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.

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).

This paper is a study of similarities and differences between strong and weak quantum consequence operations determined by a given class of ortholattices. We prove that the only strong orthologics which admits the deduction theorem (the only strong orthologics with algebraic semantics, the only equivalential strong orthologics, respectively) is the classical logic.

This volume clusters together issues centered upon the variety of types of intensional semantics. Consisting of 10 contributions, the volume is based on papers presented at the Trends in Logic 2019 conference. The various chapters introduce readers to the topic, or apply new types of logical semantics to elucidate subtleties of logical systems and natural language semantics. The book introduces hyperintentional systems that aim at solving some open philosophical problems. Specifically, the first three studies focus on relating semantics, while the (...) following ones discuss fundamental issues related to hyper-intensional semantics or develop hyper-intensional frameworks to address issues in modal, epistemic, deontic and action logic. Authors in this volume present original results on logical systems but also extend beyond this by offering philosophical considerations on the topic as well. This volume will appeal to students and researchers in the field of logic. (shrink)

The aim of this paper is to analyze the differences and similarities between the linguistic and the logical meaning of a sentence and propose a uniform point of view on the notion of the meaning of utterances. The proposed notion differs from the notion of the logical meaning as well as from the linguistic one. It may be considered to be a kind of composition of both of them.

In this paper we investigate the relation between the axiomatization of a given logical consequence operation and axiom systems defining the class of algebras related to that consequence operation. We show examples which prove that, in general there are no natural relation between both ways of axiomatization.

In this paper we investigate Boolean connexive logics in a language with modal operators: □, ◊. In such logics, negation, conjunction, and disjunction behave in a classical, Boolean way. Only implication is non-classical. We construct these logics by mixing relating semantics with possible worlds. This way, we obtain connexive counterparts of basic normal modal logics. However, most of their traditional axioms formulated in terms of modalities and implication do not hold anymore without additional constraints, since our implication is weaker than (...) the material one. In the final section, we present a tableau approach to the discussed modal logics. (shrink)

This volume investigates what is beyond the Principle of Non-Contradiction. It features 14 papers on the foundations of reasoning, including logical systems and philosophical considerations. Coverage brings together a cluster of issues centered upon the variety of meanings of consistency, contradiction, and related notions. Most of the papers, but not all, are developed around the subtle distinctions between consistency and non-contradiction, as well as among contradiction, inconsistency, and triviality, and concern one of the above mentioned threads of the broadly understood (...) non-contradiction principle and the related principle of explosion. Some others take a perspective that is not too far away from such themes, but with the freedom to tread new paths. Readers should understand the title of this book in a broad way,because it is not so obvious to deal with notions like contradictions, consistency, inconsistency, and triviality. The papers collected here present groundbreaking ideas related to consistency and inconsistency. (shrink)

This book is dedicated to the life and work of logician Janusz Czelakowski on the topic of logical consequence. It consists of three parts – a biography, a survey and research sections. The volume begins with an autobiographic chapter by Janusz Czelakowski followed by a historical chapter written by Jacek Malinowski. The survey section forms the backbone of the volume with each chapter covering one of Janusz Czelakowski’s results. They focus on his results in the area of logical (...) consequence, demonstrate how his results influenced following research, and presents potential future results, problems and applications. This volume is of interest to logicians and mathematicians. (shrink)

The aim of this book is to present essays centered upon the subjects of Formal Ontology and Logical Philosophy. The idea of investigating philosophical problems by means of logical methods was intensively promoted in Torun by the Department of Logic of Nicolaus Copernicus University during last decade. Another aim of this book is to present to the philosophical and logical audience the activities of the Torunian Department of Logic during this decade. The papers in this volume contain the results concerning (...) Logic and Logical Philosophy, obtained within the confines of the projects initiated by the Department of Logic and other research projects in which the Torunian Department of Logic took part. (shrink)

According to a brief and very general definition Cognitive Science is an interdisciplinary scientific study of how information is represented and transformed in a human nervous system. “Information”, “representation” and “transformation” are keywords here. Many disciplines bring considerable contribution to Cognitive Science. Logic is one of them. Logic investigates these rules which allow us to recognize valid reasonings and distinguish them from those that fail to fulfill the condition of valid- ity. Thus logic investigates some representation (or representations) of reasoning. (...) Significant part of information transformed in nervous system is related to reasoning and inference. This fact opens special perspectives on applying Logic in Cognitive Science both in representing as well as in transforming information. Any formal logical system constitutes a kind of representation of a class of propositions considered as sentence content. In this way each logical system provides a representation of a broad class of belief states. At the same time any inference relation, related to a given logical system, represents a transformation of some type of information. As a consequence it would be hard to find logical investigations which could not be applied in Cognitive Science. Such an idea guided us while we were preparing the present volume. (shrink)

The main aim of this paper is to elucidate, from a logical point of view, the phenomenon of Simpson reversal — the paradox of a statistical reasoning. We define a binary relation of supporting in the following way: a sentence A supports a sentence B if and only if the probability of B is higher when A is true, than when A is false. It appears that a statistical argument occurring in Simpson paradox cannot be formalized by means of a (...) binary relation. We generalize the relation of support introducing the third parameter. Then we argue that it properly mirrors main features of the statistical argument occurring in Simpson paradox. (shrink)

In this paper we analyze the Strawson's notion of presupposition proposed in his book Introduction to Logical Theory. Strawsonian notion of presupposition is dependent on the notion of logical entailment. We make use of the theory of logical consequence operation as a general framework to show that it is impossible to find a logical consequence operation which mirrors the philosophical intuitions of the Strawson's notions of presupposition. The aim of this paper is to present in details the philosophical backgrounds of (...) the formal analysis presented in the author's paper "Strawsonian presuppositions and logical entailment". (shrink)

We define and investigate from a logical point of view a family of consequence relations defined in probabilistic terms. We call them relations of supporting, and write: |≈w where w is a probability function on a Boolean language. A |≈w B iff the fact that A is the case does not decrease a probability of being B the case. Finally, we examine the intersection of |≈w, for all w, and give some formal properties of it.

In 1953, exactly 50 years ago to this day, the first volume of Studia Logica appeared under the auspices of The Philosophical Committee of The Polish Academy of Sciences. Now, five decades later the present volume is dedicated to a celebration of this 50th Anniversary of Studia Logica. The volume features a series of papers by distinguished scholars reflecting both the aim and scope of this journal for symbolic logic.

Building on our diverse research traditions in the study of reasoning, language and communication, the Polish School of Argumentation integrates various disciplines and institutions across Poland in which scholars are dedicated to understanding the phenomenon of the force of argument. Our primary goal is to craft a methodological programme and establish organisational infrastructure: this is the first key step in facilitating and fostering our research movement, which joins people with a common research focus, complementary skills and an enthusiasm to work (...) together. This statement—the Manifesto—lays the foundations for the research programme of the Polish School of Argumentation. (shrink)

In this review I briefly analyse the main elements of each chapter of the book centred in the general areas of logic, epistemology, philosophy and history of science. Most of them are developed around a fine-grained investigation on the principle of non-contradiction and the concept of consistency, inquired mainly into the broad area of paraconsistent logics. The book itself is the result of a work that was initiated on the Studia Logica conference "Trends in Logic XVI: Consistency, Contradiction, Paraconsistency and (...) Reasoning - 40 years of CLE", held at the State University of Campinas, Brazil, between September 12-15, 2016. (shrink)

The paper is concerned with the problem of characterization of strengthenings of the so-called Lukasiewicz-like sentential calculi. The calculi under consideration are determined byn-valued Lukasiewicz matrices (n>2,n finite) with superdesignated logical values. In general. Lukasiewicz-like sentential calculi are not implicative in the sense of [7]. Despite of this fact, in our considerations we use matrices analogous toS-algebras of Rasiowa. The main result of the paper says that the degree of maximality of anyn-valued Lukasiewicz-like sentential calculus is finite and equal to (...) the degree of maximality of the correspondingn-valued Lukasiewicz calculus. (shrink)

The paper is concerned with the problem of characterization of strengthenings of the so-called Łukasiewicz-like sentential calculi. The calculi under consideration are determined by n-valued Łukasiewicz matrices with superdesignated logical values. In general, Łukasiewicz-like sentential calculi are not implicative in the sense of [7]. Despite of this fact, in our considerations we use matrices analogous to S-algebras of Rasiowa. The main result of the paper says that the degree of maximality of any n-valued Łukasiewicz-like sentential calculus is finite and equal (...) to the degree of maximality of the corresponding n-valued Łukasiewicz calculus. (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)

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)

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.

This study investigated the link between meditation, self-reported mindfulness and cognitive flexibility as well as other attentional functions. It compared a group of meditators experienced in mindfulness meditation with a meditation-naïve control group on measures of Stroop interference and the “d2-concentration and endurance test”. Overall the results suggest that attentional performance and cognitive flexibility are positively related to meditation practice and levels of mindfulness. Meditators performed significantly better than non-meditators on all measures of attention. Furthermore, self-reported mindfulness was higher in (...) meditators than non-meditators and correlations with all attention measures were of moderate to high strength. This pattern of results suggests that mindfulness is intimately linked to improvements of attentional functions and cognitive flexibility. The relevance of these findings for mental balance and well-being are discussed. (shrink)

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.

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.