budget. If the company can not determine the sales force size, it will make a bad culture and business would not run properly. Through this research, the simply formulation will be applied at Jakarta Branch of a general insurance company LIGI (JLIGI) to their sales force at the existing condition and including in 2011. The formulations that will be applied for JLIGI are using breakdown method, workload method, and incremental method. Those three methods have each advantage and disadvantage, whereas breakdown method is a simple and general method, workload method is a more structural method and incremental method needs cost and profitability analysis of the years. 

scholarly journals General approach to the sensitivity of the optics of an eye to change in elementary parameters with application to the Gaussian optics of a reduced eye

2009 ◽  
Vol 68 (4) ◽  
Author(s):  
W. F. Harris
Keyword(s):  
Optical Properties ◽  
Index Of Refraction ◽  
The Other ◽  
Radius Of Curvature ◽  
Corneal Curvature ◽  
Independent Variables ◽  
Gaussian Optics ◽  
Clear Statement ◽  
Two Independent Variables ◽  
General Method

Optical properties of the eye, including the refractive compensation, for example, may change if there are changes in any of the components that make up the eye.  The sensitivity to such changes isquantified via the derivative.  This paper employs the reduced eye and Gaussian optics to illustrate a general method for the analysis of sensitivity in eyes.  The method requires a clear statement of the dependent variable as a function of independent variables.  A symbolism is offered that makes the function unambiguous.  Sensitivities are determined for the fundamental optical properties,the transference and the corneal-plane refractivecompensation of a reduced eye to change in corneal power, curvature and radius of curvature and to change in axial length and index of refraction.  Emsley’s reduced eye is examined in particular.  Its corneal-plane refractive compensation has a sensitivity of  135 −135 D to change in refractive index,  1 −2.7 D/mm to change in length and  135 −1/3 to change in corneal curvature when the other two independent variables are held fixed.  The method has the potential to develop guidelines that are useful clini-cally.

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