Paraconsistent Double Negation That Can Simulate Classical Negation

2016 ◽  
Author(s):  
Norihiro Kamide
Keyword(s):  
Double Negation ◽  
Classical Negation

Test d’Indépendance au Contexte (TIC) et Structure des Représentations Sociales

2008 ◽  
Vol 67 (2) ◽  
pp. 119-123 ◽  
Author(s):  
Grégory Lo Monaco ◽  
Florent Lheureux ◽  
Séverine Halimi-Falkowicz
Keyword(s):  
Double Negation ◽  
Représentations Sociales ◽  
Representations Sociales

Deux techniques permettent le repérage systématique du système central d’une représentation sociale: la technique de la mise en cause (MEC) et le modèle des schèmes cognitifs de base (SCB). Malgré cet apport, ces techniques présentent des inconvénients: la MEC, de par son principe de double négation, et les SCB, de par la longueur de passation. Une nouvelle technique a été développée: le test d’indépendance au contexte (TIC). Elle vise à rendre compte des caractères trans-situationnel ou contingent des éléments représentationnels, tout en présentant un moindre coût cognitif perçu. Deux objets de représentation ont été étudiés auprès d’une population étudiante. Les résultats révèlent que le TIC paraît, aux participants, cognitivement moins coûteux que la MEC. De plus, le TIC permet un repérage du noyau central identique à celui offert par la MEC.

scholarly journals Negation in Berber: Variation, evolution, and typology

Linguistics ◽  
2020 ◽  
Vol 58 (4) ◽  
pp. 967-1008
Author(s):  
Mena B. Lafkioui ◽  
Vermondo Brugnatelli
Keyword(s):  
North Africa ◽  
North African ◽  
Double Negation ◽  
New Developments ◽  
Area North

AbstractDouble and triple negation marking is an ancient and deep-rooted feature that is attested in almost the entire Berber-speaking area (North Africa and diaspora), regardless of the type of negators in use; i. e., discontinuous markers (preverbal and postverbal negators) and dedicated negative verb stem alternations. In this article, we deal with the main stages that have led to the present Berber negation patterns and we argue, from a typological viewpoint, that certain morphophonetic mechanisms are to be regarded as a hitherto overlooked source for new negators. Moreover, we present a number of motivations that account for the hypothesis that, in Berber, those languages with both a preverbal and a postverbal negator belong to a diachronic stage prior to the attested languages with a preverbal negator only. Consequently, the study demonstrates that the Jespersen Cycle is back to the beginning in certain Berber languages. In doing so, we also show that Berber is to be regarded as a substrate in the development of double negation in North African Arabic. In addition, the study accounts for the asymmetric nature of Berber negation, although some new developments towards more symmetrical negation configurations are also attested.

scholarly journals On Correspondence between Selective CPS Transformation and Selective Double Negation Translation

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 385
Author(s):  
Hyeonseung Im
Keyword(s):  
Programming Languages ◽  
Intuitionistic Logic ◽  
Reference Point ◽  
Classical Logic ◽  
Proof System ◽  
Double Negation

A double negation translation (DNT) embeds classical logic into intuitionistic logic. Such translations correspond to continuation passing style (CPS) transformations in programming languages via the Curry-Howard isomorphism. A selective CPS transformation uses a type and effect system to selectively translate only nontrivial expressions possibly with computational effects into CPS functions. In this paper, we review the conventional call-by-value (CBV) CPS transformation and its corresponding DNT, and provide a logical account of a CBV selective CPS transformation by defining a selective DNT via the Curry-Howard isomorphism. By using an annotated proof system derived from the corresponding type and effect system, our selective DNT translates classical proofs into equivalent intuitionistic proofs, which are smaller than those obtained by the usual DNTs. We believe that our work can serve as a reference point for further study on the Curry-Howard isomorphism between CPS transformations and DNTs.

scholarly journals Double Negation in a Negative Concord language: An experimental investigation

Lingua ◽  
2015 ◽  
Vol 163 ◽  
pp. 75-107 ◽  
Author(s):  
Viviane Déprez ◽  
Susagna Tubau ◽  
Anne Cheylus ◽  
M. Teresa Espinal
Keyword(s):  
Experimental Investigation ◽  
Negative Concord ◽  
Double Negation

Correction to a definition of negation

1984 ◽  
Vol 49 (1) ◽  
pp. 47-50 ◽  
Author(s):  
Frederic B. Fitch
Keyword(s):  
Fixed Point ◽  
Personal Communication ◽  
The Other ◽  
Transfinite Induction ◽  
Original Form ◽  
Basic Logic ◽  
Double Negation ◽  
Original Letter ◽  
The Law ◽  
Definition Of

In [3] a definition of negation was presented for the system K′ of extended basic logic [1], but it has since been shown by Peter Päppinghaus (personal communication) that this definition fails to give rise to the law of double negation as I claimed it did. The purpose of this note is to revise this defective definition in such a way that it clearly does give rise to the law of double negation, as well as to the other negation rules of K′.Although Päppinghaus's original letter to me was dated September 19, 1972, the matter has remained unresolved all this time. Only recently have I seen that there is a simple way to correct the definition. I am of course very grateful to Päppinghaus for pointing out my error in claiming to be able to derive the rule of double negation from the original form of the definition.The corrected definition will, as before, use fixed-point operators to give the effect of the required kind of transfinite induction, but this time a double transfinite induction will be used, somewhat like the double transfinite induction used in [5] to define simultaneously the theorems and antitheorems of system CΓ.

scholarly journals THE UNITY AND IDENTITY OF DECIDABLE OBJECTS AND DOUBLE-NEGATION SHEAVES

2018 ◽  
Vol 83 (04) ◽  
pp. 1667-1679
Author(s):  
MATÍAS MENNI
Keyword(s):  
Differential Geometry ◽  
Algebraic Geometry ◽  
Algebraic Topology ◽  
Full Subcategory ◽  
Sufficient Conditions ◽  
Double Negation ◽  
Synthetic Differential Geometry ◽  
Simplicial Sets ◽  
Image Position

AbstractLet ${\cal E}$ be a topos, ${\rm{Dec}}\left( {\cal E} \right) \to {\cal E}$ be the full subcategory of decidable objects, and ${{\cal E}_{\neg \,\,\neg }} \to {\cal E}$ be the full subcategory of double-negation sheaves. We give sufficient conditions for the existence of a Unity and Identity ${\cal E} \to {\cal S}$ for the two subcategories of ${\cal E}$ above, making them Adjointly Opposite. Typical examples of such ${\cal E}$ include many ‘gros’ toposes in Algebraic Geometry, simplicial sets and other toposes of ‘combinatorial’ spaces in Algebraic Topology, and certain models of Synthetic Differential Geometry.

On the Subject of Negative Auxiliary Inversion

2018 ◽  
Vol 64 (1) ◽  
pp. 32-61 ◽  
Author(s):  
Frances Blanchette ◽  
Chris Collins
Keyword(s):  
Word Order ◽  
Negative Polarity ◽  
Subject Position ◽  
Left Periphery ◽  
Negative Concord ◽  
Double Negation ◽  
Polarity Items ◽  
West Texas ◽  
The Subject ◽  
Scope Freezing

AbstractThis article presents a novel analysis ofNegative Auxiliary Inversion(NAI) constructions such asdidn't many people eat, in which a negated auxiliary appears in pre-subject position. NAI, found in varieties including Appalachian, African American, and West Texas English, has a word order identical to a yes/no question, but is pronounced and interpreted as a declarative. We propose that NAI subjects are negative DPs, and that the negation raises from the subject DP to adjoin to Fin (a functional head in the left periphery). Three properties of NAI motivate this analysis: (i) scope freezing effects, (ii) the various possible and impossible NAI subject types, and (iii) the incompatibility of NAI constructions with true Double-Negation interpretations. Implications for theories of Negative Concord, Negative Polarity Items, and the representation of negation are discussed.

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