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.

The intuitionistic consequence operation restricted to the language with (equivalence) and (negation) as the only connectives is axiomatized by means of a finite set of sequential rules of inference.

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 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)

The aim of the paper is twofold. First, we want to recapture the genesis of the logics of order. The origin of this notion is traced back to the work of Jerzy Kotas, Roman Suszko, Richard Routley and Robert K. Meyer. A further development of the theory of logics of order is presented in the papers of Jacek K. Kabziński. Quite contemporarily, this notion gained in significance in the papers of Carles Noguera and Petr Cintula. Logics of order are (...) named there _logics of weak implications_. They play a crucial role in their monograph (Noguera and Cintula _Logic and Implication. An Introduction to the General Algebraic Study of Non-Classical Logics_, Trends in Logic 57, Springer, Berlin, 2021). But, more importantly, the other goal is to define some subclasses of the logics of order in reference to later results of Jacek K. Kabziński and Michael Dunn. The original conception of implication is due to Kabziński. Implication is a stronger notion than the notion of the connective of order aka weak implication. As a result, the three subclasses of logics of order are isolated: logics of implication, logics of symmetry, and tonoidal logics. These notions are uniformly defined and investigated from various viewpoints in terms of consequence operations. The emphasis is put on their semantics. (shrink)

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.

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 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.

This paper discusses the problem of inconsistencies in the metaphorical conceptualizations of time that involve motion within the framework of conceptual metaphor theory (CMT). It demonstrates that the TIME AS A PURSUER metaphor contrasts with the reverse variant TIME AS AN OBJECT OF PURSUIT, just as the MOVING TIME metaphor contrasts with the MOVING OBSERVER variant. Such metaphorical conceptualizations of time functioning as pairs of minimally differing variants based on Figure-Ground reversal are, strictly speaking, inconsistent with one another. Looking at (...) these inconsistencies from a wider perspective suggests that time may belong to a separate category of conceptual phenomena. This paper puts forward a proposal to approach time from the perspective of “phenomena of the third kind”, which according to Keller’s thesis include conceptual establishments resulting from human cognition, but not of human design. (shrink)

Obcy Inny. Analiza przypadków. 2017, ed. Małgorzata Karwatowska, Robert Litwiński, AdamSiwiec. Wydawnictwo UMCS, Lublin.Obcy/Inny, Propozycje aplikacji pojęciowych. 2018, ed. M. Karwatowska, R. Litwiński, A. Siwiec,Wydawnictwo Uniwersytetu Marii Curie-Skłodowskiej, Lublin.

In 1968 the authors of the so-called Harvard Report, proposed the recognition of an irreversible coma as a new criterion for death. The proposal was accepted by the medical, legal, religious and political circles in spite of the lack of any explanation why the irreversible coma combined with the absence of brainstem reflexes, including the respiratory reflex might be equated to death. Such an explanation was formulated in the President’s Commission Report published in 1981. This document stated, that the brain (...) is the central integrator of the body, therefore the destruction of the brain results in the lack of that integration and the death of the organism. Therefore, according to that document, the so-called “brain dead” patients are really, biologically dead; strictly speaking they are not any more biological organisms but collections of organs and tissues. Their death was masked by the use of the medical equipment, but it was a real, biological death. Thus, the explanation given by the President’s Commission Report constituted a biological rationale for the new concept of death, known as “brain death.” However, after the long discussion, this rationale was refuted because of the evidence given by many medical authorities, that the bodies of the “brain dead” and “brainstem dead” patients are alive. In the context of the discussion about the neurological criteria for death, some authors follow the idea of Plato, that human being is the soul or mind, and the body does not belong to the human essence. Therefore, the loss of consciousness, which may be identified with the mind, constitutes the loss of personhood and may be interpreted as human death. The other group stresses the Aristotelian and Thomistic concept that the body belongs to the essence of every living creature, including human. Therefore, as long as the body is alive, the human being is alive and we cannot call the given patient dead even if he is deeply comatose. Moreover, in spite of the opinions dominating in the mass-media, these patients should be considered not only alive but also may be conscious to some degree and their state can be reversible. Their brains are lacking the electrical functions, but the neuronal tissue is alive and that state is reversible for at least first 48 hours since the onset of coma; this phenomenon is called “global ischemic penumbra” and is responsible for the regularly happening events interpreted as miracles, when some of the “brain dead” or “brainstem dead” patients turn to be alive and come back to normal life. Therefore, the neurological criteria of death are still lacking generally accepted scientific basis and should not be used in medicine and in the legal systems as a basis for diagnosing comatose/having no brainstem reflexes/apneic patients dead. (shrink)

Der vorliegende Aufsatz berührt zwei bis heute nur im geringen Maße erforschte und thematisierte Probleme der Übersetzungstheorie. Es geht hier vor allem um eine möglichst kompakte Darstellung einer Diskussion über solche Begriffe wie Kultur, Fremderfahrung, Fremdverstehen, oder Alienation und Alterität. Der wissenschaft1iche Diskurs, in welchem beide der erwähnten Themen immer wieder zur Sprache kommen, gewinnt heutzutage für eine einheitliche Beschreibung der literarischen Übersetzung einen interessanten, obwohl methodologisch noch nicht ganz sicheren Boden. In erster Linie liegt das Problem des Kulturphänomens auf (...) dem Gebiet der Übersetzung in der Art und Weise seiner Analyse. Wie funktioniert der fremde und fremdsprachige Kontext in der kommunikativen Situation der Übersetzung, was doch eine Begegnung der Kulturen bedeutet? Wie ist es mit den Artefakten der fremden Kultur, Kunst und Literatur umzugehen? Welche Sprache soll die Aufgabe der Beschreibung leisten? Es werden hier nur die wichtigsten Fragen einer kulturspezifisch orientierten Übersetzungswissenchaft aufgezahlt. Ein Versuch, nur auf diese Fragen eine allgemeine Antwort zu erteilen, würde den Rahmen jenes kurzen Aufsatzes mit großter Sicherheit sprengen. Nichtsdestotrotz lohnt es sich über die immer aktuellen Quästionen der literarischen Übersetzung ein paar Worte zu sagen. Ich heiter, meine kurze und notwendigerweise oberflächliche Arbeit möge doch als ein guter Ansatz zum Thema: Kultur in der literarischen Übersetzung dienen. (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.

In her books Szymborska touches many diverte subjects but it is easy to notice her predilection for some topics with which she deals in her successive books of poems. Unplanned haphazard happenings, their category and their role in the life of the man, in reality and in the world, are her main preocupations. As our century has witnessed a breakthrough in indeterminacy due to surprising discoveries in natural sciences the question of haphazard happenings has become more important and intriguing. It (...) has a great fascination for artistics. W. Szymborska giving so much attention to the category of haphazards familiorizes the man with the reality in dissaway that can result in a chaos. In her poems influenced by natural sciences the category of haphazards is not only a leitmotif but also a fascinating enigma. For her casualness and situations resulting from chance are the main mechanism that controls the course of events. In her many poems she focuses on the mystery of haphazards and their inevitability. Her poem Wszelki wypadek (It Might Have Happened) is, perhaps, her first work where she doesn’t deal but with the role of haphazards played in the life of the man. She directs her attention to situations happening in unplanned or disorderly manner thus making possible to save one’s life. Haphazards not only can save the man’s life but they also determine the angle from which he sees the world where the haphazard is ruling. Haphazards can influence all the spheres that are important for the man. The world full of haphazards pictured in the poem is mosaic-like – a number of happenings, various possibilities for the course of particular events. The language describing those events matches the structure of composition. What is happening in the sphere of the language it is precisely reflected in the meaning. Her symmetric and precise structure of the poem results in a scheme called “the tree of decision” transformed by Szymborska in a “tree of possibilities”. In the poem Terrorysta, on patrzy (He is Watching, the Terrorist) the poetess tries to paint the ruthless mechanism of a haphazard meaning the life of people. A terrorist, after having planted a bomb in a bar, is watching people coming in and out of the bar. The whole poem is a silent question about the aim and the sense of the events impossible to understand for people who are involved in them. Szymborska’s latest book of poems (Koniec i początek, The End And The Beginning) confirms her strong interest in haphazards (especially in the poem Seans). The title of the poem is a metaphor between the casualness and the man. Again one focuses on the surprised man who cannot understand the sense of the events happening with his participation. The spectators are surprised because they don’t know the way the illusionist plays his tricks. Szymborska’s man is dependent on something over which he has no influence. He is the passive protagonist of events he takes part in. At the same time the category of haphazard stresses the joyful aspect of human existence. For Szymborska both haphazards are important: the one that threatens the man’s life and the other that makes possible to save his life. So the pessimism in the poem It Might Have Happened is balanced by optimism. The poetess, inspired by everyday world and new achievements in sciences, pictures a world where the haphazard and invitability coexist and integrate and interrelate. Szymborska, in her poetry, surmounts the contradiction between those categories. (shrink)