The following logics are the most noteworthy from the perspective of the calculus of combinators: the Hilbert’s positive implicational logic , the Church’s weak theory of implication , the BCK-logic, and the BCI-logic. Their significance is due to a certain correspondence between combinators and implicational formulas . The first three logics mentioned have been immensely investigated but it was not so in case of the remaining one. The BCI-logics was mentioned by A. N. Prior in the second edition of his (...) Formal Logic of 1962 where it was credited to C. A. Meredith and dated in 1956 . A. (shrink)

In this paper we investigate some basic semantic and syntactic conditions characterizing the equivalence connective. In particular we define three basic classes of algebras: the class of weak equivalential algebras, the class of equivalential algebras and the class of regular equivalential algebras.Weak equivalential algebras can be used to study purely equivalential fragments of relevant logics and strict equivalential fragments of some modal logics. Equivalential algebras are suitable to study purely equivalential fragment of BCI and BCK logic. A subclass of the (...) class of regular equivalential algebras is suitable to study equivalential fragments of ukasiewicz logics. Some subvarieties of the class of regular equivalential algebras provide natural semantics for equivalential fragments of the intuitionistic prepositional logic and various intermediate logics. (shrink)

The quasivariety of BCK-algebras is widely known and investigated class of algebras. It is a natural semantic for the BCK-logic but there are also others quasivarieties of algebras with the above property and there are even some varieties among them. The aim of this note is to bring to the reader’s a attention the lattice they form. In what follows we shall only consider classes of algebras of type.

BackgroundPrenatal and early postnatal choline supplementation reduces cognitive and behavioral deficits in animal models of Fetal Alcohol Spectrum Disorder. In a previously published 9-month clinical trial of choline supplementation in children with FASD, we reported that postnatal choline was associated with improved performance on a hippocampal-dependent recognition memory task. The current paper describes the neurophysiological correlates of that memory performance for trial completers.MethodsChildren with FASD who were enrolled in a clinical trial of choline supplementation were followed for 9 months. Delayed (...) recall on a 9-step elicited imitation task served as the behavioral measure of recognition memory. Neurophysiological correlates of memory were assessed via event-related potentials.ResultsDelayed recall on EI was correlated with two ERP components commonly associated with recognition memory in young children: middle latency negative component and positive slow wave. No significant ERP differences were observed between the choline and placebo groups at the conclusion of the trial.ConclusionAlthough the small sample size limits the ability to draw clear conclusions about the treatment effect of choline on ERP, the results suggest a relationship between memory performance and underlying neurophysiological status in FASD. This trial was registered.1. (shrink)

The aim of this note is to give an example of application of model theory to the theory of logical matrices. . More precisely, we show that Wojtylak's representation theorem is an immediate consequence of a result due to Mal'cev . Throughout the present note we assume that matrices, and classes of matrices under consideration are of the same xed similarity type. Suppose that K is an arbitrary class of matrices, and M is a matrix . We say that M1 (...) 2 K is called a replica of M in the class K i there is a homomorphism h of M onto M1 such that for every homomorphism g of M into arbitrary N 2 K there exists a homomorphism f of M1 into N such that g = f h. (shrink)

x1. This paper is a contribution to matrix semantics for sentential logics as presented in Los and Suszko [1] and Wojcicki [3], [4]. A generalization of Lindenbaum completeness lemma says that for each sentential logic there is a class K of matrices of the form such that the class is adequate for the logic, i.e., C = CnK.

The goal of the article is to compare methods of financing ARs and ERs based on the data from the 1st half of 2013 and 1st half of 2014 from the K. Jonscher 3rd Municipal Hospital in Lodz. All the stays in the AR/ER in the 1st half of 2013 and the 1st half of 2014 were analysed. Based on the presented data, it can be clearly seen that the new method of financing AR/ER services proposed by the NFZ will (...) beyond doubt have negative outcomes, and will certainly not improve the financial situation of hospitals. (shrink)

The European Summer Schools in Logic, Language and Information (ESSLLI) have been organised every year since 1989 under the auspices of the Association for Logic, Language and Information (FoLLI) in different cities around Europe. The 24th European Summer School in Logic, Language and Information (ESSLLI 2012) took place at the University of Opole, Poland, during August 6-17, 2012. The organisation committee was chaired by Janusz Czelakowski and Urszula Wybraniec-Skardowska (Institute of Mathematics and Informatics, University of Opole) and the programme committee (...) was chaired by Andreas Herzig (University of Toulouse and CNRS). During two weeks, over 340 participants from 36 countries were offered a rich academic program of their choice from 9 foundational, 16 introductory and 17 advanced courses and 6 workshops. Just as in the previous years, the 17th conference on Formal Grammar collocated with ESSLLI. Besides the regular courses, a traditional highlight of the summer school were the 4 evening lectures by distinguished academics: - Johan van Benthem (Institute for Logic, Language & Computation (ILLC), Amsterdam and Department of Philosophy, Stanford University), "Computation as Agency''; - Melvin Fitting (Department of Mathematics and Computer Science, City University of New York), "Reasoning About Games''; - Jonathan Ginzburg (UFR Études anglophones, Université Paris-Diderot (Paris 7)), "False starts, jokes, and music:semantics in the 21st century''; - Adam Przepiórkowski (Institute of Computer Science, Polish Academy of Sciences, Warsaw), "Secret life of corpora''. Another traditional event was the student session, organised by a student programme committee chaired by Rasmus K. Rendsvig (University of Copenhagen): master and doctoral students presented 16 papers and 5 posters, and Michał Zawidzki obtained the best paper award and Raul Fervari obtained the best poster award. Moreover, the Beth Dissertation Prizes were announced at the FoLLI General Meeting and went to Andreas Kapsner (University of Barcelona) and Daniel R. Licata (Carnegie Mellon University). Apart from the busy academic programme, participants of the summer school were offered an exciting social program as well. In addition to the traditional ESSLLI Party and the famous Students vs. Lecturers Soccer Match (also called `Johan van Benthem Cup'), kayaking, and excursions to Kraków and Wrocław were offered. -/- . (shrink)

Let J be any proper ideal of subsets of the real line R which contains all finite subsets of R. We define an ideal J * ∣B as follows: X ∈ J * ∣B if there exists a Borel set $B \subset R \times R$ such that $X \subset B$ and for any x ∈ R we have $\{y \in R: \langle x,y\rangle \in B\} \in \mathscr{J}$ . We show that there exists a family $\mathscr{A} \subset \mathscr{J}^\ast\mid\mathscr{B}$ of power ω (...) 1 such that $\bigcup\mathscr{A} \not\in \mathscr{J}^\ast\mid\mathscr{B}$ . In the last section we investigate properties of ideals of Lebesgue measure zero sets and meager sets in Cohen extensions of models of set theory. (shrink)

In this paper we present a characterization of hyper-connexivity by means of a relating semantics for Boolean connexive logics. We also show that the minimal Boolean connexive logic is Abelardian, strongly consistent, Kapsner strong and antiparadox. We give an example showing that the minimal Boolean connexive logic is not simplificative. This shows that the minimal Boolean connexive logic is not totally connexive.

The author presents Leszek Kołakowski from the perspective of his private acquaintanceship, lasting for about 47 years, as a witty man and a workaholic. L. Kołakowski never formed a classic “school”, but there is something all his disciples share: a thesis, key to understanding his ideas, which holds that “THERE IS MORE THAN ONE CORRECT OPINION IN THE HUMANITIES”, i.e. we will ALWAYS have opinions for and against, which goes against any dogmatism, wherever it may appear; this also bears consequences (...) in diagnosing the socio-political reality past and present. (shrink)

The aim of this article is to show the influence of Jacques Maritain’s philosophical work Art et scolastique on the young Czesław Miłosz and his work, and how it shaped the poet’s views on art in subsequent years. The author analyzes Maritain’s work on art in the context of theology and Miłosz’s articles published between the two world wars. In terms of methodology, the article draws on the concept of intertextuality, pointing to the dependence of the poet’s thinking during this (...) period on that of the French philosopher. Maritain’s aesthetic creationism was seen by some inter-war literary critics, including Miłosz himself, as a third way between the mimetic aesthetics or art in the service of ideas and the “angelism” of symbolic art and art for art’s sake. In Maritain’s aesthetics, the writer found a system of concepts through which he opened himself up to issues related to human spirituality, ontology and religion. Maritain’s distinction between the purpose of the work and the purpose of the maker directed Miłosz’s attention to the author, as one that has been singled out as bound to strive for self-improvement and self-development. To a much lesser extent, this concept influenced his poetics. His works written in the twenty-year interwar period are saturated with dark symbolism and modernistic mannerisms. (shrink)

In his 1913 behaviourist manifesto John B Watson urged psychologists to adopt "a unitary scheme of animal response...(that) recognizes no dividing line between man and brute." His call was heeded. By the 1930s, methodological behaviourism and animal behaviour research were dominant features of the psychological landscape. To document the origins of behaviourism, this series collects the theoretical and empirical articles that set the terms of the behaviourist debate. It includes the most important pre-Watsonian monographic contributions to objectivism and reprints the (...) first full text of the new behaviourism. (shrink)

In this article we consider linear isomorphisms over the field of rational numbers between the linear spaces ℝ2 and ℝ. We prove that if f is such an isomorphism, then the image by f of the unit disk is a strictly nonmeasurable subset of the real line, which has different properties than classical non-measurable subsets of reals. We shall also consider the question whether all images of bounded measurable subsets of the plane via a such mapping are non-measurable.

In this paper the notion of unifier is extended to the infinite set case. The proof of existence of the most general unifier of any infinite, unifiable set of types (terms) is presented. Learning procedure, based on infinite set unification, is described.

We prove that no logic (i.e. consequence operation) determined by any class of orthomodular lattices admits the deduction theorem (Theorem 2.7). We extend those results to some broader class of logics determined by ortholattices (Corollary 2.6).

We assess Cartwright's models for probabilistic causality, and in particular, her models for EPR-like experiments of quantum mechanics. We show that her models for the EPR are mathematically incorrect and physically implausible. Finally, we argue that her models are not adequate for EPR-phenomena, since they ignore modal and spatiotemporal aspects inherent in their setup.

We assess Cartwright's models for probabilistic causality and, in particular, her models for EPR-like experiments of quantum mechanics. Our first objection is that, contrary to econometric linear models, her quasi-linear models do not allow for the unique estimation of parameters. We next argue that although, as Cartwright proves, Reichenbach's screening-off condition has only limited validity, her generalized condition is not empirically applicable. Finally, we show that her models for the EPR are mathematically incorrect and physically implausible.

The first part of the paper is a reminder of fundamental results connected with the adequacy problem for sentential logics with respect to matrix semantics. One of the main notions associated with the problem, namely that of the degree of complexity of a sentential logic, is elucidated by a couple of examples in the second part of the paper. E.g., it is shown that the minimal logic of Johansson and some of its extensions have degree of complexity 2. This is (...) the first example of an exact estimation of the degree of natural complex logics, i.e. logics whose deducibility relation cannot be represented by a single matrix. The remaining examples of complex logics are more artificial, having been constructed for the purpose of checking some theoretical possibilities. (shrink)

The present narrative describes and problematizes one year of Educational and philosophical work with illiterate adults in contexts of urban poverty in the Public School Joaquim da Silva Peçanha, city of Duque de Caxias, suburbs of the State of Rio de Janeiro during 2008. The project, “Em Caxias a Filosofia En-caixa?!”, consists of a teacher education program in which public school teachers study and practice the art of composing philosophical experiences with their students, and the realization of actual experiences of (...) philosophy in classrooms with children and students in an adult literacy class. This narrative is concerned with the latter aspect of the project, more specifically experiences working with adult students practicing philosophy. The thirty students and three teachers involved in the course do not study the history of philosophy, nor do they create philosophical systems or theories. Rather they participate in a philosophical experience that might best be able to understand by examining Pierre Hadot’s concept of philosophy “as a way of living”. (shrink)

The purpose of the paper is to rethink the role of actuality in the branching model of possibilities. We investigate the idea that the model should be enriched with an additional factor—the so-called Thin Red Line—which is supposed to represent the single possible course of events that gets actualized in time. We believe that this idea was often misconceived which prompted some unfortunate reactions. On the one hand, it suggested problematic semantic models of future tense and and on the other, (...) it provoked questionable lines of criticism. We reassess the debate and point to potential pitfalls, focusing on the semantic dimension of the Thin Red Line theory. Our agenda transcends the semantics, however. We conclude that semantic considerations do not threaten the Thin Red Line theory and that the proper debate should be carried in the domain of metaphysics. (shrink)