The first edition of the Handbook of Philosophical Logic (four volumes) was published in the period 1983-1989 and has proven to be an invaluable reference work ...

Modal logics, originally conceived in philosophy, have recently found many applications in computer science, artificial intelligence, the foundations of mathematics, linguistics and other disciplines. Celebrated for their good computational behaviour, modal logics are used as effective formalisms for talking about time, space, knowledge, beliefs, actions, obligations, provability, etc. However, the nice computational properties can drastically change if we combine some of these formalisms into a many-dimensional system, say, to reason about knowledge bases developing in time or moving objects. To study (...) the computational behaviour of many-dimensional modal logics is the main aim of this book. On the one hand, it is concerned with providing a solid mathematical foundation for this discipline, while on the other hand, it shows that many seemingly different applied many-dimensional systems (e.g., multi-agent systems, description logics with epistemic, temporal and dynamic operators, spatio-temporal logics, etc.) fit in perfectly with this theoretical framework, and so their computational behaviour can be analyzed using the developed machinery. We start with concrete examples of applied one- and many-dimensional modal logics such as temporal, epistemic, dynamic, description, spatial logics, and various combinations of these. Then we develop a mathematical theory for handling a spectrum of 'abstract' combinations of modal logics - fusions and products of modal logics, fragments of first-order modal and temporal logics - focusing on three major problems: decidability, axiomatizability, and computational complexity. Besides the standard methods of modal logic, the technical toolkit includes the method of quasimodels, mosaics, tilings, reductions to monadic second-order logic, algebraic logic techniques. Finally, we apply the developed machinery and obtained results to three case studies from the field of knowledge representation and reasoning: temporal epistemic logics for reasoning about multi-agent systems, modalized description logics for dynamic ontologies, and spatio-temporal logics. The genre of the book can be defined as a research monograph. It brings the reader to the front line of current research in the field by showing both recent achievements and directions of future investigations (in particular, multiple open problems). On the other hand, well-known results from modal and first-order logic are formulated without proofs and supplied with references to accessible sources. The intended audience of this book is logicians as well as those researchers who use logic in computer science and artificial intelligence. More specific application areas are, e.g., knowledge representation and reasoning, in particular, terminological, temporal and spatial reasoning, or reasoning about agents. And we also believe that researchers from certain other disciplines, say, temporal and spatial databases or geographical information systems, will benefit from this book as well. Key Features: Integrated approach to modern modal and temporal logics and their applications in artificial intelligence and computer science Written by internationally leading researchers in the field of pure and applied logic Combines mathematical theory of modal logic and applications in artificial intelligence and computer science Numerous open problems for further research Well illustrated with pictures and tables. (shrink)

This paper suggests that most of the FTSE-listed firms in the United Kingdom use corporate environmental policy statements to communicate their strategic intent of what environmental and social targets to attain, and broad guidelines of how they will progressively achieve all the required changes and new developments. In this paper, we link the contents of CEPS of a sample of FTSE-listed firms to the voluntary participation in the environmental benchmarking exercise and the various levels of environmental performance therein. The findings (...) suggest that in contrast to their non-participating counterparts, the strategic focus of the participating firms transcends from simply mitigating any potential damages that their operations might have on the environment to business process reengineering and building new implementation capabilities. However, not all of the participating firms achieved excellence in their environmental performance, the high performing firms outweighed their counterparts on their emphasis on technological competence and competitiveness, and interestingly, the average-performing firms would use the strategic emphasis on social responsibility to compensate for their mediocre technological competence. (shrink)

From the point of view of non-classical logics, Heyting's implication is the smallest implication for which the deduction theorem holds. This book studies properties of logical systems having some of the classical connectives and implication in the neighbourhood of Heyt ing's implication. I have not included anything on entailment, al though it belongs to this neighbourhood, mainly because of the appearance of the Anderson-Belnap book on entailment. In the later chapters of this book, I have included material that might be (...) of interest to the intuitionist mathematician. Originally, I intended to include more material in that spirit but I decided against it. There is no coherent body of material to include that builds naturally on the present book. There are some serious results on topological models, second order Beth and Kripke models, theories of types, etc., but it would require further research to be able to present a general theory, possibly using sheaves. That would have postponed pUblication for too long. I would like to dedicate this book to my colleagues, Professors G. Kreisel, M.O. Rabin and D. Scott. I have benefited greatly from Professor Kreisel's criticism and suggestions. Professor Rabin's fun damental results on decidability and undecidability provided the powerful tools used in obtaining the majority of the results reported in this book. Professor Scott's approach to non-classical logics and especially his analysis of the Scott consequence relation makes it possible to present Heyting's logic as a beautiful, integral part of non-classical logics. (shrink)

Modern applications of logic in mathematics, computer science, and linguistics use combined systems of different types of logic working together. This book develops a method for combining--or fibring--systems by breaking them into simple components which can be manipulated easily and recombined.

This much-needed book provides a thorough account of temporal logic, one of the most important areas of logic in computer science today. The book begins with a solid introduction to semantical and axiomatic approaches to temporal logic. It goes on to cover predicate temporal logic, meta-languages, general theories of axiomatization, many dimensional systems, propositional quantifiers, expressive power, Henkin dimension, temporalization of other logics, and decidability results. With its inclusion of cutting-edge results and unifying methodologies, this book is an indispensable reference (...) for both the pure logician and the theoretical computer scientist. (shrink)

This essay evaluates the moral logic of ‘liberal eugenics’: the ideal of genetic control which leaves decisions about what sort of people to produce in the hands of individual parents, absent government intervention. I argue that liberal eugenics cannot be justified on the basis of the underlying liberal theory which inspires it. I introduce an alternative to Rawls's social primary goods that might be called natural primary goods: hereditable mental and physical capacities and dispositions that are valued across a range (...) of projects and pursuits. I suggest that reproductive genetic biotechnologies like embryo selection, cellular surgery, and genetic engineering, which aim to enhance ‘general purpose’ traits in offspring are less like childrearing practices a liberal government leaves to the discretion of parents than like practices the state makes compulsory. I argue that if the liberal commitment to autonomy is important enough for the state to mandate childrearing practices such as health care and basic education, that very same interest is important enough for the state to mandate safe, effective, and functionally integrated genetic practices that act on analogous all‐purpose traits such as resistance to disease and general cognitive functioning. I conclude that the liberal case for compulsory eugenics is a reductio against liberal theory. (shrink)

In this paper we show that some versions of Dung’s abstract argumentation frames are equivalent to classical propositional logic. In fact, Dung’s attack relation is none other than the generalised Peirce–Quine dagger connective of classical logic which can generate the other connectives ${\neg, \wedge, \vee, \to}$ of classical logic. After establishing the above correspondence we offer variations of the Dung argumentation frames in parallel to variations of classical logic, such as resource logics, predicate logic, etc., etc., and create resource argumentation (...) frames, predicate argumentation frames, etc., etc. We also offer the notion of logic proof as a geometrical walk along the nodes of a Dung network and thus we are able to offer a geometrical abstraction of the notion of inference based argumentation. Thus our paper is also a contribution to the question: “What is a logical system” in as much as it integrates logic with abstract argumentation networks. (shrink)

The Handbook of the Logic of Argument and Inference is an authoritative reference work in a single volume, designed for the attention of senior undergraduates, graduate students and researchers in all the leading research areas concerned with the logic of practical argument and inference. After an introductory chapter, the role of standard logics is surveyed in two chapters. These chapters can serve as a mini-course for interested readers, in deductive and inductive logic, or as a refresher. Then follow two chapters (...) of criticism; one the internal critique and the other the empirical critique. The first deals with objections to standard logics (as theories of argument and inference) arising from the research programme in philosophical logic. The second canvasses criticisms arising from work in cognitive and experimental psychology. The next five chapters deal with developments in dialogue logic, interrogative logic, informal logic, probability logic and artificial intelligence. The last chapter surveys formal approaches to practical reasoning and anticipates possible future developments. Taken as a whole the Handbook is a single-volume indication of the present state of the logic of argument and inference at its conceptual and theoretical best. Future editions will periodically incorporate significant new developments. (shrink)

The properties of negation, in combination with those of other logical operations and structural features of the deductibility relation, serve as gateways among logical systems. Negation therefore plays an important role in selecting logical systems for particular applications. This volume provides a thorough treatment of this concept, based on contributions written by authors from various branches of logic. The resulting 14 research papers address a variety of topics including negation in relevant logics; a defense of dialetheic theory of negation; stable (...) negation in logic programming; antirealism and falsity; and negation, denial, and language change in philosophical logic. Suited to scholars and graduate students in the fields of philosophy, logic mathematics, computer science, and linguistics. Annotation copyrighted by Book News, Inc., Portland, OR. (shrink)

This paper is part of a research program centered around argumentation networks and offering several research directions for argumentation networks, with a view of using such networks for integrating logics and network reasoning. In Section 1 we introduce our program manifesto. In Section 2 we motivate and show how to substitute one argumentation network as a node in another argumentation network. Substitution is a purely logical operation and doing it for networks, besides developing their theory further, also helps us see (...) how to bring logic and networks closer together. Section 3 develops the formal properties of the new kind of network and Section 4 offers general discussion and comparison with the literature. (shrink)

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. 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 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. (shrink)

Liberal theory seeks to achieve toleration, civil peace, and mutual respect in pluralistic societies by making public policy without reference to arguments arising from within formative ideals about what gives value to human life. Does it make sense to set aside such conceptions of the good when it comes to controversies about stem cell research and the genetic engineering of people or animals? Whether it is reasonable to bracket our worldviews in such cases depends on how we answer the moral (...) questions that the use of these biotechnologies presuppose. I argue that the moral language of liberal justice – of rights and duties, interests and opportunities, freedom and consent, equality and fairness – cannot speak to these underlying concerns about what the human embryo is, why the natural lottery matters to us, and whether 'animal nature' is worth preserving. I conclude that liberal theory is incapable of furnishing a coherent or desirable account to govern the way we use our emerging powers of biotechnology. (shrink)

If we arrange in chronological order the various statements Darwin made about God, creation, design, plan, law, and so forth, that I have discussed, there emerges a picture of a consistent development in Darwin's religious views from the orthodoxy of his youth to the agnosticism of his later years. Numerous sources attest that at the beginning of the Beagle voyage Darwin was more or less orthodox in religion and science alike.78 After he became a transmutationist early in 1837, he concluded (...) that the doctrine of secondary causes must be extented even to the history of life and that after the first forms of life were created, there was no further need for divine intervention, except where man was concerned. Man's body, he thought, was produced by the process of transmutation, but he believed for a time that man's soul was “superadded.” By mid-1838 he had become convinced that nothing, after the creation of life, was due to miracles. God works only through laws, which are capable of producing “every effect of evey kind which surrounds us.” The existence of man, the idea of God in man's mind, and the harmony of the whole system were in his eyes prearranged goals of deterministic laws imposed by God. Such a conception excludes the miracles on which Christianity depends; but it is not possible to say whether Darwin's loss of Christian faith, which occurred at about this same time, preceded and made possible his “materialism” or was rather caused or hastened by it.79 In the weeks after his reading of Malthus, Darwin's belief in a plan of creation gave way to the belief that God created matter and life and designed their laws, leaving the details, however, to the workings of chance. This remained his view until the 1860s.There is no exact parallel between this development of Darwin's religious views and the development of his ideas on evolution, but there is a general correspondence. When he believed in a plan of creation, Darwin's theory of transmutation did not depend on struggle or the selection of chance variations. Adaptation was, for him, an automatic response to environmental chance. From late 1838 to 1859 he believed in designed laws and chance, and this belief, too, has its parallel in his theory. The element of chance in natural selection meant that there could be no detailed plan,in which even man's idea of God would be a necessary outcome of nature's laws (man himself is not a necessary outcome of the working of natural selection).80 But Darwin still believed nature was programmed to achieve certain general ends. We might say that he believed in a general, though not a special, teleology. Natural selection was for him a law to maximize utility, creating useful organs, retaining vestiges for future use. For many years it was a law designed to produce organisms perfectly adapted to their environments. Only later did Darwin come to doubt even this sort of design in nature.81 One way of describing the development of Darwin's evolutionary thought is to say that it shows a gradual abandoning of his “theistic” assumptions, so that by the late 1860s his theory was informed to a slighter extent by notions of purpose and design than it was in 1838 or 1844 or 1859. (shrink)

We describe the state of the Talmudic Logic project as of end of 2019. The Talmud is the most comprehensive and fundamental work of Jewish religious law, employing a large number of logical components centuries ahead of their time. In many cases the basic principles are not explicitly formulated, which makes it difficult to formalize and make available to the modern student of Logic. This project on Talmudic Logic, aims to present logical analysis of Talmudic reasoning using modern logical tools. (...) We investigate principles of Talmudic Logic and publish a series of books, one book or more for each principle. The series begins with the systematic analysis of Talmudic inference rules. The first book shows that we can present Talmudic reasoning intuitions as a systematic logical system basic to modern non-deductive reasoning, such as Argumentum A Fortiori, Abduction and Analogy. The second book offers a systematic common sense method for intuitively defining sets and claims that this method adequately models the Talmudic use of the rules Klal uPrat. These books also criticize modern Talmudic research methodology. Later books deal with additional topics like Deontic logic, and Temporal logic, Agency and processes in the Talmud and more. The aims of the project are two fold: 1. To import into the Talmudic study modern logical methods with a view to help understand complicated Talmudic passages, which otherwise cannot be addressed. 2. To export from the Talmud new logical principles which are innovative and useful to modern contemporary logic. (shrink)

One of our purposes here is to expose something of the elementary logical structure of abductive reasoning, and to do so in a way that helps orient theorists to the various tasks that a logic of abduction should concern itself with. We are mindful of criticisms that have been levelled against the very idea of a logic of abduction; so we think it prudent to proceed with a certain diffidence. That our own account of abduction is itself abductive is methodological (...) expression of this diffidence. A second objective is to test our conception of abduction's logical structure against some of the more promising going accounts of abductive reasoning. We offer our various suggestions in a benignly advisory way. The primary targets of our advice is ourselves, meant as guides to work we have yet to complete or, in some instances, start. It is possible that our colleagues in the abduction research communities will find our counsel to be of some interest. But we repeat that our first concern is to try to get ourselves straight about what a logic of abduction should encompass. (shrink)

The present collection of essays honours John Woods on the occasion of his eightieth birthday from contributors who wish to pay homage to this remarkable researcher whom they see not only as a scholar of prodigious energy and insight, but as a friend, colleague, collaborator, or former teacher. All of the essays touch upon topics Woods has taken a direct or indirect interest in, ranging from technical problems of mathematical logic and applications of formal methods through philosophical logic, philosophy of (...) language, epistemology and history of ancient and modern logic. The sections themselves of the book cover relevance, paradoxes, inconsistency, fallacies, abduction, fictions, logic naturalized, law, argumentation and narratives, and many other topics: and represent the main research areas which have profited from Woods' reflections. (shrink)

The modem age reflects a pluralistic mentality of norms and regularities assuming a dualistic polar character. Man lives in this dualistically conditioned time and space--topos gaios (earthly sphere). In ancient times, attempts were made to transcend this situation via distinct temple cultures involving colorful sacrificial systems. Eventually, there was a transition from empirical temple cultures to mental and metaphysical ones involving laws, norms, and ascetic practices. However, the human heart, the source of all contradictions and cravings, remained unchanged. There is (...) a perennial impetus to overcome human bondage to all the laws of dualistic world structures and return to the original primeval state of the universe-topos ouranios (heavenly sphere). Yet there is no bridge between the earthly and heavenly spheres other than Jesus Christ Who was the first to proclaim the arrival of the Kingdom of Heaven. Christ removed the barrier between "above" and "below" by pacifying the wrath of the transcendent, and introducing the heavenly sphere to man whose heart is opened by the Holy Spirit and cleansed by grace. This represents Christianity's conceptual transformation. (shrink)

In this paper we propoee a logic programming language which supports hypothetical updates together with integrity constraints. The language makes use of a revision mechanism, which is needed to restore consistency when an update violates some integrity constraint. The revision policy adopted is based on the simple idea that more recent information is preferred to earlier one. We show how this language can be used to represent and perform several types of defeasible reasoning. We develop a logical characterization of the (...) language in a three-valued conditional logic, by introducing a completion construction. We show that the operational semantics is sound and complete with respect to the completion construction. (shrink)

The American Journal of Bioethics, Volume 12, Issue 4, Page 45-47, April 2012.

Философ, который подобным образом озаглавил свою работу, тем самым утверждает, что он знает, как выглядит непротиворечивая онтология, теория познания, что такое реальность, как, скажем, решается проблема непротиворечивости математики и т.д.