We study logics determined by matrices consisting of a De Morgan lattice with an upward closed set of designated values, such as the logic of non‐falsity preservation in a given finite Boolean algebra and Shramko's logic of non‐falsity preservation in the four‐element subdirectly irreducible De Morgan lattice. The key tool in the study of these logics is the lattice‐theoretic notion of an n‐filter. We study the logics of all (complete, consistent, and classical) n‐filters on De Morgan (...) class='Hi'>lattices, which are non‐adjunctive generalizations of the four‐valued logic of Belnap and Dunn (of the three‐valued logics of Priest and Kleene, and of classical logic). We then show how to find a finite Hilbert‐style axiomatization of any logic determined by a finite family of prime upsets of finite De Morgan lattices and a finite Gentzen‐style axiomatization of any logic determined by a finite family of filters on finite De Morgan lattices. As an application, we axiomatize Shramko's logic of anything but falsehood. (shrink)

This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be (...) preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

. Relational semantics for nonclassical logics lead straightforwardly to topological representation theorems of their algebras. Ortholattices and De Morgan lattices are reducts of the algebras of various nonclassical logics. We define three new classes of topological spaces so that the lattice categories and the corresponding categories of topological spaces turn out to be dually isomorphic. A key feature of all these topological spaces is that they are ordered relational or ordered product topologies.

Originally published in 1966 On the Syllogism and Other Logical Writings assembles for the first time the five celebrated memoirs of Augustus De Morgan on the syllogism. These are collected together with the more condensed accounts of his researches given in his Syllabus of a Proposed System of Logic an article on Logic contributed to the English Cyclopaedia. De Morgan was among the most distinguished of nineteenth century British mathematicians but is chiefly remembered today as one of the (...) founders of modern mathematical logic. His writings on this subject have been little read, however since apart from his Formal Logic, they lie buried for the most part in inaccessible periodicals. De Morgan's own later amendments are inserted in the text and the editorial introduction gives a summary of the whole and traces in some detail the course of the once-famous feud with Sir William Hamilton of Edinburgh. (shrink)

DeMorgan lattice logic is the consecution version of Anderson/Belnap’s calculus of First Degree Entailments [1]. Theorems of DML are of the form Γ ` A, where Γ is a non-empty set of formulae. Let Γ = {A1, . . . , An}, then Γ ` A is a theorem of DML if and only if A1& . . . &An → A is a theorem of F DE. The Gentzenization of DML offered in this paper, LDML, derives from the worlds (...) semantics for F DE, first presented in [3]. It is for this reason that LDML may be called a “Gentzen semantics” for DML. (shrink)

Augustus De Morgan was a British mathematician and logician. He formulated De Morgan's laws and introduced the term mathematical induction, making its idea rigorousFrom the introduction:"If I had before me a fly and an elephant, having never seen more than one such magnitude of either kind; and if the fly were to endeavor to persuade me that he was larger than the elephant, I might by possibility be placed in a difficulty. The apparently little creature might use such (...) arguments about the effect of distance, and might appeal to such laws of sight and hearing as I, if unlearned in those things, might be unable wholly to reject. But if there were a thousand flies, all buzzing, to appearance, about the great creature; and, to a fly, declaring, each one for himself, that he was bigger than the quadruped; and all giving different and frequently contradictory reasons; and each one despising and opposing the reasons of the others-I should feel quite at my ease. I should certainly say, My little friends, the case of each one of you is destroyed by the rest. I intend to show flies in the swarm, with a few larger animals, for reasons to be given.In every age of the world there has been an established system, which has been opposed from time to time by isolated and dissentient reformers. The established system has sometimes fallen, slowly and gradually: it has either been upset by the rising influence of some one man, or it has been sapped by gradual change of opinion in the many.I have insisted on the isolated character of the dissentients, as an element of the a priori probabilities of the case. Show me a schism, especially a growing schism, and it is another thing. The homeopathists, for instance, shall be, if any one so think, as wrong as St. John Long; but an organized opposition, supported by the efforts of many acting in concert, appealing to common arguments and experience, with perpetual succession and a common seal, as the Queen says in the charter, is, be the merit of the schism what it may, a thing wholly different from the case of the isolated opponent in the mode of opposition to it which reason points out.During the last two centuries and a half, physical knowledge has been gradually made to rest upon a basis which it had not before. It has become mathematical. The question now is, not whether this or that hypothesis is better or worse to the pure thought, but whether it accords with observed phenomena in those consequences which can be shown necessarily to follow from it, if it be true. Even in those sciences which are not yet under the dominion of mathematics, and perhaps never will be, a working copy of the mathematical process has been made. This is not known to the followers of those sciences who are not themselves mathematicians and who very often exalt their horns against the mathematics in consequence. They might as well be squaring the circle, for any sense they show in this particular.". (shrink)

We investigate the class of those algebras in which is a de Morgan algebra, is a quasi-Stone algebra, and the operations \ and \ are linked by the identity x**º = x*º*. We show that such an algebra is subdirectly irreducible if and only if its congruence lattice is either a 2-element chain or a 3-element chain. In particular, there are precisely eight non-isomorphic subdirectly irreducible Stone de Morgan algebras.

De Morgan's Formal Logic, which was published on virtually the same day in 1847 as Boole's The Mathematical Analysis of Logic, contains a logic of complex terms (LCT) which has been sadly neglected. It is surprising to find that LCT contains almost a full theory of Boolean algebra. This paper will: (1) provide some background to LCT; (2) outline its main features; (3) point out some gaps in it; (4) compare it with Boole's algebra; (5) show that it is (...) a lattice-theoretical formulation of Boolean algebra; (6) discuss some issues of historical priority; and (7) conclude with the puzzle of LCT's lack of influence. (shrink)

The aim of this paper is technically to study Belnap's four-valued sentential logic . First, we obtain a Gentzen-style axiomatization of this logic that contains no structural rules while all they are still admissible in the Gentzen system what is proved with using some algebraic tools. Further, the mentioned logic is proved to be the least closure operator on the set of {Λ, V, ⌝}-formulas satisfying Tarski's conditions for classical conjunction and disjunction together with De Morgan's laws for negation. (...) It is also proved that Belnap's logic is the only sentential logic satisfying the above-mentioned conditions together with Anderson-Belnap's Variable-Sharing Property. Finally, we obtain a finite Hilbert-style axiomatization of this logic. As a consequence, we obtain a finite Hilbert-style axiomatization of Priest's logic of paradox. (shrink)

In this note we introduce the variety $${{\mathcal C}{\mathcal D}{\mathcal M}_\square}$$ of classical modal De Morgan algebras as a generalization of the variety $${{{\mathcal T}{\mathcal M}{\mathcal A}}}$$ of Tetravalent Modal algebras studied in [ 11 ]. We show that the variety $${{\mathcal V}_0}$$ defined by H. P. Sankappanavar in [ 13 ], and the variety S of Involutive Stone algebras introduced by R. Cignoli and M. S de Gallego in [ 5 ], are examples of classical modal De (...) class='Hi'>Morgan algebras. We give a representation theory, and we study the regular filters, i.e., lattice filters closed under an implication operation. Finally we prove that the variety $${{{\mathcal T}{\mathcal M}{\mathcal A}}}$$ has the Amalgamation Property and the Superamalgamation Property. (shrink)

In this paper we use Hobby's duality for semi-De Morgan algebras, to characterize those algebras having only principal congruences in the classes of semi-De Morgan algebras, demi-pseudocomplemented lattices and almost pseudocomplemented lattices. This work extends some of the results reached by Beazer in [3] and [4].

O objetivo do estudo foi investigar a prevalência e motivos do uso de álcool, tabaco e outras drogas por acadêmicos. A amostra foi composta por 560 estudantes, entre 17 e 74 anos ( M = 31,16, DP = 11,10). As substâncias com maior prevalência de uso na vida foram álcool e tabaco. Dentre as drogas ilí..

O climatério/menopausa é caracterizado por intensas alterações morfofisiológicas e comportamentais. O objetivo foi identificar os sinais e sintomas do climatério/menopausa e a sua relação com a Imagem corporal de mulheres ribeirinhas de uma região da Amazônia Brasileira. Estudo incluiu 100 mulheres de seis comunidades ribeirinhas de Itaituba/Pará. Os instrumentos utilizados foram: o questionário sociodemográfico, a Escala dos Sinais e Sintomas da Menopausa (MRS) e a Escala de Silhuetas de Stunkard. Para avaliar as associações entre as variáveis categóricas, o teste qui-quadrado (...) de Pearson e teste exato de Fisher foram utilizados, (p≤0,05). Os resultados indicaram que 76% das mulheres estavam insatisfeitas com a sua imagem corporal, seja porque queriam ter corpos menores ou corpos maiores. Em relação aos sintomas do climatério/menopausa, estes são percebidos de forma moderada pelas mulheres. Conclusão: Se faz necessário levar as mulheres o conhecimento desta fase da vida e assim promover saúde neste importante período da vida. (shrink)

The only complete edition in English of Baruch Spinoza's works, this volume features Samuel Shirley's preeminent translations, distinguished at once by the lucidity and fluency with which they convey the flavor and meaning of Spinoza's original texts. Michael L. Morgan provides a general introduction that places Spinoza in Western philosophy and culture and sketches the philosophical, scientific, religious, moral and political dimensions of Spinoza's thought. Morgan's brief introductions to each work give a succinct historical, biographical, and philosophical overview. (...) A chronology and index are included. (shrink)

In this paper we obtain characterizations of subalgebras of Heyting algebras and De Morgan Heyting algebras. In both cases we obtain these characterizations by defining certain equivalence relations on the Priestley-type topological representations of the corresponding algebras. As a particular case we derive the characterization of maximal subalgebras of Heyting algebras given by M. Adams for the finite case.

An algebra A is said to be congruence coherent if every subalgebra of A that contains a class of some congruence on A is a union of -classes. This property has been investigated in several varieties of lattice-based algebras. These include, for example, de Morgan algebras, p-algebras, double p-algebras, and double MS-algebras. Here we determine precisely when the property holds in the class of symmetric extended de Morgan algebras.

The variety DMM of De Morgan monoids has just four minimal subvarieties. The join-irreducible covers of these atoms in the subvariety lattice of DMM are investigated. One of the two atoms consisting of idempotent algebras has no such cover; the other has just one. The remaining two atoms lack nontrivial idempotent members. They are generated, respectively, by 4-element De Morgan monoids C4 and D4, where C4 is the only nontrivial 0-generated algebra onto which finitely subdirectly irreducible De (...) class='Hi'>Morgan monoids may be mapped by noninjective homomorphisms. The homomorphic preimages of C4 within DMM constitute a proper quasivariety, which is shown to have a largest subvariety U. The covers of the variety within U are revealed here. There are just ten of them. In exactly six of these ten varieties, all nontrivial members have C4 as a retract. In the varietal join of those six classes, every subquasivariety is a variety—in fact, every finite subdirectly irreducible algebra is projective. Beyond U, all covers of [or of ] within DMM are discriminator varieties. Of these, we identify infinitely many that are finitely generated, and some that are not. We also prove that there are just 68 minimal quasivarieties of De Morgan monoids. (shrink)

In quantum logic, introduced by Birkhoff and von Neumann, De Morgan's Laws play an important role in the projection-valued truth value assignment of observational propositions in quantum mechanics. Takeuti's quantum set theory extends this assignment to all the set-theoretical statements on the universe of quantum sets. However, Takeuti's quantum set theory has a problem in that De Morgan's Laws do not hold between universal and existential bounded quantifiers. Here, we solve this problem by introducing a new truth value (...) assignment for bounded quantifiers that satisfies De Morgan's Laws. To justify the new assignment, we prove the Transfer Principle, showing that this assignment of a truth value to every bounded ZFC theorem has a lower bound determined by the commutator, a projection-valued degree of commutativity, of constants in the formula. We study the most general class of truth value assignments and obtain necessary and sufficient conditions for them to satisfy the Transfer Principle, to satisfy De Morgan's Laws, and to satisfy both. For the class of assignments with polynomially definable logical operations, we determine exactly 36 assignments that satisfy the Transfer Principle and exactly 6 assignments that satisfy both the Transfer Principle and De Morgan's Laws. (shrink)

In our paper, monadic modal pseudocomplemented De Morgan algebras are considered following Halmos’ studies on monadic Boolean algebras. Hence, their topological representation theory is used successfully. Lattice congruences of an mmpM is characterized and the variety of mmpMs is proven semisimple via topological representation. Furthermore and among other things, the poset of principal congruences is investigated and proven to be a Boolean algebra; therefore, every principal congruence is a Boolean congruence. All these conclusions contrast sharply with known results for (...) monadic De Morgan algebras. Finally, we show that the above results for mmpM are verified for monadic tetravalent modal algebras. (shrink)

De la philosophie de la nature de Schelling à l'intérêt de Mallarmé pour la psychophysique d'Eugène de Roberty, cet ouvrage tenté de mettre en lumière un infini immanent au fini, qui prend la forme d'un panthéisme organique. L'organisme permet de dépasser la substance fixe de Spinoza et d'élaborer une doctrine du Dieu vivant.

This paper has two aims. The first concerns the question of whether there is any essential involvement of perspectival thought in intentional agency. I defend the view that the answer is ‘no’ for one kind of perspectival thought, and ‘yes’ for a different kind. Agency does not depend on de se thought, but it does depend on de nunc thought. The second aim of the paper is to defend a claim about the significance of this de se–de nunc contrast as (...) a case study. I argue that the contrast is best explained by a picture on which different kinds of perspectival thought are seen as islands. On this picture, an account of the conceptual role of one kind of perspectival thought won’t settle much about any other kind of perspectival thought. The picture is proposed as a replacement for the standard picture, on which perspectival thought is seen as a natural cognitive kind. (shrink)

In this paper we exhibit a non-finitely based, finitely generated quasi-variety of De Morgan algebras and determine the bottom of the lattices of sub-quasi-varieties of Kleene and De Morgan algebras.

In this paper we exhibit a non-finitely based, finitely generated quasi-variety of De Morgan algebras and determine the bottom of the lattices of sub-quasi-varieties of Kleene and De Morgan algebras.

Enjeu de pouvoir et reflet de controverses sur le rôle et la finalité de l’entreprise, l’intérêt social a fait son entrée dans le code civil, de manière éclatante, à la faveur de la « loi PACTE ». Contrairement à l’idée répandue selon laquelle cette consécration législative ne serait qu’une formalisation – à droit constant – de la jurisprudence, il est soutenu ici que le législateur a affirmé pour la première fois, bien qu’implicitement, une conception inédite, élargie, de l’intérêt social. En (...) imposant une obligation de gérer la société conformément à son intérêt social en prenant en considération les enjeux sociaux et environnementaux liés à son activité, l’article 1833 alinéa 2 du code civil recèle cependant une ambiguïté fondamentale : le législateur a entendu faire des enjeux sociaux et environnementaux une composante de l’intérêt social, tout en exigeant qu’ils soient simplement « pris en considération ». Cet apparent paradoxe traduit en réalité un nouveau modèle normatif. Contournant l’obstacle qui aurait consisté – aux prix d’une insécurité juridique majeure – à imposer directement aux sociétés de se conformer à des enjeux sociaux et environnementaux indéterminés, le législateur a érigé une obligation de réflexion et de délibération sur ces enjeux au cours du processus de décision sociale, faisant le pari que cet impératif procédural modifiera l’agir pratique des acteurs concernés. Ce nouveau modèle normatif traduit une conception renouvelée du rôle et de la finalité de l’entreprise sociétaire, expressément dépositaire d’une certaine conception de l’intérêt général. (shrink)

Goal: To assess public knowledge and attitudes towards the family’s role in deceased organ donation in Europe. -/- Methods: A systematic search was conducted in CINHAL, MEDLINE, PAIS Index, Scopus, PsycINFO, and Web of Science on December 15th, 2017. Eligibility criteria were socio-empirical studies conducted in Europe from 2008 to 2017 addressing either knowledge or attitudes by the public towards the consent system, including the involvement of the family in the decision-making process, for post-mortem organ retrieval. Screening and data collection (...) were performed by two or more independent reviewers for each record. -/- Results: Of the 1482 results, 467 studies were assessed in full-text form, and 33 were included in this synthesis. When the deceased has not expressed any preference, a majority of the public support the family's role as a surrogate decision-maker. When the deceased expressly consented, the respondents' answers depend on whether they see themselves as potential donors or as a deceased's next-of-kin. Answers also depend on the relationship between the deceased and the decision-maker(s) within the family, and on their ethnic or cultural background. -/- Conclusions: Public views on the authority of the family in organ donation decision-making require further research. A common conceptual framework and validated well-designed questionnaires are needed for future studies. The findings should be considered in the development of Government policy and guidance regarding the role of families in deceased organ donation. (shrink)

Dans ses écrits sur l�esthétique, Friedrich Schleiermacher s�est attaché à formuler une critique de la philosophie de l�art de son contemporain Schelling. Schleiermacher en ressort comme un penseur du savoir-faire artistique, à la fois opposé à l�idéalisme schellingien pour lequel l�art demeure un organe de l�absolu placé sous le signe du génie, et engagé dans une définition de l��uvre d�art comme manière de former le monde à l�aide du sentiment de la raison (Vernunftgefu¨hl).

Dans la deuxième moitié des années 1980 s’est développée, dans l’ensemble du champ de la culture, une véritable esthétique de la bêtise. Quelques jeunes critiques d’art se sont alors emparés du phénomène et ont tenté de le théoriser, entre 1994 et 1998, dans les revues les plus lues de l’époque : Flash Art International, Artpress, Frieze. L’étude de ce corpus d’articles (signés par Joshua Decter, Éric Troncy, Jon Savage, Andrew Hulktrans et Jean-Yves Jouannais) témoigne à la fois des mutations de (...) la critique d’art de l’époque et de l’enjeu que représente alors l’art délibérément bête. On remarquera que la critique d’art se fait alors critique culturelle : elle regarde peu les œuvres, réduites au statut d’illustrations et d’arguments visuels. On s’interrogera également sur la place que les revues d’art contemporain ont accordée à la culture populaire médiatique la plus régressive du temps. Beavis & Butt-Head, Melrose Place ou encore Alerte à Malibu ont été ainsi disséqués dans les colonnes d’ Artforum ou de Flash Art. Alors que les œuvres d’art estampillées « art contemporain » donnaient lieu à des analyses étonnamment sommaires, ce sont les séries télévisées et les dessins animés qui ont conduit aux analyses les plus stimulantes. Elles l’ont fait en recourant au paradigme de la méta-criticalité cher au modernisme, conférant aux œuvres les plus régressives le statut d’image spéculaire, à la fois duplice et critique, de la culture de la bêtise qui les générait. Pointe alors le paradoxe suivant : alternant entre l’enthousiasme forcené et la déploration, la critique d’art des années 1990 a intellectualisé l’anti-intellectualisme le plus radical. (shrink)

Résumé L’Utopie de Thomas More est composée de deux livres : Le Livre Premier, vite escamoté par les rêveurs d’avenir que l’histoire ennuie, nous parle de l’Europe de 1515 à l’aube d’une révolution de tous les savoirs, dominée par un pouvoir politique qui utilise la religion, la peur et l’ ignorance afin de satisfaire un appétit hégémonique insatiable, infiniment corrompu mais parlant haut valeurs morales et familiales. Le Livre Second nous fait miroiter un avenir à l’échelle de l’humanité qui utiliserait (...) les nouvelles techniques, la raison et la bonne gestion de ses ressources pour concilier bien commun et plaisir individuel. Ce Livre est le texte fondateur de notre modernité. C’est la Bible païenne adoptée par les Lumières et que nous avons inscrite dans la charte des institutions de notre temps. Cinq cents ans plus tard et les livres se réécrivent en miroir : le grand rêve humain initié par le Livre Second de 1516 s’englue dans la réalité de 2005. Les nouvelles promesses de l’économisme du libre choix de 2005 ne sont qu’un hallucinant retour en arrière, aux postulats du Livre Premier. (shrink)

Couvrant soixante ans d’histoire, depuis l’adoption de la première loi fédérale en matière d’assurance chômage en 1924, jusqu’à la mise en œuvre de la Loi fédérale sur l’assurance chômage obligatoire et l’indemnité en cas d’insolvabilité (LACI) en 1982, l’ouvrage de Carola Togni donne à voir la genèse de l’assurance chômage sous un jour inédit, soit comme un outil de gestion sexuée du chômage et de l’emploi. Cette analyse socio-historique constitue une contribution importante à l’histoire de...