In our paper “A general characterization of the variable-sharing property by means of logical matrices”, a general class of so-called “Relevant logical matrices”, RMLs, is defined. The aim of this paper is to define a class of simpler Relevant logical matrices RMLs′serving the same purpose that RMLs, to wit: any logic verified by an RML′has the variable-sharing property and related properties predicable of the logic of entailment E and of the logic of relevance R.

Łukasiewicz 3-valued logic Ł3 is often understood as the set of all valid formulas according to Łukasiewicz 3-valued matrices MŁ3. Following Wojcicki, in addition, we shall consider two alternative interpretations of Ł3: ‘truth-preserving’ Ł3a and ‘well-determined’ Ł3b defined by two different consequence relations on the 3-valued matrices MŁ3. The aim of this article is to provide a Routley–Meyer ternary semantics for each one of these three versions of Łukasiewicz 3-valued logic: Ł3, Ł3a and Ł3b.

The logic BKc1 is the basic constructive logic in the ternary relational semantics adequate to consistency understood as the absence of the negation of any theorem. Negation is introduced in BKc1 with a negation connective. The aim of this paper is to define the logic BKc1F. In this logic negation is introduced via a propositional falsity constant. We prove that BKc1 and BKc1F are definitionally equivalent.

Our question is: can we embed minimal negation in implicative logics weaker than I→? Previous results show how to define minimal negation in the positive fragment of the logic of relevance R and in contractionless intuitionistic logic. Is it possible to endow weaker positive logics with minimal negation? This paper prooves that minimal negation can be embedded in even such a weak system as Anderson and Belnap’s minimal positive logic.

This lavishly illustrated book highlights the conservation importance of congregatory animals species--those which gather in vast groups. It also focuses on the irreplaceability of the congregation sites which are able to support such large gatherings of animals, fish, or birds.

The Converse Ackermann Property is the unprovability of formulas of the form (A -> B) -> C when C does contain neither -> nor ¬. Intuitively, the CAP amounts to rule out the derivability of pure non-necessitive propositions from non-necessitive ones. A constructive negation of the sort historically defined by, e.g., Johansson is added to positive logics with the CAP in the spectrum delimited by Ticket Entailment and Dummett’s logic LC.

Teoría del derecho / G.R.Morchon. - v.1.

Let MK3 I and MK3 II be Kleene's strong 3-valued matrix with only one and two designated values, respectively. Next, let MK3 G be defined exactly as MK3 I, except th...

This chapter contains sections titled: Sweat, Stretch, and Practical Philosophy ‘I'm Spiritual, but not Religious.’ What's the Difference? A ‘Spiritual Science’ is not just an Oxymoron A Bull Market (or a Market of Bull) Any God You Like Into the Future.

La "Conversa de la Propiedad Ackermann" (CAP) es la no demostrabilidad de proposiciones puramente no-necesitivas a partir de proposiciones necesitivas. En nuestro trabajo definimos las dos restricciones básicas de la lógica intuicionista mínima con la CAP.

Objectives: Recent legislative changes within the United Kingdom have stimulated professional debate about access to patient data within research. However, there is currently little awareness of public views about such research. The authors sought to explore attitudes of the public, and their lay representatives, towards the use of primary care medical record data for research when patient consent was not being sought.Methods: 49 members of the public and four non-medical members of local community health councils in South Wales, UK gave (...) their views on the value and acceptability of three current research scenarios, each describing access to data without patient consent.Results: Among focus group participants, awareness of research in primary care was low, and the appropriateness of general practitioners as researchers was questioned. There was general support for research but also concerns expressed about data collection without consent. These included lack of respect and patient control over the process. Unauthorised access to data by external agencies was a common fear. Current data collection practices, including population based disease registers elicited much anxiety. The key informants were equally critical of the scenarios and generally less accepting.Conclusions: This exploratory study has highlighted a number of areas of public concern when medical records are accessed for research without patient consent. Public acceptability regarding the use of medical records in research cannot simply be assumed. Further work is required to determine how widespread such views are and to inform those advising on confidentiality issues. (shrink)

Resumen Los enfoques tradicionales en el estudio de la comunión fática han examinado el concepto en términos de la función social, la función del lenguaje así como su ocurrencia en las etapas iniciales y de cierre de una interacción. Intentos por clasificar la comunión fática en términos universalistas predeterminados corrieron el riesgo de alejarse del concepto de entendimientos cotidianos donde interactuantes emplean el uso del lenguaje dinámico para lograr los objetivos de comunicación específicos en contextos particulares. Los enfoques contemporáneos tratan (...) de redefinir la comunión fática en términos interpersonales. La investigación sobre el uso del lenguaje fático en América Latina ha sido muy limitada, con contadas excepciones. Con la finalidad de investigar el tema en el contexto mexicano, donde todavía se considera en términos convencionales, examinamos un corpus formado por 92 instancias de comunión fática, recabadas en Guadalajara, México. Sostenemos que en el corpus antes aludido se emplea la comunión fática a fin de expresar y destacar la cortesía positiva en maneras poco convencionales, dado que el término tiene un alcance muy amplio en el que abarca: la anticortesía, el uso del lenguaje creativo, los juegos lingüísticos, la ironía, y los anglicismos. (shrink)

We make use of natural induction to propose, following John Ju Sakurai, a generalization of Bell's inequality for two spin s=n/2(n=1,2,...) particle systems in a singlet state. We have found that for any finite integer or half-integer spin Bell's inequality is violated when the terms in the inequality are calculated from a quantum mechanical point of view. In the final expression for this inequality the two members therein are expressed in terms of a single parameter θ. Violation occurs for θ (...) in some interval of the form (α,π/2) where α parameter becomes closer and closer to π/2, as the spin grows, that is, the greater the spin number the size of the interval in which violation occurs diminishes to zero. Bell's inequality is a relationship among observables that discriminates between Einstein's locality principle and the non-local point of view of orthodox quantum mechanics. So our conclusion may also be stated by saying that for large spin numbers the non-local and local points of view agree. (shrink)

This is a welcome reprint of a book that continues to grow in importance.

ABSTRACTA conditional is natural if it fulfils the three following conditions. It coincides with the classical conditional when restricted to the classical values T and F; it satisfies the Modus Ponens; and it is assigned a designated value whenever the value assigned to its antecedent is less than or equal to the value assigned to its consequent. The aim of this paper is to provide a ‘bivalent’ Belnap-Dunn semantics for all natural implicative expansions of Kleene's strong 3-valued matrix with two (...) designated elements. (shrink)

El ánimo de esta investigación es la de valorar a través de la revisión documental, uno de los aspectos fundamentales para el aprendizaje y el desarrollo de destrezas musicales como es la velocidad de procesamiento (VP). Además, se aborda la estimulación cognitiva (EC) y la atención, como elementos propios del ser humano, que proporcionan aprendizajes significativos. Por otro lado, y para la consecución de contenidos musicales, se establece una relación de procedimientos para la secuenciación docente y a modo de herramientas (...) innovadoras, Music Mind Games, sistema de enseñanza de lenguaje musical, inspirado por la metodología Suzuki. (shrink)

As is well known, the variable-sharing property (vsp) is, according to Anderson and Belnap, a necessary property of any relevant logic. In this paper, we shall consider two versions of the vsp, what we label the "weak vsp" (wvsp) and the "strong vsp" (svsp). In addition, the "no loose pieces property," a property related to the wvsp and the svsp, will be defined. Each one of these properties shall generally be characterized by means of a class of logical matrices. In (...) this way, any logic verified by an actual matrix in one of these classes has the property the class generally represents. Particular matrices (and so, logics) in each class are provided. (shrink)

The logic E4 is related to Brady’s BN4 in a similar way to which Anderson and Belnap’s logic of entailment E is related to their logic of the relevant implication R. In ‘A companion to Brady’s 4-valued relevant logic: the 4-valued logic of entailment E4’, quoted in this paper, three alternatives to BN4 and another three to E4 are summarily introduced in a couple of pages as the only alternatives containing Routley and Meyer’s basic logic B, provided some conditions are (...) fulfilled. The aim of this note is to prove BN4 and its three alternatives are the same logic up to some point, since they are functionally equivalent to each other, as it is the case with E4 and its three alternatives, which are also functionally equivalent to each other; to some extent, E4 is superior to BN4, since the latter is functionally included in the former, but not conversely. (shrink)

A classical result by Słupecki states that a logic L is functionally complete for the 3-element set of truth-values THREE if, in addition to functionally including Łukasiewicz’s 3-valued logic Ł3, what he names the ‘$T$-function’ is definable in L. By leaning upon this classical result, we prove a general theorem for defining binary expansions of Kleene’s strong logic that are functionally complete for THREE.

This article examines a productive use of communicating gender stereotypes in interpersonal conversation: to resist activities traditionally prescribed according to gender. The analyses video-taped naturally occurring US household interactions and present three techniques participants may deploy to contest gender expectations: mobilizing categories, motivating alignment and reframing action. We show how gender is an accountable category in relation to household labor, and how gender categories provide a resource by which participants can non-seriously solicit and resist participation in domestic gender-prescribed activities. Our (...) analysis provides some insight into how participants use gender stereotypes in everyday talk and what functions such talk serves. (shrink)

This paper is a sequel to ‘Belnap-Dunn semantics for natural implicative expansions of Kleene's strong three-valued matrix with two designated values’, where a ‘bivalent’ Belnap-Dunn semantics is provided for all the expansions referred to in its title. The aim of the present paper is to carry out a parallel investigation for all natural implicative expansions of Kleene's strong 3-valued matrix now with only one designated value.

A simple Henkin-style completeness proof for Gödel 3-valued propositional logic G3 is provided. The idea is to endow G3 with an under-determined semantics of the type defined by Dunn. The key concept in u-semantics is that of “under-determined interpretation”. It is shown that consistent prime theories built upon G3 can be understood as u-interpretations. In order to prove this fact we follow Brady by defining G3 as an extension of Anderson and Belnap’s positive fragment of First Degree Entailment Logic.

Routley-Meyer type ternary relational semantics are defined for relevant logics including Routley and Meyer’s basic logic B plus the reductio rule and the disjunctive syllogism. Standard relevant logics such as E and R (plus γ ) and Ackermann’s logics of ‘strenge Implikation’ Π and Π ′ are among the logics considered.

Routley–Meyer semantics (RM-semantics) is defined for Gödel 3-valued logic G3 and some logics related to it among which a paraconsistent one differing only from G3 in the interpretation of negation is to be remarked. The logics are defined in the Hilbert-style way and also by means of proof-theoretical and semantical consequence relations. The RM-semantics is defined upon the models for Routley and Meyer’s basic positive logic B+, the weakest positive RM-semantics. In this way, it is to be expected that the (...) models defined can be adapted to other related many-valued logics. (shrink)