We show the undecidability of the equational theories of some classes of BAOs with a non-associative, residuated binary extra-Boolean operator. These results solve problems in Jipsen [9], Pratt [21] and Roorda [22], [23]. This paper complements Andréka-Kurucz-Németi-Sain-Simon [3] where the emphasis is on BAOs with an associative binary operator.

We prove that the equational theory of a semigroups becomes undecidable if we add a semilattice structure with a ‘touch of symmetric difference’. As a corollary we obtain that the variety of all Boolean algebras with an associative binary operator has a ‘hereditarily’ undecidable equational theory. Our results have implications in logic, e.g. they imply undecidability of modal logics extending the Lambek Calculus and undecidability of Arrow Logics with an associative arrow modality.

As the number of consumer transgressions continues to increase, so do their financial repercussions for companies. Though academic and managerial interest in addressing this issue is growing, research on how to dissuade consumers from committing transgressions remains scarce. Drawing on the mental imagery literature and normative moral theory, the present research examines a novel way of reducing consumers’ appraisals of their own transgressions. Whereas an actor-imagery perspective fosters a teleological, egoistic view of morality and, in turn, induces moral leniency, having (...) consumers adopt an observer-imagery perspective fosters a deontological view of morality and, in turn, induces moral stringency. The effects are robust across various types of consumer transgressions, including the purchase of counterfeit products and return fraud in the form of wardrobing. Study 2 also rules out vividness as an alternative explanation for these effects. Theoretical and managerial implications are discussed. (shrink)

Biró, B. and I. Sain, Peano arithmetic as axiomatization of the time frame in logics of programs and in dynamic logics, Annals of Pure and Applied Logic 63 201-225. We show that one can prove the partial correctness of more programs using Peano's axioms for the time frames of three-sorted time models than using only Presburger's axioms, that is it is useful to allow multiplication of time points at program verification and in dynamic and temporal logics. We organized the (...) paper as follows: 1. Preliminaries, 2. The main result, 3. Peano arithmetic with bounded multiplication, 4. Connections with temporal logics and dynamic logics, Acknowledgements, References. (shrink)

En el siguiente trabajo me encargaré de estudiar la noción de cuerpo en el Banquete de Platón a partir del discurso de Aristófanes, pretendiendo con esto revisar al mismo tiempo la tradicional lectura del diálogo —que hace foco únicamente en el personaje de Sócrates— y la interpretación más aceptada del lugar que ocupa el cuerpo en el pensamiento platónico —el cual es relegado a una esfera de negatividad aparentemente insalvable. En una primera parte mostraré que Aristófanes, en tanto poeta, busca (...) elementos a la mano para inspirar su relato; elementos que encuentra en su interacción con el médico Erixímaco. A partir de esto, Aristófanes tejerá un esquema conceptual con nociones médicas en el que el cuerpo cobrará el rol de «síntoma», i.e expresión visible, de un estado enfermo y corrompido. Como conclusión, la idea de cuerpo como «síntoma» resultará para la lectura propuesta un indicio de que Platón presenta en el Banquete al cuerpo de manera positiva como despertador de un deseo que estimulará la búsqueda hacia la verdad. (shrink)

Among others we will see that the equational theory of ω dimensional representable polyadic equality algebras. We will also see that the complexity of the equational theory of RPEAω is also extremely high in the recursion theoretic sense. Finally, comparing the present negative results with the positive results of Ildiko Sain and Viktor Gyuris [10], the following methodological conclusions will be drawn: the negative properties of polyadic algebras can be removed by switching from what we call the `polyadic algebraic (...) paradigm' to the `cylindric algebraic paradigm'. (shrink)

After identifying points of agreement between Karl Rahner and Hans Urs von Balthasar on topics raised by Dr. Sain’s essay, this response raises questions about the deeper foundations of the substantial differences between them. It suggests that the appeal to contrast in their starting-points (Goethe versus Kant) as an explanation is not adequate and suggests lines of further inquiry which might be pursued further.

The main result of this paper belongs to the field of the comparative study of program verification methods as well as to the field called nonstandard logics of programs. We compare the program verifying powers of various well-known temporal logics of programs, one of which is the Intermittent Assertions Method, denoted as Bur. Bur is based on one of the simplest modal logics called S5 or sometime-logic. We will see that the minor change in this background modal logic increases the (...) program verifying power of Bur. The change can be described either technically as replacing the reflexive version of S5 with an irreflexive version, or intuitively as using the modality some-other-time instead of sometime. Some insights into the nature of computational induction and its variants are also obtained. (shrink)

Theorem 1 states a negative result about the classical semantics j= ! of program schemes. Theorem 2 investigates the reason for this. We conclude that Theorem 2 justies the Henkin-type semantics j= for which the opposite of the present Theorem 1 was proved in [1]{[3] and also in a dierent form in part III of [5]. The strongest positive result on j= is Corollary 6 in [3].

The central question of Hans Urs von Balthasar’s Theo-Logic is how the infinite truth of God can be manifested in the finite structures of the created world. In the course of answering this question, Balthasar presents a philosophical understanding of expressive form and a theology of Christ as the expression of divine truth in the world. The philosophical discussion of truth provides support for the intelligibility of the theological claim that God’s truth has been manifested in the world in Christ. (...) The fullest expression of divine truth and the highest realization of worldly truth are found together in Christ, whom Balthasar calls the “truth of God.” Balthasar’s philosophical and theological understanding of expression, as set forth in the Theo-Logic, provides helpful insights for comparing his thought to that of Karl Rahner. (shrink)

In this paper we investigate total correctness in Nonstandard Dynamic Logic . Here we show that despite of the celebrated Kfoury-Park [5] result, termination is a rst order notion if approached properly.

Collaborative filtering recommender system (CFRS) plays a vital role in today’s e-commerce industry. CFRSs collect ratings from the users and predict recommendations for the targeted product. Conventionally, CFRS uses the user-product ratings to make recommendations. Often these user-product ratings are biased. The higher ratings are called push ratings (PRs) and the lower ratings are called nuke ratings (NRs). PRs and NRs are injected by factitious users with an intention either to aggravate or degrade the recommendations of a product. Hence, it (...) is necessary to investigate PRs or NRs and discard them. In this work, opinion mining approach is applied on textual reviews that are given by users for a product to detect the PRs and NRs. The work also examines the effect of PRs and NRs on the performance of CFRS by evaluating various measures such as precision, recall, F-measure and accuracy. (shrink)

The class \ of t rue p airing a lgebras is defined to be the class of relation algebras expanded with concrete set theoretical projection functions. The main results of the present paper is that neither the equational theory of \ nor the first order theory of \ are decidable. Moreover, we show that the set of all equations valid in \ is exactly on the \ level. We consider the class \ of the relation algebra reducts of \ ’s, (...) as well. We prove that the equational theory of \ is much simpler, namely, it is recursively enumerable. We also give motivation for our results and some connections to related work. (shrink)

We give an overview of decidability results for modal logics having a binary modality. We put an emphasis on the demonstration of proof-techniques, and hope that this will also help in finding the borderlines between decidable and undecidable fragments of usual first-order logic.

Recommender system depends on the thoughts of numerous users to predict the favourites of potential consumers. RS is vulnerable to malicious information. Unsuitable products can be offered to the user by injecting a few unscrupulous “shilling” profiles like push and nuke attacks into the RS. Injection of these attacks results in the wrong recommendation for a product. The aim of this research is to develop a framework that can be widely utilized to make excellent recommendations for sales growth. This study (...) uses the methodology that presents an enhanced clustering algorithm named as modified density peak clustering algorithm on the consumer review dataset to ensure a well-formed cluster. An improved recurrent neural network algorithm is proposed to detect these attacks in hybrid RS, which uses the content-based RS and collaborative filtering RS. The results are compared with other state of the art algorithms. The proposed method is more suitable for E-commerce applications where the number of customers and products grows rapidly. (shrink)

The class $$\mathsf{TPA}$$ TPA of t rue p airing a lgebras is defined to be the class of relation algebras expanded with concrete set theoretical projection functions. The main results of the present paper is that neither the equational theory of $$\mathsf{TPA}$$ TPA nor the first order theory of $$\mathsf{TPA}$$ TPA are decidable. Moreover, we show that the set of all equations valid in $$\mathsf{TPA}$$ TPA is exactly on the $$\Pi ^1_1$$ Π 1 1 level. We consider the class $$\mathsf{TPA}^-$$ (...) TPA - of the relation algebra reducts of $$\mathsf{TPA}$$ TPA ’s, as well. We prove that the equational theory of $$\mathsf{TPA}^-$$ TPA - is much simpler, namely, it is recursively enumerable. We also give motivation for our results and some connections to related work. (shrink)

Reseña de Suñol, V.; Miranda, L. R. (eds.). La educación en la filosofía antigua: Ética, retórica y arte en la formación del ciudadano. Buenos Aires, Miño y Dávila.

In this article we consider certain elements of the normative theory of Jürgen Habermas in the light of the proposals of Bruce Ackerman, with a view to strengthening a concept of deliberative democracy applied to the legitimation of juridical rules. We do not construct a hierarchy of the two positions, but seek to bring together certain elements to achieve a common project. As the starting point for examining the work of the two authors, we take the scheme proposed by Habermas (...) in Faktizität und Geltung. In this connection, through the work of Ackerman, we intend to fill in some of the gaps that Habermas appears to have left in the theory of radical democracy applied to the law. The work of Ackerman can make a significant contribution to deliberative democracy, to the discourse principle that Habermas defines, and to the contractualist theories from a liberal perspective. The study of these contributions makes possible a critical judgment that enables the legitimation of juridical rules carried out by Habermas to acquire greater practicity. In examining the epistemological status of juridical science and law, we attempt to determine the weight and the performance of normative democracy. In Tarr's view, it is a matter for philosophers to examine direct democracy and its desirability. (shrink)