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 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)

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).

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)

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)

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.

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.

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.

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)

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.

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)

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)

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)

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.