The aim of this paper is to investigate the variety of symmetric closure algebras, that is, closure algebras endowed with a De Morgan operator. Some general properties are derived. Particularly, the lattice of subvarieties of the subvariety of monadic symmetric algebras is described and an equational basis for each subvariety is given.
In this paper we extend Mundici's functor? to the category of monadic MV- algebras. More precisely, we define monadic?- groups and we establish a natural equivalence between the category of monadic MV- algebras and the category of monadic?- groups with strong unit. Some applications are given thereof.
In this paper I examine Chalmers and Jackson’s defence of the a priori entailment thesis, that is, the claim that microphysical truths a priori entail ordinary non-phenomenal truths such as ‘water covers 60% of the Earth surface’, which they use as a premise for an argument against the possibility of a reductive explanation of consciousness. Their argument relies on a certain view about the possession conditions of macroscopic concepts such as WATER, known as ascriptivism. In the paper I distinguish two (...) versions of ascriptivism: reductive versus non-reductive ascriptivism. According to reductive ascriptivism, competent users of a concept have the ability to infer truths involving such concept from lower-level truths, whereas according to non-reductive ascriptivism, all that is required in order to be a competent user of a concept is to be able to infer truths involving that concept from other truths, which need not be lower-level truths. I argue, first, that the a priori entailment thesis is committed to reductive ascriptivism, and secondly, that reductive ascriptivism is problematic because it trivializes the notion of a priori knowledge. Therefore, I conclude that Chalmers and Jackson have not presented a convincing case for the claim that microphysical truths entail ordinary non-phenomenal truths a priori, especially when we understand this claim in the sense that is relevant for their argument against the possibility of a reductive explanation of consciousness. (shrink)
In this paper we prove that the free pseudocomplemented residuated lattices are decomposable if and only if they are Stone, i.e., if and only if they satisfy the identity ¬ x ∨ ¬¬ x = 1. Some applications are given.
In this paper we study some questions concerning Łukasiewicz implication algebras. In particular, we show that every subquasivariety of Łukasiewicz implication algebras is, in fact, a variety. We also derive some characterizations of congruence permutable algebras. The starting point for these results is a representation of finite Łukasiewicz implication algebras as upwardly-closed subsets in direct products of MV-chains.
Perkins, Patricio Agustín. Respuesta al comentario de Juan Diego Bogotá “La relación filosófica entre Husserl y Avenarius en Problemas fundamentales de la fenomenología.” Ideas y Valores 65.160 (2016): 286-289.
On philosophical and historical perspectives of education : with special reference to Sri Aurobindo, 1872-1950, Indian philosopher and John Dewey, 1859-1952, an American philosopher and educational reformer.
Łukasiewicz implication algebras are the {→,1}-subreducts of MV- algebras. They are the algebraic counterpart of Super-Łukasiewicz Implicational Logics investigated in Komori (Nogoya Math J 72:127–133, 1978). In this paper we give a description of free Łukasiewicz implication algebras in the context of McNaughton functions. More precisely, we show that the |X|-free Łukasiewicz implication algebra is isomorphic to ${\bigcup_{x\in X} [x_\theta)}$ for a certain congruence θ over the |X|-free MV-algebra. As corollary we describe the free algebras in all subvarieties of Łukasiewicz (...) implication algebras. (shrink)
Łukasiewicz implication algebras are {→,1}-subreducts of Wajsberg algebras (MV-algebras). They are the algebraic counterpart of Super-Łukasiewicz Implicational logics investigated in Komori, Nogoya Math J 72:127–133, 1978. The aim of this paper is to study the direct decomposability of free Łukasiewicz implication algebras. We show that freely generated algebras are directly indecomposable. We also study the direct decomposability in free algebras of all its proper subvarieties and show that infinitely freely generated algebras are indecomposable, while finitely free generated algebras can be (...) only decomposed into a direct product of two factors, one of which is the two-element implication algebra. (shrink)
ABSTRACT The variety O2 of double Ockham algebras consists of the algebras of type where and are Ockham algebras. In [16], M. Sequeira introduced several subvarieties of O2. In this paper we give a construction of free double Ockham algebras on a partially ordered set. We also describe free objects for the subvarieties of O2 considered in [16].
In this paper we continue the study of the variety \ of monadic Gödel algebras. These algebras are the equivalent algebraic semantics of the S5-modal expansion of Gödel logic, which is equivalent to the one-variable monadic fragment of first-order Gödel logic. We show three families of locally finite subvarieties of \ and give their equational bases. We also introduce a topological duality for monadic Gödel algebras and, as an application of this representation theorem, we characterize congruences and give characterizations of (...) the locally finite subvarieties mentioned above by means of their dual spaces. Finally, we study some further properties of the subvariety generated by monadic Gödel chains: we present a characteristic chain for this variety, we prove that a Glivenko-type theorem holds for these algebras and we characterize free algebras over n generators. (shrink)
The pressure for publication is ever present in academe. Rules for submission are elucidated by conferences, proceedings and journals for the benefit of authors; however, the rules for reviewers and editors are not so well established or consistent. This treatise examines examples of abuse of the editorial process and points to a need for formal recognition of rules for review. The manuscript culminates with proposed Codes of Ethics for researchers, referees and editors and suggestions for improvement of the peer review (...) process. (shrink)
Against the background of the current European competitive media landscape, the media are more and more compelled to legitimize their activities in their own national context as well as at a European level. Meanwhile, the nature of the media diversity in The Netherlands has changed tremendously; from a society divided along political and religious lines, it has evolved towards a multi-ethnic society. Hence, both the conceptualizing and operationalizing of media diversity from an academic as well as a media practical perspective (...) prove to be hot topics. An expert meeting was held at the Department of Communication at Radboud University Nijmegen in December 2004 in which the contours of media diversity in general and in The Netherlands in particular were explored. Institutional performance as well as program-related aspects linked to the notion of media diversity were discussed. Media diversity was explored from the angle of media economics as well as from the perspective of the program/format level. In addition, the audience reception perspective as well as methodologically problematic aspects one encounters when measuring media diversity were assessed. What follows here is a selection of several most pertinent views on this complex topic. We welcome each critical insight from other geographical contexts which might stimulate the debate on measures of open and reflective diversity in the media. (shrink)
In this paper we prove that the free algebras in a subvariety equation image of the variety equation image of semi-Heyting algebras are directly decomposable if and only if equation image satisfies the Stone identity.
The author reconstructs the theory of F. Varela with relevance to the hard problem of consciousness. This problem was touched by Varela in relatively late period of his work. However, the implications for dissolution of this problem can be found in his earlier works with H. Maturana. Theory of autopoietic systems ties life and cognition together, resulting in natural historical comprehension of consciousness and its functioning. Autopoiesis, understood as network of processes of production of components used as resources (...) for maintaining these processes, sets organizational invariances, distinguishing living system from its milieu. The main criterion of living system is an ability to maintain autopoietic organization while undergoing structural transformations with environment. Structural plasticity leads to multiple realizability of autopoietic organizations, which, in turn, leads to radical conclusion on nature of knowledge. One can distinguish the knower and the known only contingently, as the structure of knowledge reflects cognitive structure of the knower. This intertwinement permits Varela to introduce the enactivist program, which presupposes not simply reform in the scientific research of consciousness but also rethinking the implications of scientific knowledge itself. Cognition is a sensorimotor constitution of the world. Therefore, consciousness is not an object of material nature among other objects but provides our cognitive access to nature. Varela intended to abandon the theoretical approach to the problem of consciousness. His aim was not to provide a new argument. This is a consequence of the enactivist position which, according to theory of autopoiesis, must be applicable to the knower himself. (shrink)
This paper responds to the issues raised by D. Chalmers by offering a research direction which is quite radical because of the way in which methodological principles are linked to scientific studies of consciousness. Neuro-phenomenology is the name I use here to designate a quest to marry modern cognitive science and a disciplined approach to human experience, thereby placing myself in the lineage of the continental tradition of Phenomenology. My claim is that the so-called hard problem that animates these Special (...) Issues can only be addressed productively by gathering a research community armed with new pragmatic tools for the development of a science of consciousness. I will claim that no piecemeal empirical correlates, nor purely theoretical principles, will really help us at this stage. We need to turn to a systematic exploration of the only link between mind and consciousness that seems both obvious and natural: the structure of human experience itself. In what follows I motivate my choice by briefly examining the current debate about consciousness at the light of Chalmer’s hard problem. Next, I outline the phenomenological strategy. Finally I conclude by discussing some of the main difficulties and consequences of this strategy. (shrink)
An algebraically expandable (AE) class is a class of algebraic structures axiomatizable by sentences of the form $\forall \exists! \mathop{\boldsymbol {\bigwedge }}\limits p = q$. For a logic L algebraized by a quasivariety $\mathcal {Q}$ we show that the AE-subclasses of $\mathcal {Q}$ correspond to certain natural expansions of L, which we call algebraic expansions. These turn out to be a special case of the expansions by implicit connectives studied by X. Caicedo. We proceed to characterize all the AE-subclasses of (...) abelian $\ell $ -groups and perfect MV-algebras, thus fully describing the algebraic expansions of their associated logics. (shrink)
