A selection of papers presented at the international conference Applied Logic: Logic at Work', held in Amsterdam in December 1992. Nowadays, the term applied logic' has a very wide meaning, as numerous applications of logical methods in computer science, formal linguistics and other fields testify. Such applications are by no means restricted to the use of known logical techniques: at its best, applied logic involves a back-and-forth dialogue between logical theory and the problem domain. The papers focus on the application of logic to the study of natural language, in syntax, semantics and pragmatics, and the effect of these studies on the development of logic. In the last decade, the dynamic nature of natural language has been the most interesting challenge for logicians. Dynamic semantics is here applied to new topics, the dynamic approach is extended to syntax, and several methodological issues in dynamic semantics are systematically investigated. Other methodological issues in the formal studies of natural language are discussed, such as the need for types, modal operators and other logical operators in the formal framework. Further articles address the scope of these methodological issues from other perspectives ranging from cognition to computation. The volume presents papers that are interesting for graduate students and researchers in the field of logic, philosophy of language, formal semantics and pragmatics, and computational linguistics.

This three volume collection gathers together responses to Weber's sociology in the period 1920-1945. Bryan Turner provides an extensive analysis of the reception of Weber.

Husserl's "Logical Investigations" is designed to help students and specialists work their way through Husserl's expansive text by bringing together in a single volume six self-contained, expository yet critical essays, each the work of an international expert on Husserl's thought and each devoted to a separate Logical Investigation.

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 weIl as to consumers of logic in many applied areas. The main logic artiele in the Encyelopaedia 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 0/ Mathematical Logic, published in 1977, edited by the late Jon Barwise. The four volume Handbook 0/ Philosophical Logic, published 1983-1989 came at a fortunate at the evolution of logic. This was the time when logic temporal junction was gaining ground in computer science and artificial intelligence cireles. These areas were under increasing commercial pressure to provide devices which help andjor 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.

Relevant to philosophy, law, management, and artificial intelligence, these papers explore the applicability of nonmonotonic or defeasible logic to normative reasoning. The resulting systems purport to solve well-known deontic paradoxes and to provide a better treatment than classical deontic logic does of prima facie obligation, conditional obligation, and priorities of normative principles.

This book defines a logical system called the Protocol-theoretic Logic of Epistemic Norms (PLEN), it develops PLEN into a formal framework for representing and reasoning about epistemic norms, and it shows that PLEN is theoretically interesting and useful with regard to the aims of such a framework. In order to motivate the project, the author defends an account of epistemic norms called epistemic proceduralism. The core of this view is the idea that, in virtue of their indispensable, regulative role in cognitive life, epistemic norms are closely intertwined with procedural rules that restrict epistemic actions, procedures, and processes. The resulting organizing principle of the book is that epistemic norms are protocols for epistemic planning and control. The core of the book is developing PLEN, which is essentially a novel variant of propositional dynamic logic (PDL) distinguished by more or less elaborate revisions of PDL's syntax and semantics. The syntax encodes the procedural content of epistemic norms by means of the well-known protocol or program constructions of dynamic and epistemic logics. It then provides a novel language of operators on protocols, including a range of unique protocol equivalence relations, syntactic operations on protocols, and various procedural relations among protocols in addition to the standard dynamic (modal) operators of PDL. The semantics of the system then interprets protocol expressions and expressions embedding protocols over a class of directed multigraph-like structures rather than the standard labeled transition systems or modal frames. The intent of the system is to better represent epistemic dynamics, build a logic of protocols atop it, and then show that the resulting logic of protocols is useful as a logical framework for epistemic norms. The resulting theory of epistemic norms centers on notions of norm equivalence derived from theories of process equivalence familiar from the study of dynamic and modal logics. The canonical account of protocol equivalence in PLEN turns out to possess a number of interesting formal features, including satisfaction of important conditions on hyperintensional equivalence, a matter of recently recognized importance in the logic of norms, generally. To show that the system is interesting and useful as a framework for representing and reasoning about epistemic norms, the author applies the logical system to the analysis of epistemic deontic operators, and, partly on the basis of this, establishes representation theorems linking protocols to the action-guiding content of epistemic norms. The protocol-theoretic logic of epistemic norms is then shown to almost immediately validate the main principles of epistemic proceduralism.

Perspectives on Time deals with the problem of time from different perspectives such as logic, physics and philosophy. It contains 18 previously unpublished papers, written by philosophers from various European countries, as well as a large introduction about the history and the main situation in the respective fields today. The prominent issues which are addressed in this book concern the direction of time, the reality of tenses, the objectivity of becoming, the existence in time, and the logical structures of reasoning about time. The papers have been written based on different approaches, partly depending on whether the authors subscribe to an A-theory or a B-theory of time. Audience: Due to the broad variety of approaches the book contains important contributions both for philosophers, philosophers of science, logicians and for scientists working in the field of language and AI.

Knocking on Heaven's Door is the oldest human dream that seems unrealized still. Religious discourse does show the road, but it requires a blind faith in return. In this book logicians try to hear Heaven's Call and to analyze religious discourse. As a result, the notion of religious logic as a part of philosophical logic is introduced. Its tasks are (1) to construct consistent logical systems formalizing religious reasoning that at first sight seems inconsistent (this research is fulfilled within the limits of modal logic, paraconsistent logic and many-valued logic), (2) to carry out an illocutionary analysis of religious discourse (this research is fulfilled in frames of illocutionary logics), and (3) to formalize Ancient and Medieval logical theories used in the theology of an appropriate religion (they could be studied within the limits of unconventional logics, such as non-monotonic logics, non-well-founded logics, etc.).

These two volumes contain all of my articles published between 1956 and 1975 which might be of interest to readers in the English-speaking world. The first three essays in Vol. 1 deal with historical themes. In each case I have attempted a rational reconstruction which, as far as possible, meets con temporary standards of exactness. In The Problem of Universals Then and Now some ideas of W.V. Quine and N. Goodman are used to create a modem sketch of the history of the debate on universals beginning with Plato and ending with Hao Wang's System: E. The second article concerns Kant's Philosophy of Science. By analyzing his position vis-a-vis I. Newton, Christian Wolff, and D. Hume, it is shown that for Kant the very notion of empirical knowledge was beset with a funda mental logical difficulty. In his metaphysics of experience Kant offered a solution differing from all prior as well as subsequent attempts aimed at the problem of establishing a scientific theory. The last of the three historical papers utilizes some concepts of modem logic to give a precise account of Wittgenstein's so-called Picture Theory of Meaning. E. Stenius' interpretation of this theory is taken as an intuitive starting point while an intensional variant of Tarski's concept of a relational system furnishes a technical instrument. The concepts of model world and of logical space, together with those of homomorphism and isomorphism be tween model worlds and between logical spaces, form the conceptual basis of the reconstruction."

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.

The tableau methodology, invented in the 1950's by Beth and Hintikka and later perfected by Smullyan and Fitting, is today one of the most popular proof theoretical methodologies. Firstly because it is a very intuitive tool, and secondly because it appears to bring together the proof-theoretical and the semantical approaches to the presentation of a logical system. The increasing demand for improved tableau methods for various logics is mainly prompted by extensive applications of logic in computer science, artificial intelligence and logic programming, as well as its use as a means of conceptual analysis in mathematics, philosophy, linguistics and in the social sciences. In the last few years the renewed interest in the method of analytic tableaux has generated a plethora of new results, in classical as well as non-classical logics. On the one hand, recent advances in tableau-based theorem proving have drawn attention to tableaux as a powerful deduction method for classical first-order logic, in particular for non-clausal formulas accommodating equality. On the other hand, there is a growing need for a diversity of non-classical logics which can serve various applications, and for algorithmic presentations of these logicas in a unifying framework which can support (or suggest) a meaningful semantic interpretation. From this point of view, the methodology of analytic tableaux seems to be most suitable. Therefore, renewed research activity is being devoted to investigating tableau systems for intuitionistic, modal, temporal and many-valued logics, as well as for new families of logics, such as non-monotonic and substructural logics. The results require systematisation. This Handbook isthe first to provide such a systematisation of this expanding field. It contains several chapters on the use of tableaux methods in classical logic, but also contains extensive discussions on: the uses of the methodology in intuitionistic logics modal and temporal logics substructural logics, nonmonotonic and many-valued logics the implementation of semantic tableaux a bibliography on analytic tableaux theorem proving. The result is a solid reference work to be used by students and researchers in Computer Science, Artificial Intelligence, Mathematics, Philosophy, Cognitive Sciences, Legal Studies, Linguistics, Engineering and all the areas, whether theoretical or applied, in which the algorithmic aspects of logical deduction play a role.

An accessible guide for those facing the study of Logic for the first time, this book covers key thinkers, terms and texts. "The Key Terms in Philosophy" series offers clear, concise and accessible introductions to the central topics in philosophy. Each book offers a comprehensive overview of the key terms, concepts, thinkers and major works in the history of a key area of philosophy. Ideal for first-year students starting out in philosophy, the series will serve as the ideal companion to study of this fascinating subject. "Key Terms in Logic" offers the ideal introduction to this core area in the study of philosophy, providing detailed summaries of the important concepts in the study of logic and the application of logic to the rest of philosophy. A brief introduction provides context and background, while the following chapters offer detailed definitions of key terms and concepts, introductions to the work of key thinkers and lists of key texts. Designed specifically to meet the needs of students and assuming no prior knowledge of the subject, this is the ideal reference tool for those coming to Logic for the first time. "The Key Terms" series offers undergraduate students clear, concise and accessible introductions to core topics. Each book includes a comprehensive overview of the key terms, concepts, thinkers and texts in the area covered and ends with a guide to further resources.

Offering a bold new vision on the history of modern logic, Lukas M. Verburgt and Matteo Cosci focus on the lasting impact of Aristotle's syllogism between the 1820s and 1930s. For over two millennia, deductive logic was the syllogism and syllogism was the yardstick of sound human reasoning. During the 19th century, this hegemony fell apart and logicians, including Boole, Frege and Peirce, took deductive logic far beyond its Aristotelian borders. However, contrary to common wisdom, reflections on syllogism were also instrumental to the creation of new logical developments, such as first-order logic and early set theory. This volume presents the period under discussion as one of both tradition and innovation, both continuity and discontinuity. Modern logic broke away from the syllogistic tradition, but without Aristotle's syllogism, modern logic would not have been born. A vital follow up to The Aftermath of Syllogism, this book traces the longue duree history of syllogism from Richard Whately's revival of formal logic in the 1820s through the work of David Hilbert and the Goettingen school up to the 1930s. Bringing together a group of major international experts, it sheds crucial new light on the emergence of modern logic and the roots of analytic philosophy in the 19th and early 20th centuries.

Aristotle's treatise De Interpretatione is one of his central works; it continues to be the focus of much attention and debate. C. W. A. Whitaker presents the first systematic study of this work, and offers a radical new view of its aims, its structure, and its place in Aristotle's system, basing this view upon a detailed chapter-by-chapter analysis. By treating the work systematically, rather than concentrating on certain selected passages, Dr Whitaker is able to show that, contrary to traditional opinion, it forms an organized and coherent whole. He argues that the De Interpretatione is intended to provide the underpinning for dialectic, the system of argument by question and answer set out in Aristotle's Topics ; and he rejects the traditional view that the De Interpretatione concerns the assertion and is oriented towards the formal logic of the Prior Analytics. In doing so, he sheds valuable new light on some of Aristotle's most famous texts.

such questions for centuries (unrestricted by the capabilities of any ha- ware). Theprinciplesgoverningtheinteractionofseveralprocesses, forexample, are abstract an similar to principles governing the cooperation of two large organisation. A detailed rule based e?ective but rigid bureaucracy is very much similar to a complex computer program handling and manipulating data. My guess is that the principles underlying one are very much the same as those underlying the other. Ibelievethedayisnotfarawayinthefuturewhenthecomputerscientist will wake up one morning with the realisation that he is actually a kind of formal philosopher! The projected number of volumes for this Handbook is about 18. The subjecthasevolvedanditsareashavebecomeinterrelatedtosuchanextent that it no longer makes sense to dedicate volumes to topics. However, the volumes do follow some natural groupingsof chapters. Iwould liketothank our authorsand readersfor their contributionsand their commitment in making this Handbook a success. Thanksalso to our publication administrator Mrs J. Spurr for her usual dedication and excellence and to Kluwer Academic Publishers (now Springer) for their continuing support for the Handbook. Dov Gabbay King's College London 10 Logic IT Natural Program Arti?cial in- Logicp- language control spec- telligence gramming processing i?cation, veri?cation, concurrency Temporal Expressive Expressive Planning. Extension of logic power of tense power for re- Time depen- Horn clause operators. current events. dent data. with time Temporal Speci?cation Eventcalculus. capability. indices. Sepa- of tempo- Persistence Event calculus. ration of past ral control. through time- Temporal logic from future Decision prob- theFrame programming. lems. Model Problem. T- checking. poral query language. temporal transactions.

Plural predication is a pervasive part of ordinary language. We can say that some people are fifty in number, are surrounding a building, come from many countries, and are classmates. These predicates can be true of some people without being true of any one of them; they are non-distributive predications. Yet the apparatus of predication and quantification in standard modern logic does not allow a place for such non-distributive predicates. Thomas McKay's book explores the enrichment of modern logic with plural predication and quantification. We can have genuinely non-distributive predication without relying on singularizing procedures from set theory and mereology. The fundamental 'among' relation can be understood in a way that does not generate any hierarchy of plurals analogous to a hierarchy of types or a hierarchy of higher-order logics. Singular quantification can be understood as a special case, with the general type being quantifiers that allow both singular and plural quantification. The 'among' relation is formally similar to a 'part of' relation, but the relations are distinct, so that mass quantification and plural quantification cannot be united in the same way that plural and singular are united. Analysis of singular and plural definite descriptions follows, with a defense of a fundamentally Russellian analysis, but coupled with some new ideas about how to be sensitive to the role of context. This facilitates an analysis of some central features of the use of pronouns, both singular and plural.

This monograph shows that, through a recourse to the concepts and methods of abstract algebraic logic, the algebraic theory of regular varieties and the concept of analyticity in formal logic can profitably interact. By extending the technique of Plonka sums from algebras to logical matrices, the authors investigate the different classes of models for logics of variable inclusion and they shed new light into their formal properties. The book opens with the historical origins of logics of variable inclusion and on their philosophical motivations. It includes the basics of the algebraic theory of regular varieties and the construction of Plonka sums over semilattice direct systems of algebra. The core of the book is devoted to an abstract definition of logics of left and right variable inclusion, respectively, and the authors study their semantics using the construction of Plonka sums of matrix models. The authors also cover Paraconsistent Weak Kleene logic and survey its abstract algebraic logical properties. This book is of interest to scholars of formal logic.

Logic has attained in our century a development incomparably greater than in any past age of its long history, and this has led to such an enrichment and proliferation of its aspects, that the problem of some kind of unified recom prehension of this discipline seems nowadays unavoidable. This splitting into several subdomains is the natural consequence of the fact that Logic has intended to adopt in our century the status of a science. This always implies that the general optics, under which a certain set of problems used to be con sidered, breaks into a lot of specialized sectors of inquiry, each of them being characterized by the introduction of specific viewpoints and of technical tools of its own. The first impression, that often accompanies the creation of one of such specialized branches in a diSCipline, is that one has succeeded in isolating the 'scientific core' of it, by restricting the somehow vague and redundant generality of its original 'philosophical' configuration. But, after a while, it appears that some of the discarded aspects are indeed important and a new specialized domain of investigation is created to explore them. By follOwing this procedure, one finally finds himself confronted with such a variety of independent fields of research, that one wonders whether the fact of labelling them under a common denomination be nothing but the contingent effect of a pure historical tradition."