In this paper we obtain a finite Hilbert-style axiomatization of the implicationless fragment of the intuitionistic propositional calculus. As a consequence we obtain finite axiomatizations of all structural closure operators on the algebra of {–}-formulas containing this fragment.

In this paper we study the relations between the fragment L of classical logic having just conjunction and disjunction and the variety D of distributive lattices, within the context of Algebraic Logic. We prove that these relations cannot be fully expressed either with the tools of Blok and Pigozzi's theory of algebraizable logics or with the use of reduced matrices for L. However, these relations can be naturally formulated when we introduce a new notion of model of a sequent calculus. (...) When applied to a certain natural calculus for L, the resulting models are equivalent to a class of abstract logics (in the sense of Brown and Suszko) which we call distributive. Among other results, we prove that D is exactly the class of the algebraic reducts of the reduced models of L, that there is an embedding of the theories of L into the theories of the equational consequence (in the sense of Blok and Pigozzi) relative to D, and that for any algebra A of type (2,2) there is an isomorphism between the D-congruences of A and the models of L over A. In the second part of this paper (which will be published separately) we will also apply some results to give proofs with a logical flavour for several new or well-known lattice-theoretical properties. (shrink)

In this paper we prove the equivalence between the Gentzen system G LJ*\c , obtained by deleting the contraction rule from the sequent calculus LJ* (which is a redundant version of LJ), the deductive system IPC*\c and the equational system associated with the variety RL of residuated lattices. This means that the variety RL is the equivalent algebraic semantics for both systems G LJ*\c in the sense of [18] and [4], respectively. The equivalence between G LJ*\c and IPC*\c is a (...) strengthening of a result obtained by H. Ono and Y. Komori [14, Corollary 2.8.1] and the equivalence between G LJ*\c and the equational system associated with the variety RL of residuated lattices is a strengthening of a result obtained by P.M. Idziak [13, Theorem 1].An axiomatization of the restriction of IPC*\c to the formulas whose main connective is the implication connective is obtained by using an interpretation of G LJ*\c in IPC*\c. (shrink)

The object of this paper is to make a study of four systems of modal logic (S4, S5, and their intuitionistic analogues IM4 and IM5) with the techniques of the theory of abstract logics set up by Suszko, Bloom, Brown, Verdú and others. The abstract concepts corresponding to such systems are defined as generalizations of the logics naturally associated to their algebraic models (topological Boolean or Heyting algebras, general or semisimple). By considering new suitably defined connectives and by distinguishing (...) between having the rule of necessitation only for theorems or as a full inference rule (which amounts to dealing with all filters or with open filters of the algebras) we are able to reduce the study of a modal (abstract) logic L to that of two nonmodal logics L - and L + associated with L. We find that L is "of IM4 type" if and only if L - and L + are both intuitionistic and have the same theorems, and logics of type S4, IM5 or S5 are obtained from those of type IM4 simply by making classical L -, L + or both. We compare this situation with that found in recent approaches to intuitionistic modal logic using birelational models or using higher-level sequent-systems. The treatment of modal systems with abstract logics is rather new, and in our way to it we find several general constructions and results which can also be applied to other modal systems weaker than those we study in detail. (shrink)

In our previous paper Algebraic Logic for Classical Conjunction and Disjunction we studied some relations between the fragmentL of classical logic having just conjunction and disjunction and the varietyD of distributive lattices, within the context of Algebraic Logic. The central tool in that study was a class of closure operators which we calleddistributive, and one of its main results was that for any algebraA of type (2,2) there is an isomorphism between the lattices of allD-congruences ofA and of all distributive (...) closure operators overA. In the present paper we study the lattice structure of this last set, give a description of its finite and infinite operations, and obtain a topological representation. We also apply the mentioned isomorphism and other results to obtain proofs with a logical flavour for several new or well-known lattice-theoretical properties, like Hashimoto's characterization of distributive lattices, and Priestley's topological representation of the congruence lattice of a bounded distributive lattice. (shrink)

Łukasiewicz’s infinite-valued logic is commonly defined as the set of formulas that take the value 1 under all evaluations in the Łukasiewicz algebra on the unit real interval. In the literature a deductive system axiomatized in a Hilbert style was associated to it, and was later shown to be semantically defined from Łukasiewicz algebra by using a “truth-preserving” scheme. This deductive system is algebraizable, non-selfextensional and does not satisfy the deduction theorem. In addition, there exists no Gentzen calculus fully adequate (...) for it. Another presentation of the same deductive system can be obtained from a substructural Gentzen calculus. In this paper we use the framework of abstract algebraic logic to study a different deductive system which uses the aforementioned algebra under a scheme of “preservation of degrees of truth”. We characterize the resulting deductive system in a natural way by using the lattice filters of Wajsberg algebras, and also by using a structural Gentzen calculus, which is shown to be fully adequate for it. This logic is an interesting example for the general theory: it is selfextensional, non-protoalgebraic, and satisfies a “graded” deduction theorem. Moreover, the Gentzen system is algebraizable. The first deductive system mentioned turns out to be the extension of the second by the rule of Modus Ponens. (shrink)

ABSTRACT In this paper we study consequence relations on the set of many sided sequents over a propositional language. We deal with the consequence relations axiomatized by the sequent calculi defined in [2] and associated with arbitrary finite algebras. These consequence relations are examples of what we call Gentzen systems. We define a semantics for these systems and prove a Strong Completeness Theorem, which is an extension of the Completeness Theorem for provable sequents stated in [2]. For the special case (...) of the finite linear MV-algebras, the Strong Completeness Theorem was proved in [10], as a consequence of McNaughton's Theorem. The main tool to prove this result for arbitrary algebras is the deduction-detachment theorem for Gentzen systems. (shrink)

The logic of (commutative integral bounded) residuated lattices is known under different names in the literature: monoidal logic [26], intuitionistic logic without contraction [1], H BCK [36] (nowadays called by Ono), etc. In this paper we study the -fragment and the -fragment of the logical systems associated with residuated lattices, both from the perspective of Gentzen systems and from that of deductive systems. We stress that our notion of fragment considers the full consequence relation admitting hypotheses. It results that this (...) notion of fragment is axiomatized by the rules of the sequent calculus for the connectives involved. We also prove that these deductive systems are non-protoalgebraic, while the Gentzen systems are algebraizable with equivalent algebraic semantics the varieties of pseudocomplemented (commutative integral bounded) semilatticed and latticed monoids, respectively. All the logical systems considered are decidable. (shrink)

La atención es uno de los fenómenos psicológicos más presentes en la obra orteguiana y, a la vez, uno de los más desatendidos por la crítica. Habitualmente el fenómeno ha quedado eclipsado por ideas tradicionalmente más nodales como la de “perspectiva”, sin embargo, no podemos ignorar que ideas como esta hallan su fundamento precisamente sobre el fenómeno de la atención, lo que le otorga una importancia a considerar. En el presente libro, mediante una revisión crítica de los textos orteguianos, se (...) despliega y reúne un conjunto de argumentos con los que defender la centralidad de la atención en el pensamiento orteguiano ofreciendo, con ella, uno de los elementos cardinales en la estructuración sistemática de su obra, pues, como veremos, es en la atención donde el autor halla el fundamento para edi car su método perspectivista y, a su vez, donde descansa cierta posibilidad de cristalizar su doctrina raciovitalista. (shrink)

Starting from the apparently contradictory expression “nostalgia for the future”, in this article we delve into the analysis of the complex net of temporal tensions that underlie human experience, specifically under the colouring of the nostalgic mood. We will try to analyse the interdependence relations that the different temporal horizons keep, specifically in the nostalgic experience and in the original experience to which it refers and which is a matter of evocation. In this context, we will accentuate the role of (...) expectations, and their influence on the “future” emergence of nostalgic mood, a role that, even when they act preconsciously, is essential to understand the sense of loss of familiarity felt by those who see such pretensions unfulfilled. // A partir de la aparentemente contradictoria expresión “nostalgia de futuro”, en el presente artículo nos adentramos en el análisis del complejo entramado de tensiones temporales que subyacen a la experiencia humana, en concreto bajo la coloración del tono nostálgico. Trataremos de analizar las relaciones de interdependencia que guardan los distintos horizontes temporales, tanto en la experiencia nostálgica como en la experiencia originaria a la que esta refiere y que es materia de evocación. En tal contexto, pondremos especial énfasis en el papel de las expectativas, y en su influencia en la “futura” emergencia del temple nostálgico, un papel que, aun cuando actúan de manera preconsciente, resulta esencial para comprender la sensación de pérdida de familiaridad que siente quien ve incumplidas tales pretensiones. (shrink)

Hilden and Gammelgaard's comments on the evaluation and application of statistical trials and on informed consent lead to the same conclusion that there are special circumstances when clinical trials are performed in emergency situations.The decision to comment on the work that H&G responded to was motivated by the wish to manifest the need to reach a consensus on modifying the conditions in which clinical trials should be performed in special circumstances.One unquestionable fact must first be addressed: clinical trials are necessary (...) for acquiring new knowledge and consequent improvements in health care services. At the same time, patient participation should be encouraged under conditions that respect patients' decision making capability.Are these conditions being met at present? An answer to this is given below. (shrink)

The problem of non-compliance with treatment and its repercussions on the clinical evolution of different conditions has been widely investigated.1–4 Non-compliance has also been shown to have significant economic implications, not only as a result of product loss but also indirectly through the complication of disease management and its subsequent healthcare and social costs.5–7Non-compliance as a health problemThe term “non-compliance” might be taken to refer both to the failure to follow a drug regimen and to the failure to adopt other (...) measures that contribute to improvement in health—for example, changes in lifestyle or diet. This letter focuses on the former.Non-compliance with a drug regimen can be the result of a number of different factors9–11 and a variety of techniques have been developed in an attempt to control it.12,13 Of these, the few techniques that have been shown to be effective have only managed to solve the problem in specific situations over short periods of time. The use of such techniques to control non-compliance, particularly where these are effective, raises interesting ethical questions about the extent to which their application constitutes an infringement of the patient’s right to decide on how to manage their own health.8 Here we suggest that in some cases one factor that leads to non-compliance is the tendency to provide extensive and exhaustive information on side effects in …. (shrink)

Advances in medicine are closely linked to clinical research, but certain study procedures may be in conflict with the fundamental principles of ethics and codes of conduct in medicine. Following an analysis of two studies involving treatments for acute myocardial infarction (AMI), the admissibility of continuing a study was questioned after the initial results for two types of treatment showed that one was significantly better than the other. Also considered doubtful was the information provided to patients with the object of (...) obtaining their informed consent. (shrink)

For over a decade neuroscience has uncovered that appropriate decision-making in daily life decisions results from a strong interplay between cognition and covert biases produced by emotional processes. This interplay is particularly important in social contexts: lesions in the pathways supporting these processes provoke serious impairments on social behavior. One important mechanism in social contexts is empathy, fundamental for appropriate social behavior. This paper presents arguments supporting this connection between cognition and emotion, in individual as well as in social contexts. (...) The central claim of this paper is that biologically inspired cognitive architectures ought to include these mechanisms. A taxonomy of computational models addressing emotions is presented, together with a brief survey of the research published in this area. The Prisoner Dilemma game is used as a case study exposing the trade-off between individual rationality and cooperative behavior. Experiments using a simple implementation of empathy and emotion expression, employing an Iterated Prisoner Dilemma setup, illustrate the emergence of a cooperative behavior mutually beneficial for both players. (shrink)

A partir de la aparentemente contradictoria expresión “nostalgia de futuro”, en el presente artículo nos adentramos en el análisis del complejo entramado de tensiones temporales que subyacen a la experiencia humana, en concreto bajo la coloración del tono nostálgico. Trataremos de analizar las relaciones de interdependencia que guardan los distintos horizontes temporales, tanto en la experiencia nostálgica como en la experiencia originaria a la que esta refiere y que es materia de evocación. En tal contexto, pondremos especial énfasis en el (...) papel de las expectativas, y en su influencia en la “futura” emergencia del temple nostálgico, un papel que, aun cuando actúan de manera preconsciente, resulta esencial para comprender la sensación de pérdida de familiaridad que siente quien ve incumplidas tales pretensiones. (shrink)

Nostalgia refers to that painful experience due to the impossibility of recovering a past whose memory provokes a feeling of comforting happiness and which, nevertheless, inevitably attracts us. This leads us to a reiterated tendency to remember in search of that space of familiarity, of sense, which we know is lost, although we trust that it’s still redeemable. In this article we will analyze this possibility of reencounter that, in its expression, enables a potential recognition of oneself, that is, an (...) opportunity to reaffirm the past-present continuity that reinforces the unfolding of a life project today, looking at the future. (shrink)

Attention is an essential phenome-non to understand the scope of the perspectival methodology in Ortega; therefore, it’s a useful tool to go further in the study of the applicability of ratiovitalism. At the same time, for it is easy tracking in the Ortega’s work, it’s a good knoll to investigate the sources which influenced Ortega in the establishment and, therefore, to explore the shaping of his meth-odology. Our study, based on an analysis of the phenomenon of attention in Ortega's work, (...) guides us to find, in the phenomenolog-ical studies of perception, the core of such influence, thereby accentuating the role of phenomenology in the establishment of Ortega's thought. (shrink)

Many times we have discussed about the appropriateness of situating to Vygotski in the Olympus of psychology. Even today, 80 years later, his theories continue creating as many supporters, defenders of his originality, as effusive critics who accuse the methodological shortcomings of his work. In our view, one of the shortcomings that have accused more his work is the lack of a solid theoretical foundation that endows meaning with the available host of data and results. Therefore, the objective of this (...) article is to show a feasible solution that would be to approach, sometimes encounter with certain phenomenological propositions, for that matter, from the phenomenological studies of perception and its attention to the weight of cultural predicates, where the language is the main element and, at the same time, the meeting point with Vygotski which will help strengthen the foundations of its proposal. (shrink)

La “percepción” es uno de los elementos imprescindibles para la comprensión del pensamiento orteguiano: es la vía por la que nuestra consciencia se abre a lo circundante, fundamento de toda perspectiva y, en consecuencia, elemento fundamental para el autor. A su vez, es uno de los elementos que convierte al pensador madrileño en uno de los estudiosos más originales en este campo. El presente artículo pretende mostrar cómo, para Ortega, ya desde sus inicios, su filosofía de la percepción –de matriz (...) perspectivista–, al fundamentarse en la mundaneidad del individuo y apoyar su percepción cognoscitiva sobre el fenómeno de la atención, incluye o muda, de un modo nada forzado, a una filosofía de la cultura, pues cuando Ortega habla de percepción, lo hace siempre en tanto percepción con predicados culturales. Fue Ortega uno de los primeros en advertir lo ineludible de dicha cualidad. (shrink)

This paper focuses on the 1986 Amendments to the False Claims Act of 1863, which offers whistle-blowers financial rewards for disclosing fraud committed against the U.S. government. This law provides an opportunity to examine underlying assumptions about the morality of whistle-blowing and to consider the merits of increased reliance on whistle-blowing to protect the public interest. The law seems open to a number of moral objections, most notably that it exerts a morally corrupting influence on whistle-blowers. We answer these objections (...) and argue that the law is not objectionable on these grounds. Since there are no compelling moral objections to the law, it is appropriate and acceptable to judge the law in terms of its economic costs and benefits. We assess the most salient of these and conclude that the benefits outweigh the costs. We suggest that a mechanism similar to the Act should be considered for protecting stockholders’ interests in the private sector. We conclude by making several proposals for improving the existing legislation. (shrink)

This paper focuses on the 1986 Amendments to the False Claims Act of 1863, which offers whistle-blowers financial rewards for disclosing fraud committed against the U.S. government. This law provides an opportunity to examine underlying assumptions about the morality of whistle-blowing and to consider the merits of increased reliance on whistle-blowing to protect the public interest. The law seems open to a number of moral objections, most notably that it exerts a morally corrupting influence on whistle-blowers. We answer these objections (...) and argue that the law is not objectionable on these grounds. Since there are no compelling moral objections to the law, it is appropriate and acceptable to judge the law in terms of its economic costs and benefits. We assess the most salient of these and conclude that the benefits outweigh the costs. We suggest that a mechanism similar to the Act should be considered for protecting stockholders' interests in the private sector. We conclude by making several proposals for improving the existing legislation. (shrink)