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)

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)

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)

This text argues that psychoanalytic philosophy is a valuable tool for the Philosophy of Sport. To situate it within the philosophical tradition, I place Freud’s ideas as an heir to the Philosophy of Impulse of Schopenhauer and Nietzsche. Then, I explain how psychoanalytic philosophy can be understood as a form of hermeneutics, which aligns well with the interests of the field. I also recognise the importance of questioning whether we can consider sports and their events as analysable psychoanalytic facts. To (...) this purpose, I use Paul Ricoeur’s methodological approach, which proposes to analyse collective and common phenomena hermeneutically as psychoanalytic facts. I demonstrate the consistency of this method and adapt it to the Philosophy of Sport. The method involves a triangular operation that analyses psychoanalytic facts by articulating their relationships of meaning (narratives, manifest content, memories and objects), their relationships of force (resistances, neurotic repetitions, symptoms, latent contents and transfers), and psychoanalytic theory. As an example, I apply this method to conduct a micro-psychoanalytic analysis of Brazil’s defeat to Germany in the 2014 FIFA World Cup, which the Brazilian coach referred to as a ‘blanked out’ moment. I observe that the destiny of drives, which Freud understood as the tendency of unconscious material to return to consciousness in the form of commitments to objects and symptoms, is prominent in sports reality. This may encourage us to see the potential of promising interpretations grounded in the Psychoanalytic Philosophy of Sport. (shrink)

Łukasiewicz three-valued logic Ł3 is often understood as the set of all 3-valued valid formulas according to Łukasiewicz’s 3-valued matrices. Following Wojcicki, in addition, we shall consider two alternative interpretations of Ł3: “well-determined” Ł3a and “truth-preserving” Ł3b defined by two different consequence relations on the 3-valued matrices. The aim of this paper is to provide (by using Dunn semantics) dual equivalent two-valued under-determined and over-determined interpretations for Ł3, Ł3a and Ł3b. The logic Ł3 is axiomatized as an extension of Routley (...) and Meyer’s basic positive logic following Brady’s strategy for axiomatizing many-valued logics by employing two-valued under-determined or over-determined interpretations. Finally, it is proved that “well determined” Łukasiewicz logics are paraconsistent. (shrink)

Łukasiewicz three-valued logic Ł3 is often understood as the set of all 3-valued valid formulas according to Łukasiewicz’s 3-valued matrices. Following Wojcicki, in addition, we shall consider two alternative interpretations of Ł3: “well-determined” Ł3a and “truth-preserving” Ł3b defined by two different consequence relations on the 3-valued matrices. The aim of this paper is to provide dual equivalent two-valued under-determined and over-determined interpretations for Ł3, Ł3a and Ł3b. The logic Ł3 is axiomatized as an extension of Routley and Meyer’s basic positive (...) logic following Brady’s strategy for axiomatizing many-valued logics by employing two-valued under-determined or over-determined interpretations. Finally, it is proved that “well determined” Łukasiewicz logics are paraconsistent. (shrink)

This is a correction to: Gemma Robles, José M. Méndez, A note on functional relations in a certain class of implicative expansions of FDE related to Brady’.

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)

Routley-Meyer Ternary Relational Semantics for Intuitionistic-type Negations examines how to introduce intuitionistic-type negations into RM-semantics. RM-semantics is highly malleable and capable of modeling families of logics which are very different from each other. This semantics was introduced in the early 1970s, and was devised for interpreting relevance logics. In RM-semantics, negation is interpreted by means of the Routley operator, which has been almost exclusively used for modeling De Morgan negations. This book provides research on particular features of intuitionistic-type of negations (...) in RM-semantics, while also defining the basic systems and many of their extensions by using models with or without a set of designated points. (shrink)

The paraconsistent and paracomplete 4-valued logic PŁ4 is originally interpreted with a two-valued Belnap-Dunn semantics. In the present paper, PŁ4 is endowed with both a ternary Routley-Meyer semantics and a binary Routley semantics together with their respective restriction to the 2 set-up cases.

We consider the logics determined by the set of all natural implicative expansions of Kleene’s strong 3-valued matrix and select the class of all logics functionally equivalent to Łukasiewicz’s 3-valued logic Ł3. The concept of a “natural implicative matrix” is based upon the notion of a “natural conditional” defined in Tomova.

The role of demographic terminology in the fields of medicine and public health is critical in the identification and allocation of resources to the communities that most benefit from intervention...

In this paper, consistency is understood as the absence of the negation of a theorem, and not, in general, as the absence of any contradiction. We define the basic constructive logic BKc1 adequate to this sense of consistency in the ternary relational semantics without a set of designated points. Then we show how to define a series of logics extending BKc1 within the spectrum delimited by contractionless minimal intuitionistic logic. All logics defined in the paper are paraconsistent logics.

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.

En un escenario internacional cada vez más incierto, en el que todavía no se ha dejado atrás la pandemia de Covid-19, y hay que gestionar la ilegítima invasión rusa de Ucrania así como unas relaciones entre Estados Unidos y China cada vez más tensas, Europa y Japón han reafirmado sus vínculos históricos, económicos y políticos con dos acuerdos de asociación, uno de carácter económico y otro estratégico, en vigor desde 2019. El continente asiático se ha convertido además en el principal (...) eje geopolítico del mundo, y Japón quiere tener un papel relevante en el nuevo escenario al que ha respondido mediante su iniciativa del _Free and Open Indo-Pacific_, a la que Europa ha respondido con ciertas reservas. ¿Deben Europa y Japón seguir profundizando en su relación? ¿Cuáles son los ámbitos susceptibles de mejora? El marco adecuado debe ser, en nuestra opinión, el “orden internacional basado en normas” del que ambos actores son claros defensores, y los valores comunes de democracia, Estado de Derecho y protección de derechos fundamentales que los unen. (shrink)

The logic BN4 was defined by R.T. Brady in 1982. It can be considered as the 4-valued logic of the relevant conditional. E4 is a variant of BN4 that can be considered as the 4-valued logic of entailment. The aim of this paper is to define reduced general Routley-Meyer semantics for BN4 and E4. It is proved that BN4 and E4 are strongly sound and complete w.r.t. their respective semantics.

Sylvan and Plumwood’s is the relevant De Morgan minimal logic in the Routley-Meyer semantics with a set of designated points. The aim of this paper is to define the logic and some of its extensions. The logic is the non-relevant De Morgan minimal logic in the Routley-Meyer semantics without a set of designated points.

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.

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.

The well-known logic first degree entailment logic (FDE), introduced by Belnap and Dunn, is defined with |$\wedge $|⁠, |$\vee $| and |$\sim $| as the sole primitive connectives. The aim of this paper is to establish the lattice formed by the class of all 4-valued C-extending implicative expansions of FDE verifying the axioms and rules of Routley and Meyer’s basic logic B and its useful disjunctive extension B|$^{\textrm {d}}$|⁠. It is to be noted that Boolean negation (so, classical propositional logic) (...) is definable in the strongest element in the said class. (shrink)

In Rogerson and Restall’s, the “class of implication formulas known to trivialize ” is recorded. The aim of this paper is to show how to invalidate any member in this class by using “weak relevant model structures”. Weak relevant model structures verify deep relevant logics only.

Texto presentado en el Congreso Internacional “Recepciones de Ortega y Gasset en Chile” celebrado en el Centro Cultural de España en Santiago durante los días 30 y 31 de mayo de 2018, en Santiago de Chile. Forma parte de la compilación recogida en número especial de la Revista de Filosofía Otrosiglo, en junio del 2023.

En este escrito se presenta la perspectiva de la Escuela Mexicana de Análisis y TerapiaExistencial. No es fácil distinguir cómo se aplica la fenomenología-existencial a unapráctica terapéutica, ya que plantea aspectos divergentes con respecto a la psicologíaclínica tradicional. Esta propuesta se fundamenta, tanto en una forma de comprender laexistencia, como en cierta forma de entender el propósito del proceso terapéutico. Lafenomenología-existencial propone una práctica terapéutica que no busque curar osolucionar problemas, sino clarificar la situación existencial del cliente. Esto tiene variasimplicaciones (...) para los terapeutas, como la invitación a: describir en vez de explicar –descripciones que realizan tanto paciente como terapeuta–, explorar la tensión que existeentre lo que está ocurriendo y lo que suponemos que debería ocurrir, aceptar lo relativode las posibilidades y perspectivas que se despliegan en diversos contextos, examinar lacomplejidad de cada situación, preguntar –por tonta que pueda parecer la pregunta–,reconocer nuestra incapacidad para renunciar a nuestras preferencias, estar disponiblepara evidenciar nuestras dudas e incomprensiones, y a lograr una “actitud de no-saber” –la humildad de reconocer que todos nuestros conocimientos no son suficientes paraconocer con certeza la realidad–. (shrink)

Equivalent overdetermined and underdetermined bivalent Belnap–Dunn type semantics for the logics determined by all natural implicative expansions of Kleene’s strong 3-valued matrix with only one designated value are provided.

In this paper, consistency is understood in the standard way, i.e. as the absence of a contradiction. The basic constructive logic BKc4, which is adequate to this sense of consistency in the ternary relational semantics without a set of designated points, is defined. Then, it is shown how to define a series of logics by extending BKc4 up to minimal intuitionistic logic. All logics defined in this paper are paraconsistent logics.

As it is well known, in the forties of the past century, Curry proved that in any logic S closed under Modus Ponens, uniform substitution of propositional variables and the Contraction Law, the naïve Comprehension axiom trivializes S in the sense that all propositions are derivable in S plus CA. Not less known is the fact that, ever since Curry published his proof, theses and rules weaker than W have been shown to cause the same effect as W causes. Among (...) these, the Contraction rule or the Modus Ponens axiom, for example, are to be noted. But, moreover, as Brady has proved, even the Generalized Modus Ponens axiom or the Generalized Contraction rule give rise to “Curry’s Paradox” under the same circumstances as W does. In some previous work by us, “weak relevant model structures” are defined on “weak relevant matrices” by generalizing Brady’s model structure MCL built upon Meyer’s Crystal matrix CL. We have proved that wr-ms only verify logics with the “depth relevance condition”. The aim of this paper is to show how to falsify gMPa and gRW in certain wr-ms. In particular, it will be shown that gMPa is falisfied in any wr-ms and gRW in any wr-ms verifying Routley and Meyer’s basic positive logic B+. (shrink)

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.

The logic BN4 can be considered as the 4-valued logic of the relevant conditional and the logic E4, as the 4-valued logic of entailment. The aim of this paper is to endow E4 with a 2-set-up Routley-Meyer semantics. It is proved that E4 is strongly sound and complete w.r.t. this semantics.

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)

“Weak relevant model structures” (wr-ms) are defined on “weak relevant matrices” by generalizing Brady’s model structure ${\mathcal{M}_{\rm CL}}$ built upon Meyer’s Crystal matrix CL. It is shown how to falsify in any wr-ms the Generalized Modus Ponens axiom and similar schemes used to derive Curry’s Paradox. In the last section of the paper we discuss how to extend this method of falsification to more general schemes that could also be used in deriving Curry’s Paradox.