Labelled deduction is an approach to providing frameworks for presenting and using different logics in a uniform and natural way by enriching the language of a logic with additional information of a semantic proof-theoretical nature. Labelled deduction systems often possess attractive properties, such as modularity in the way that families of related logics are presented, parameterised proofs of metatheoretic properties, and ease of mechanisability. It is thus not surprising that labelled deduction has been applied to problems in computer science, AI, mathematical logic, cognitive science, philosophy and computational linguistics - for example, formalizing and reasoning about dynamic state oriented' properties such as knowledge, belief, time, space, and resources.

Hilbert's Program was founded on a concern for the phenomenon of paradox in mathematics. To Hilbert, the paradoxes, which are at once both absurd and irresistible, revealed a deep philosophical truth: namely, that there is a discrepancy between the laws accord ing to which the mind of homo mathematicus works, and the laws governing objective mathematical fact. Mathematical epistemology is, therefore, to be seen as a struggle between a mind that naturally works in one way and a reality that works in another. Knowledge occurs when the two cooperate. Conceived in this way, there are two basic alternatives for mathematical epistemology: a skeptical position which maintains either that mind and reality seldom or never come to agreement, or that we have no very reliable way of telling when they do; and a non-skeptical position which holds that there is significant agree ment between mind and reality, and that their potential discrepan cies can be detected, avoided, and thus kept in check. Of these two, Hilbert clearly embraced the latter, and proposed a program designed to vindicate the epistemological riches represented by our natural, if non-literal, ways of thinking. Brouwer, on the other hand, opted for a position closer (in Hilbert's opinion) to that of the skeptic. Having decided that epistemological purity could come only through sacrifice, he turned his back on his classical heritage to accept a higher calling."

It is with great pleasure that we are presenting to the community the second edition of this extraordinary handbook. It has been over 15 years since the publication of the first edition and there have been great changes in the landscape of philosophical logic since then. The first edition has proved invaluable to generations of students and researchers in formal philosophy and language, as well as to consumers of logic in many applied areas. The main logic article in the Encyclopaedia Britannica 1999 has described the first edition as 'the best starting point for exploring any of the topics in logic'. We are confident that the second edition will prove to be just as good, The first edition was the second handbook published for the logic commu nity. It followed the North Holland one volume Handbook of Mathematical Logic, published in 1977, edited by the late Jon Barwise. The four volume Handbook of Philosophical Logic, published 1983-1989 came at a fortunate temporal junction at the evolution of logic. This was the time when logic was gaining ground in computer science and artificial intelligence circles. These areas were under increasing commercial pressure to provide devices which help and/or replace the human in his daily activity. This pressure required the use of logic in the modelling of human activity and organisa tion on the one hand and to provide the theoretical basis for the computer program constructs on the other."

This book presents a systematic treatment of deductive aspects and structures of fuzzy logic understood as many valued logic sui generis. It aims to show that fuzzy logic as a logic of imprecise (vague) propositions does have well-developed formal foundations and that most things usually named 'fuzzy inference' can be naturally understood as logical deduction. It is for mathematicians, logicians, computer scientists, specialists in artificial intelligence and knowledge engineering, and developers of fuzzy logic.

This book creates a conceptual schema that acts as a correlation between Epistemology and Epistemic Logic. It connects both fields and offers a proper theoretical foundation for the contemporary developments of Epistemic Logic regarding the dynamics of information. It builds a bridge between the view of Awareness Justification Internalism, and a dynamic approach to Awareness Logic. The book starts with an introduction to the main topics in Epistemic Logic and Epistemology and reviews the disconnection between the two fields. It analyses three core notions representing the basic structure of the conceptual schema: "Epistemic Awareness", "Knowledge" and "Justification". Next, it presents the Explicit Aware Knowledge (EAK) Schema, using a diagram of three ellipses to illustrate the schema, and a formal model based on a neighbourhood-model structure, that shows one concrete application of the EAK-Schema into a logical structure. The book ends by presenting conclusions and final remarks about the uses and applications of the EAK-Schema. It shows that the most important feature of the schema is that it serves both as a theoretical correlate to the dynamic extensions of Awareness Logic, providing it with a philosophical background, and as an abstract conceptual structure for a re-interpretation of Epistemology.

The relation between logic and knowledge provoked a heated debate since the 1960s. The epistemic approaches, found their formal argument in the mathematics of Brouwer and intuitionistic logic. And following Michael Dummett - started to call themselves: antirealists'. Others persisted with the formal background of the Frege-Tarski tradition, where Cantorian set theory is linked via model theory to classical logic. Jaakko Hintikka tried to join both traditions by means of what is now known as explicit epistemic logic'. Here the epistemic content is introduced into the object language as an operator which yield propositions from propositions rather than as metalogical constraint on the notion of inference. The Realism-Antirealism debate had thus three players: classical logicians, intuitionists and explicit epistemic logicians. The editors of the present volume think that in these days and age of Alternative Logics, where manifold developments in logic happen in a breathtaking pace, this debate should be revisited. Using the most recent logical and epistemological tools, this book provides a novel and refreshing view on the most important topics of the Realism vs. Antirealism debate. Its general scope is to show the most recent developments in philosophical logic to deal with problems inherited from this debate. It is meant for researcher and advanced students in philosophy, logic, formal methods. It's complete collection with a variety of approaches, it is written by leading authors in the fields, every chapter is self-contained.

The main purpose of this work is to provide an English translation of and commentary on a recently published Arabic text dealing with con ditional propositions and syllogisms. The text is that of A vicenna (Abu represents his views on the subject as they were held throughout his life.

First published in 2005. Routledge is an imprint of Taylor & Francis, an informa company.

This book presents an in-depth and critical reconstruction of Prawitz's epistemic grounding, and discusses it within the broader field of proof-theoretic semantics. The theory of grounds is also provided with a formal framework, through which several relevant results are proved. Investigating Prawitz's theory of grounds, this work answers one of the most fundamental questions in logic: why and how do some inferences have the epistemic power to compel us to accept their conclusion, if we have accepted their premises? Prawitz proposes an innovative description of inferential acts, as applications of constructive operations on grounds for the premises, yielding a ground for the conclusion. The book is divided into three parts. In the first, the author discusses the reasons that have led Prawitz to abandon his previous semantics of valid arguments and proofs. The second part presents Prawitz's grounding as found in his ground-theoretic papers. Finally, in the third part, a formal apparatus is developed, consisting of a class of languages whose terms are equipped with denotation functions associating them to operations and grounds, as well as of a class of systems where important properties of the terms can be proved.

This volume contains a selection of papers presented at a Seminar on Intensional Logic held at the University of Amsterdam during the period September 1990-May 1991. Modal logic, either as a topic or as a tool, is common to most of the papers in this volume. A number of the papers are con cerned with what may be called well-known or traditional modal systems, but, as a quick glance through this volume will reveal, this by no means implies that they walk the beaten tracks. In deed, such contributions display new directions, new results, and new techniques to obtain familiar results. Other papers in this volume are representative examples of a current trend in modal logic: the study of extensions or adaptations of the standard sys tems that have been introduced to overcome various shortcomings of the latter, especially their limited expressive power. Finally, there is another major theme that can be discerned in the vol ume, a theme that may be described by the slogan 'representing changing information. ' Papers falling under this heading address long-standing issues in the area, or present a systematic approach, while a critical survey and a report contributing new techniques are also included. The bulk of the papers on pure modal logic deal with theoreti calor even foundational aspects of modal systems."

This study looks to the work of Tarski's mentors Stanislaw Lesniewski and Tadeusz Kotarbinski, and reconsiders all of the major issues in Tarski scholarship in light of the conception of Intuitionistic Formalism developed: semantics, truth, paradox, logical consequence.

This book is intended to serve as an advanced text and reference work on modal logic, a subject of growing importance which has applications to philosophy and linguistics. Although it is based mainly on research which I carried out during the years 1969-1973, it also includes some related results obtained by other workers in the field (see the refer ences in Part 7). Parts 0, 1 and 2, can be used as the basis of a one year graduate course in modal logic. The material which they contain has been taught in such courses at Stanford since 1970. The remaining parts of the book contain more than enough material for a second course in modal logic. The exercises supplement the text and are usually difficult. I wish to thank Stanford University and Bar-Han University for making it possible for me to continue and finish this work, and A. Ungar for correcting the typescript. Bar-Ilan University, Israel Dov M. GABBA Y PART 0 AN INTRODUCTION TO GENERAL INTENSIONAL LOGICS CHAPTER 0 CONSEQUENCE RELATIONS Motivation We introduce the notions of a consequence relation (which is a generalization of the notion of a logical system) and of a semantics. We show that every consequence relation is complete for a canonical semantics. We define the notion of one semantics being Dian in another and study the basic properties of this notion. The concepts of this chapter are generalizations of the various notions of logical system and possible world semantics found in the literature."

During the last decade, argumentation has attracted growing attention as a means to elicit processes (linguistic, logical, dialogical, psychological, etc.) that can sustain or provoke reasoning and learning. Constituting an important dimension of daily life and of professional activities, argumentation plays a special role in democracies and is at the heart of philosophical reasoning and scientific inquiry. Argumentation, as such, requires specific intellectual and social skills. Hence, argumentation will have an increasing importance in education, both because it is a critical competence that has to be learned, and because argumentation can be used to foster learning in philosophy, history, sciences and in many other domains.

Argumentation and Education answers these and other questions by providing both theoretical backgrounds, in psychology, education and theory of argumentation, and concrete examples of experiments and results in school contexts in a range of domains. It reports on existing innovative practices in education settings at various levels.

Bringing together scholars from a broad range of theoretical perspectives, The Language of Argumentation offers a unique overview of research at the crossroads of linguistics and theories of argumentation. In addition to theoretical and methodological reflections by leading scholars in their fields, the book contains studies of the relationship between language and argumentation from two different viewpoints. While some chapters take a specific argumentative move as their point of departure and investigate the ways in which it is linguistically manifested in discourse, other chapters start off from a linguistic construction, trying to determine its argumentative function and rhetorical potential. The Language of Argumentation documents the currently prominent research on stylistic aspects of argumentation and illustrates how the study of argumentation benefits from insights from linguistic models, ranging from theoretical pragmatics, politeness theory and metaphor studies to models of discourse coherence and construction grammar.

Reasoning is an integral part of intelligent systems in fields like databases, logic programming, robotics, knowledge engineering, human/computer interfaces, programming environments, etc. In reality any such system has to cope with a changing world and its dynamics. Hence it is of great importance that reasoning must account for coping with change in order to be truly useful in practice. The book comprises several contributions to current ways of approaching this problem. On the one hand it surveys and synthesizes recent research work, while on the other hand new research results are included. Among the topics treated are logics for reasoning about actions and planning, belief revision and the reconciliation of logically conflicting inputs, resolving of conflicts by merging of knowledge and issues in the evolution in object-oriented databases. The book is aimed at the researcher and advanced student active in this field.

Constructibility and complexity play central roles in recent research in computer science, mathematics and physics. For example, scientists are investigating the complexity of computer programs, constructive proofs in mathematics and the randomness of physical processes. But there are different approaches to the explication of these concepts. This volume presents important research on the state of this discussion, especially as it refers to quantum mechanics. This foundational debate' in computer science, mathematics and physics was already fully developed in 1930 in the Vienna Circle. A special section is devoted to its real founder Hans Hahn, referring to his contribution to the history and philosophy of science. The documentation section presents articles on the early Philipp Frank and on the Vienna Circle in exile. Reviews cover important recent literature on logical empiricism and related topics.

This book seeks to arrive at a better understanding of the relationships between the objective and subjective aspects of time. It discusses the existence of fluent time, a controversial concept in many areas, from philosophy to physics. Fluent time is understood as directional time with a past, a present and a future. We experience fluent time in our lives and we adopt a temporal perspective in our ways of knowing and acting. Nevertheless, the existence of fluent time has been debated for both philosophical and scientific reasons, thus creating a rift between the subjective and objective aspects of time. Starting from the basic notion of points of view, or perspectives, this book explores the relationships between objective or external time, as it has been conceptualized by science, and subjective or internal time, which is involved in our lived experiences. It establishes a general framework encompassing the nature, structure and mode of existence of points of view, in which the objective and subjective aspects of time can be integrated. The book mainly addresses researchers and postgraduates in philosophy and logic. Additionally, it offers inspiration for physicists and computer scientists involved in the modeling and simulation of complex behaviors for which the representation of internal time should be considered together with the notion of objective, external time.

This introduction to modality places the emphasis on the metaphysics of modality rather than on the formal semetics of quantified modal logic. The text begins by introducing students to the "de re/de dicto" distinction, conventionalist and conceptualist theories of modality and some of the key problems in modality, particularly Quine's criticisms. It then moves on to explain how possible worlds provide a solution to many of the problems in modality and how possible worlds themselves have been used to analyse notions outside modality such as properties and propositions. Possible worlds introduce problems of their own and the book argues that to make progress with these problems a theory of possible worlds is required. The pros and cons of various theories of possible worlds are then examined in turn, including those of Lewis, Kripke, Adams, Stalnaker and Plantinga.

This introduction to modality places the emphasis on the metaphysics of modality rather than on the formal semetics of quantified modal logic. The text begins by introducing students to the "de re/de dicto" distinction, conventionalist and conceptualist theories of modality and some of the key problems in modality, particularly Quine's criticisms. It then moves on to explain how possible worlds provide a solution to many of the problems in modality and how possible worlds themselves have been used to analyse notions outside modality such as properties and propositions. Possible worlds introduce problems of their own and the book argues that to make progress with these problems a theory of possible worlds is required. The pros and cons of various theories of possible worlds are then examined in turn, including those of Lewis, Kripke, Adams, Stalnaker and Plantinga.

Paradoxes are more than just intellectual puzzles - they raise substantive philosophical issues and offer the promise of increased philosophical knowledge. In this introduction to paradox and paradoxes, Doris Olin shows how seductive paradoxes can be, why they confuse and confound, and why they continue to fascinate. Olin examines the nature of paradox, outlining a rigorous definition and providing a clear and incisive statement of what does and does not count as a resolution of a paradox. The view that a statement can be both true and false, that contradictions can be true, is seen to provide a challenge to the account of paradox resolution, and is explored. With this framework in place, the book then turns to an in-depth treatment of the Prediction Paradox, versions of the Preface/Fallibility Paradox, the Lottery Paradox, Newcomb's Problem, the Prisoner's Dilemma and the Sorites Paradox. Each of these paradoxes is shown to have considerable philosophical punch. Olin unpacks the central arguments in a clear and systematic fashion, offers original analyses and solutions, and exposes further unsettling implications for some of our most deep-seated principles and convictions.

Paradoxes are more than just intellectual puzzles - they raise substantive philosophical issues and offer the promise of increased philosophical knowledge. In this introduction to paradox and paradoxes, Doris Olin shows how seductive paradoxes can be, why they confuse and confound, and why they continue to fascinate. Olin examines the nature of paradox, outlining a rigorous definition and providing a clear and incisive statement of what does and does not count as a resolution of a paradox. The view that a statement can be both true and false, that contradictions can be true, is seen to provide a challenge to the account of paradox resolution, and is explored. With this framework in place, the book then turns to an in-depth treatment of the Prediction Paradox, versions of the Preface/Fallibility Paradox, the Lottery Paradox, Newcomb's Problem, the Prisoner's Dilemma and the Sorites Paradox. Each of these paradoxes is shown to have considerable philosophical punch. Olin unpacks the central arguments in a clear and systematic fashion, offers original analyses and solutions, and exposes further unsettling implications for some of our most deep-seated principles and convictions.

Using both Father Kevin Wall's eidetic matrix of "the relational unity of being" and Edith Stein's remarkable synoptic view of intentionality in both Aquinas and Husserl, this book uncovers purely logical ground for a subalternate eidetic science called "convergent phenomenology," itself located at the inmost depths of Husserlian phenomenology. Convergent phenomenology emerges as a distinctively new discipline dealing with relation-like objectivity as opposed to the thing-like objectivity of traditional phenomenology. This has grand implications for the way we as humans conceive of God and being. The book thus benefits theologians, logicians, and phenomenologists by revealing the constitutive interrelationality of transcendental logic in an utterly new light as already flowering forth into formal ontology itself. What emerges is a rich conception of divinity and humanity.

This book is a study in the logic of questions (sometimes called erotetic logic). The central topics in erotetic logic have been the structure of questions and the question-answer relationship. This book doesn't neglect these problems, but much of it is focussed on other issues. The main subject is the logical analysis of certain relations between questions and the contexts of their appearance. And our aim is to elaborate the conceptual apparatus of the inferential approach to the logic of questions. Questions are asked for many reasons and for different purposes. Yet, before a question is asked or posed, a questioner must arrive at it. In many cases arriving at a question resembles coming to a conclusion: there are some premises involved and some inferential thought processes take place. If we agree that a conclusion need not be "conclusive," we may say that sometimes questions can play the role of conclusions. But questions can also perform the role of premises: we often pass from some "initial" question to another question. In other words, there are inferential thought processes - we shall call them erotetic inferences - in which questions play the roles of conclusions or conclusions and premises. The inferential approach to the logic of questions focusses its attention on the analysis of erotetic inferences. This book consists of eight chapters.