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)

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)

In Section 1, we questioned the evidence for iteration of tenses, even with abstraction. To permit abstraction would in any case risk neutralizing our distinction between tensed and untensed sentences. Sequence of tense phenomena, far from supporting iteration, were incompatible with it. Instead, we argued, tense always retains its full deictic character; tenses never have scope over each other. The future modal WILL is exceptional (Section 2), but abstraction is not required to deal with this.An important suggestion, first made in (...) Section 1 and developed further in Section 3, would restrict quantification induced by the interpretation of Past to a domain determined by pragmatic factors. When Past serves as a reference time, e.g. when it forms part of would, as inSam believed that he would be in BostonJames bought a stamp that would be priceless then a previous occurrence of Past serves to define the domain relevant to the quantificational element of Past. Without semantic binding or reference, the two cases of Past in such sentences will thus be satisfied by the same interval in the past.The extension of this idea in Section 3, permits an account of the supposed incompleteness of the past tense without invoking a hidden THEN in e.g. I turned the lights off. In this case, restriction of the relevant domain does not proceed via an earlier occurrence of Past but depends solely on discourse factors.In Section 4, the analysis of have given in Part I is modified to introduce an element of ‘pastness’. The relevant sub-interval must be non-final-and perhaps need not even be a sub-interval of the evaluation interval itself. Empirically necessary, this change makes the incompatibility of Pres,have and a definite adverb like at 6 o'clock in a single sentence even harder to explain semantically. However, the vague restrictions on domain imposed by the present tense and relevant to the sub-interval required by an embedded have below it seem clearly pragmatically incompatible with the explicit restriction of that same interval to a very specific interval in the past — a restriction which, we argue, is imposed by a definite time adverb.Thus, Part II represents a consistent, though entirely informal plea for the embedding of the semantics of Part I in a framework in which pragmatic considerations can interact freely with the semantics, to restrict the domains within which quantification is permitted. It is in effect a plea for the introduction of partial models along the lines suggested by Barwise and Perry (1981). The advantages of the basic distinctions between tense, aspect and adverbs introduced in Part I would, we have suggested in the second part, be yet more obvious in such a framework. Formalization in a system of partial models must await further work. (shrink)

This superb collection of papers focuses on a fundamental question in logic and computation: What is a logical system? With contributions from leading researchers--including Ian Hacking, Robert Kowalski, Jim Lambek, Neil Tennent, Arnon Avron, L. Farinas del Cerro, Kosta Dosen, and Solomon Feferman--the book presents a wide range of views on how to answer such a question, reflecting current, mainstream approaches to logic and its applications. Written to appeal to a diverse audience of readers, What is a Logical System? will (...) excite discussion among students, teachers, and researchers in mathematics, logic, computer science, philosophy, and linguistics. (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)

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)

This Article considers the moral and legal status of practices that aim to modify traits in human offspring. As advancements in reproductive biotechnology give parents greater power to shape the genetic constitution of their children, an emerging school of legal scholars has ushered in a privatized paradigm of genetic control. Commentators defend a constitutionally protected right to prenatal engineering by appeal to the significance of procreative liberty and the promise of producing future generations who are more likely to have their (...) lives go well. This 'new eugenics,' however, confronts us with ethical challenges that neither liberal arguments about autonomy, fairness, and consent, nor utilitarian arguments about preferences, happiness, and equality, are able to capture. I begin by analyzing the Supreme Court's modern substantive due process jurisprudence, as it bears on recent advancements and controversies in genetic science. After developing a doctrinal framework that could support an asserted right to genetic engineering, I draw on empirical research in behavioral psychology to examine the influence of eugenic norms on egalitarian attitudes and institutions. I predict that if parents become accustomed to choosing the genes of their children, it would be radically more difficult to give an influential account for why the successful should adopt a charitable posture toward those who are less fortunate. I argue that by shifting control over offspring DNA from chance to choice, enhancement will inflate a sense of individual entitlement for social and economic outcomes. I conclude that increasing willingness to prevent the birth of abnormal children distracts attention from institutions that fail to accommodate the limitations of imperfect people. Some may reply that producing people who better fit the roles society chooses to reward need not deter us from providing for people whose abilities fail to meet the demands of modern society. However, this reply misses the way that changes in reproductive practices can bring about changes in the way that we understand our identities and relationships. Eugenic solutions to social problems such as poverty, crime, and unemployment reshape the challenge of genetic disadvantage so that it is no longer one we address through collective measures such as public education, social services, and income redistribution, and instead becomes one for individual parents to prevent through donor screening, embryo discard, or selective abortion. (shrink)

Résumé La thématique du retrait traverse l’œuvre de Heidegger : elle est inséparable de sa quête de l’être (qui se dévoile en se voilant), de ses conceptions de la vérité et de la terre. Mais cette multi-présence du rapport entre don et rétraction n’est pas seulement inscrite dans la manière de penser de Heidegger. Elle concerne aussi le développement de Sein und Zeit, inachevé. La question qui s’impose est alors celle de savoir si et dans quelle mesure cette thématique ne (...) relève que d’une dimension philosophique ou bien si elle n’a pas aussi à voir, chez Heidegger, avec une dimension biographique. (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)

Inductive Logic is number ten in the 11-volume Handbook of the History of Logic. While there are many examples were a science split from philosophy and became autonomous (such as physics with Newton and biology with Darwin), and while there are, perhaps, topics that are of exclusively philosophical interest, inductive logic — as this handbook attests — is a research field where philosophers and scientists fruitfully and constructively interact. This handbook covers the rich history of scientific turning points in Inductive (...) Logic, including probability theory and decision theory. Written by leading researchers in the field, both this volume and the Handbook as a whole are definitive reference tools for senior undergraduates, graduate students and researchers in the history of logic, the history of philosophy, and any discipline, such as mathematics, computer science, cognitive psychology, and artificial intelligence, for whom the historical background of his or her work is a salient consideration. (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.

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)

Judaism is often described as a religion that tolerates, even celebrates arguments with God. In Pious Irreverence, Dov Weiss has written the first scholarly study of the premodern roots of this distinctively Jewish theology of protest, examining its origins and development in the rabbinic age (70 CE-800 CE).

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)

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)

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)

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)

Haḳdamah. Masekhet Taʻanit -- shel avotenu ṿe-shalanu -- Shaʻar 1. Ketsad medabrim ʻal birkat ha-ḥayim -- Shaʻar 2. Adam ṿe-adamah, ʻananim ṿe-heʻanut -- Shaʻar 3. ha-Homer ḥai u-medaber -- ha-ḥoḳ, ha-pele ṿeha-ʻanṿah -- Shaʻar 4. "Ka-mayim ha-panim la-panim ken lev ha-adam la-adam" -- normot ḥevratiyon u-reṿaḥat ha-adam -- Shaʻar 5. "Tefilah la-ʻani ki yaʻaṭof" -- ha-kisufim le-magaʻ -- Shaʻar 6. Nispaḥ ḥaṿayah ṿe-tiḳṿah.

Earlier investigations of the hormonal control of vitellogenin (egg‐yolk protein) synthesis in mosquitoes relied on microsurgical manipulations to identify organs that secrete the various hormones that stimulate or inhibit vitellogenesis. Advances in the last 10 years, using radioimmunoassays, HPLC, mass spectrometry and tissue‐culture incubations, have shown that the control mechanism involves a complex interaction between ecdysteroids, juvenile hormones and peptide hormones.