This book presents an English translation of a classic Russian text on duality theory for Heyting algebras. Written by Georgian mathematician Leo Esakia, the text proved popular among Russian-speaking logicians. This translation helps make the ideas accessible to a wider audience and pays tribute to an influential mind in mathematical logic. The book discusses the theory of Heyting algebras and closure algebras, as well as the corresponding intuitionistic and modal logics. The author introduces the key notion of a hybrid that "crossbreeds" topology (Stone spaces) and order (Kripke frames), resulting in the structures now known as Esakia spaces. The main theorems include a duality between the categories of closure algebras and of hybrids, and a duality between the categories of Heyting algebras and of so-called strict hybrids. Esakia's book was originally published in 1985. It was the first of a planned two-volume monograph on Heyting algebras. But after the collapse of the Soviet Union, the publishing house closed and the project died with it. Fortunately, this important work now lives on in this accessible translation. The Appendix of the book discusses the planned contents of the lost second volume.

This wide-ranging book introduces information as a key concept not only in physics, from quantum mechanics to thermodynamics, but also in the neighboring sciences and in the humanities. The central part analyzes dynamical processes as manifestations of information flows between microscopic and macroscopic scales and between systems and their environment. Quantum mechanics is interpreted as a reconstruction of mechanics based on fundamental limitations of information processing on the smallest scales. These become particularly manifest in quantum chaos and in quantum computing. Covering subjects such as causality, prediction, undecidability, chaos, and quantum randomness, the book also provides an information-theoretical view of predictability. More than 180 illustrations visualize the concepts and arguments. The book takes inspiration from the author's graduate-level topical lecture but is also well suited for undergraduate studies and is a valuable resource for researchers and professionals.

1. 1. The Principle of Universalizability-an informal explication This work is concerned with the so-called Principle of Universalizability. As we shall understand it, this principle represents a claim that moral properties of things (persons, actions, state of affairs, situations) are essentially independent of their purely 'individual' or-as one often says -'numerical' aspects. l Thus, if a thing, x, is better than another thing, y, then this fact is not dependent on x's being x nor on y's being y. If a certain person, a, has a duty to help another person, b, then this duty does not arise as a consequence of their being a and b, respectively. And if in a certain situation, W, it ought to be the case that certain goods are transferred from one person to another, then this moral obligation does not depend on the individual identities of the persons involved. The Universalizability Principle may also be expressed in terms of similarities. Instead of saying that the moral properties of x are essentially independent of the individual aspects of x, we may say that any object which is exactly similar to x, which is precisely like x in all non-individual, 'qualitative' respects, must exhibit exactly similar moral properties. Thus, if two persons are exactly similar to each other, (if they are placed in exactly similar circumstances, have exactly similar information, preferences, character, etc. ), then they will have exactly similar rights and duties.

Stig Kanger (1924-1988) made important contributions to logic and formal philosophy. Kanger's most original achievements were in the areas of general proof theory, the semantics of modal and deontic logic, and the logical analysis of the concept of rights. But he contributed significantly to action theory, preference logic and the theory of measurement as well. This is the second of two volumes dedicated to the work of Stig Kanger. The first volume is a complete collection of Kanger's philosophical papers. The present volume contains critical essays on the various aspects of Kanger's work as well as some biographical sketches. Lennart A...qvist, Jan Berg, Brian Chellas, Anatoli Degtyarev, Lars Gustafsson, SAren HalldA(c)n, Kaj BA, rge Hansen, Sven Ove Hansson, Risto Hilpinen, Jaakko Hintikka, Ghita HolmstrAm-Hintikka, Lars Lindahl, Sten LindstrAm, Ingmar PArn, Dag Prawitz, Wlodek Rabinowicz, Krister Segerberg, Amartya Sen, SAren Stenlund, GAran Sundholm, and Andrei Voronkov have contributed to this volume.

Stanislaw Lesniewski (1886-1939) was one of the leading Polish logicians and founders of the Warsaw School of Logic whose membership included, beside himself, Jan Lukasiewicz, Tadeusz Kotarbinski, Alfred Tarski, and many others. In his lifetime LeSniewski published only a few hundred pages. He produced many important results in many areas of mathematics; these stood in various relations to each other, and to materials produced by others, and, in time, created more and more editorial problems. Very many were left unpublished at the time of his death. Then in 1944 in the fire of Warsaw the whole of this material was burned and lost -a considerable loss since a great deal of what is important could have been reconstructed from these notes. The present publication aims at presenting unique Lesniewski's materials from alternative sources comprising lecture notes taken during some of Lesniewski's lectures and seminars delivered at the University of Warsaw be tween the two world wars. The editors are aware of the limitations of student notes which cannot compensate for the loss of the original materials. However, they are unique in reflecting Lesniewski's ideas as he himself presented them. Already at the time of his death it was realized that these notes would provide a unique access to Lesniewski's own thought as well as a valuable record of some of the activities of the Warsaw School of Logic."

This book focuses on the problem of responsibility voids: these are cases where responsibility for a morally undesirable outcome cannot be attributed to any of the involved agents. Responsibility voids are thought to occur in collective decision-making and in the context of artificial intelligent systems. In these cases, philosophers worry that there is a shortfall of moral responsibility. In particular, such voids are often assumed to justify a notion of collective responsibility that cannot be reduced to individual responsibility. One of the aims of the book is to study how collective responsibility and joint action relate to individual responsibility and individual actions. The book offers a unifying framework for modelling moral responsibility by drawing from modal logic and game theory. The book investigates the possibility and scope of the problem of responsibility voids. One of its characteristics is its pluralistic perspective on moral responsibility: in contrast to giving a unique and all-encompassing definition of it, the book makes progress by spelling out and modelling several conceptions of moral responsibility. One of the appealing features of the book is that a relatively small range of models is used to investigate a variety of conceptions of moral responsibility. The unifying framework can thus be used to characterize the conditions under which responsibility voids are ruled out.

Jaakko Hintikka is one of the most creative figures in contemporary philosophy. He has made significant contributions to virtually all areas of the discipline, from epistemology and the philosophy of logic to the history of philosophy and the philosophy of science. Part of the fruitfulness of Hintikka 's work is due to its opening important new lines of investigation and new approaches to traditional philosophical problems. This volume gathers together essays from some of Hintikka 's colleagues and former students exploring his influence on their work and pursuing some of the insights that we have found in his work. This book includes a comprehensive overview of Hintikka 's philosophy by Dan Kolak and John Symons and an annotated bibliography of Hintikka 's work.

This volume collects selected papers presented at the Second Chinese Conference on Logic and Argumentation in 2018 held in Hangzhou, China. The papers presented reflect recent advances in logic and argumentation, as well as the connections between the two, and also include invited papers contributed by leading experts in these fields. The book covers a wide variety of topics related to dynamics, uncertainty and reasoning. It continues discussions on the interplay between logic and argumentation which has a long history from Aristotle's ancient logic to very recent formal argumentation in AI.

This book is dedicated to V.A. Yankov's seminal contributions to the theory of propositional logics. His papers, published in the 1960s, are highly cited even today. The Yankov characteristic formulas have become a very useful tool in propositional, modal and algebraic logic. The papers contributed to this book provide the new results on different generalizations and applications of characteristic formulas in propositional, modal and algebraic logics. In particular, an exposition of Yankov's results and their applications in algebraic logic, the theory of admissible rules and refutation systems is included in the book. In addition, the reader can find the studies on splitting and join-splitting in intermediate propositional logics that are based on Yankov-type formulas which are closely related to canonical formulas, and the study of properties of predicate extensions of non-classical propositional logics. The book also contains an exposition of Yankov's revolutionary approach to constructive proof theory. The editors also include Yankov's contributions to history and philosophy of mathematics and foundations of mathematics, as well as an examination of his original interpretation of history of Greek philosophy and mathematics.

The book presents a thoroughly elaborated logical theory of generalized truth-values understood as subsets of some established set of (basic) truth values. After elucidating the importance of the very notion of a truth value in logic and philosophy, we examine some possible ways of generalizing this notion. The useful four-valued logic of first-degree entailment by Nuel Belnap and the notion of a bilattice (a lattice of truth values with two ordering relations) constitute the basis for further generalizations. By doing so we elaborate the idea of a multilattice, and most notably, a trilattice of truth values - a specific algebraic structure with information ordering and two distinct logical orderings, one for truth and another for falsity. Each logical order not only induces its own logical vocabulary, but determines also its own entailment relation. We consider both semantic and syntactic ways of formalizing these relations and construct various logical calculi.

Today's instantaneous and ever-present news stream frequently presents a sensationalized or otherwise distorted view of the world, demanding constant critical engagement on the part of everyday citizens. The Critical Thinker's Guide to Bias, Lies, and Politics in the News reveals the power of critical thinking to make sense of overwhelming and often subjective media by detecting ideology, slant, and spin at work. Building off the Richard Paul and Linda Elder framework for critical thinking, Elder focuses on the internal logic of the news as well as societal influences on the media while illustrating essential elements of trustworthy journalism. With up-to-date discussions of social media, digital journalism, and political maneuvering inside and outside the fourth estate, Fact or Fake is an essential handbook for those who want to stay informed but not influenced by our modern news reporting systems.

This book repairs and revives the Theory of Knowledge research program of Russell's Principia era. Chapter 1, 'Introduction and Overview', explains the program's agenda. Inspired by the non-Fregean logicism of Principia Mathematica, it endorses the revolution within mathematics presenting it as a study of relations. The synthetic a priori logic of Principia is the essence of philosophy considered as a science which exposes the dogmatisms about abstract particulars and metaphysical necessities that create prisons that fetter the mind. Incipient in The Problems of Philosophy, the program's acquaintance epistemology embraced a multiple-relation theory of belief. It reached an impasse in 1913, having been itself retrofitted with abstract particular logical forms to address problems of direction and compositionality. With its acquaintance epistemology in limbo, Scientific Method in Philosophy became the sequel to Problems. Chapter 2 explains Russell's feeling intellectually dishonest. Wittgenstein's demand that logic exclude nonsense belief played no role. The 1919 neutral monist era ensued, but Russell found no epistemology for the logic essential to philosophy. Repairing, Chapters 4-6 solve the impasse. Reviving, Chapters 3 and 7 vigorously defend the facts about Principia. Studies of modality and entailment are viable while Principia remains a universal logic above the civil wars of the metaphysicians.

cians concerned with using logical tools in philosophy have been keenly aware of the limitations that arise from the original con centration of symbolic logic on the idiom of mathematics, and many of them have worked to create extensions of the received logical theories that would make them more generally applicable in philosophy. Carnap's Testability and Meaning, published in 1936 and 1937, was a good early example of this sort of research, motivated by the inadequacy of first-order formalizations of dis 'This sugar cube is soluble in water'. positional sentences like And in fact there is a continuous history of work on this topic, extending from Carnap's paper to Shoham's contribution to the present volume . . Much of the work in philosophical logic, and much of what has appeared in The Journal of Philosophical Logic, was mo tivated by similar considerations: work in modal logic (includ ing tense, deontic, and epistemic logic), intensional logics, non declaratives, presuppositions, and many other topics. In this sort of research, sin.ce the main point is to devise new formalisms, the technical development tends to be rather shallow in comparison with mathematical logic, though it is sel dom absent: theorems need to be proved in order to justify the formalisms, and sometimes these are nontrivial. On the other hand, much effort has to go into motivating a logical innovation."

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.

Possibility offers a new analysis of the metaphysical concepts of possibility and necessity, one that does not rely on any sort of 'possible worlds'. The analysis proceeds from an account of the notion of a physical object and from the positing of properties and relations. It is motivated by considerations about how we actually speak of and think of objects. Michael Jubien discusses several closely related topics, including different purported varieties of possible worlds, the doctrine of 'essentialism', natural kind terms, and alleged examples of necessity a posteriori. The book also offers a new theory of the functioning of proper names, both actual and fictional, and the discussion of natural kind terms and necessity a posteriori depends in part on this theory.

The book contains a collection of chapters written by experts from the fields of philosophy, law, logic, computer science and artificial intelligence who pay tribute to Professor Risto Hilpinen's impressive work on the logic of induction, on deontic logic and epistemology, and on philosophy of science. In addition to an introduction by the editors, a section on Professor Hilpinen's positions, professional services and honors, as well as a complete bibliography of his writings, the editors, McNamara, Jones and Brown, have compiled a multidisciplinary global cross-section of academic contemporaries that provides insights and perspectives on Hilpinen's influence and legacy. The essays reflect central aspects of Risto Hilpinen's research interests, and offer further contributions to some of the philosophical fields for which he is best known: applied modal logic, including deontic logic (from the ancient Greek deon, pertaining to the concepts of duty and obligation), the semantics of normative language, the logic of action, and the theory of practical reasoning; the analysis of the concept of artifact; and the theory of semiotics in the tradition of Charles Peirce. The presence in the collection of several papers relating to deontic logic underlines Hilpinen's importance in that area, in which his publications have long been recognized as standard works. The book is an essential collection of ideas for all those who feel at home in a variety of formal disciplines, from propositional logic to the logic of artificial intelligence.

This book offers the first-ever English translation of Oskar Becker's Zur Logik der Modalitaten. This essay, published in 1930, is a pioneering yet often neglected contribution in the context of prewar modal logic research in Europe. Becker's text is complemented by an extended commentary that explains, analyzes and highlights Becker's accomplishments and the philosophical background of his investigations. The commentary provides an in-depth analysis of all of Becker's important contributions, both from a philosophical and logical perspective, making it a very useful book for scholars in both philosophy and logic.

This book argues that the primary function of human thinking in language is to make judgments, which are logical-normative connections of concepts. Robert Abele points out that this presupposes cognitive conditions that cannot be accounted for by empirical-linguistic analyses of language content or social conditions alone. Judgments rather assume both reason and a unified subject, and this requires recognition of a Kantian-type of transcendental dimension to them. Judgments are related to perception in that both are syntheses, defined as the unity of representations according to a rule/form. Perceptual syntheses are simultaneously pre-linguistic and proto-rational, and the understanding (Kant's Verstand) makes these syntheses conceptually and thus self-consciously explicit. Abele concludes with a transcendental critique of postmodernism and what its deflationary view of ontological categories-such as the unified and reasoning subject-has done to political thinking. He presents an alternative that calls for a return to normativity and a recognition of reason, objectivity, and the universality of principles.

In the great libraries of Europe and the United States, hidden in fading manuscripts on forgotten shelves, lie the works of medieval Hebrew logic. From the end of the twelfth century through the Renaissance, Jews wrote and translated commentaries and original compositions in Aristotelian logic. One can say without exaggeration that wherever Jews studied philosophy - Spain, France, Northern Africa, Germany, Palestine - they began their studies with logic. Yet with few exceptions, the manuscripts that were catalogued in the last century have failed to arouse the interest of modem scholars. While the history of logic is now an established sub-discipline of the history of philosophy, the history of Hebrew logic is only in its infancy. The present work contains a translation and commentary of what is arguably the greatest work of Hebrew logic, the Sefer ha-Heqqesh ha-Yashar (The Book of the Correct Syllogism) of Levi ben Gershom (Gersonides; 1288-1344). Gersonides is well known today as a philosopher, astronomer, mathematician, and biblical exegete. But in the Middle Ages he was also famous for his prowess as a logician. The Correct Syllogism is his attempt to construct a theory of the syllogism that is free of what he considers to be the 'mistakes' of Aristotle, as interpreted by the Moslem commentator A verroes. It is an absorbing, challenging work, first written by Gersonides when he was merely thirty-one years old, then significantly revised by him. The translation presented here is of the revised version.

This book is a collection of contributions honouring Arnon Avron's seminal work on the semantics and proof theory of non-classical logics. It includes presentations of advanced work by some of the most esteemed scholars working on semantic and proof-theoretical aspects of computer science logic. Topics in this book include frameworks for paraconsistent reasoning, foundations of relevance logics, analysis and characterizations of modal logics and fuzzy logics, hypersequent calculi and their properties, non-deterministic semantics, algebraic structures for many-valued logics, and representations of the mechanization of mathematics. Avron's foundational and pioneering contributions have been widely acknowledged and adopted by the scientific community. His research interests are very broad, spanning over proof theory, automated reasoning, non-classical logics, foundations of mathematics, and applications of logic in computer science and artificial intelligence. This is clearly reflected by the diversity of topics discussed in the chapters included in this book, all of which directly relate to Avron's past and present works. This book is of interest to computer scientists and scholars of formal logic.

ADVANGEBOOKS - UNDERSTANDING ARGUMENTS: AN INTRODUCTION TO INFORMAL LOGIC, 9E shows readers how to construct arguments in everyday life, using everyday language. In addition, this easy-to-read textbook also devotes three chapters to the formal aspects of logic including forms of argument, as well as propositional, categorical, and quantificational logic. Plus, this edition helps readers apply informal logic to legal, moral, scientific, religious, and philosophical scenarios, too.

This book is a consideration of Hegel's view on logic and basic logical concepts such as truth, form, validity, and contradiction, and aims to assess this view's relevance for contemporary philosophical logic. The literature on Hegel's logic is fairly rich. The attention to contemporary philosophical logic places the present research closer to those works interested in the link between Hegel's thought and analytical philosophy (Stekeler-Weithofer 1992 and 2019, Berto 2005, Rockmore 2005, Redding 2007, Nuzzo 2010 (ed.), Koch 2014, Brandom 2014, 1-15, Pippin 2016, Moyar 2017, Quante & Mooren 2018 among others). In this context, one particularity of this book consists in focusing on something that has been generally underrated in the literature: the idea that, for Hegel as well as for Aristotle and many other authors (including Frege), logic is the study of the forms of truth, i.e. the forms that our thought can (or ought to) assume in searching for truth. In this light, Hegel's thinking about logic is a fundamental reference point for anyone interested in a philosophical foundation of logic.

This volume presents the state of the art in the algebraic investigation into substructural logics. It features papers from the workshop AsubL (Algebra & Substructural Logics - Take 6). Held at the University of Cagliari, Italy, this event is part of the framework of the Horizon 2020 Project SYSMICS: SYntax meets Semantics: Methods, Interactions, and Connections in Substructural logics. Substructural logics are usually formulated as Gentzen systems that lack one or more structural rules. They have been intensively studied over the past two decades by logicians of various persuasions. These researchers include mathematicians, philosophers, linguists, and computer scientists. Substructural logics are applicable to the mathematical investigation of such processes as resource-conscious reasoning, approximate reasoning, type-theoretical grammar, and other focal notions in computer science. They also apply to epistemology, economics, and linguistics. The recourse to algebraic methods -- or, better, the fecund interplay of algebra and proof theory -- has proved useful in providing a unifying framework for these investigations. The AsubL series of conferences, in particular, has played an important role in these developments. This collection will appeal to students and researchers with an interest in substructural logics, abstract algebraic logic, residuated lattices, proof theory, universal algebra, and logical semantics.