This book constitutes the strictly refereed post-workshop proceedings of the 11th International Workshop on Computer Science Logic, CSL '97, held as the 1997 Annual Conference of the European Association on Computer Science Logic, EACSL, in Aarhus, Denmark, in August 1997. The volume presents 26 revised full papers selected after two rounds of refereeing from initially 92 submissions; also included are four invited papers. The book addresses all current aspects of computer science logics and its applications and (...) thus presents the state of the art in the area. (shrink)

A common reaction to Hegel’s suggestion that we collapse Kant’s distinction between form and content is that, since such a move would also deprive us of any way of distinguishing the merely logical from the real possibility of our concepts, it is incoherent and ought to be rejected. It is true that these two distinctions are intimately related in Kant, such that if one goes, the other does as well. But it is less obvious that giving them up as Kant (...) conceives them is as incoherent a proposal as many of Hegel’s critics think. It has been the point of a recent account of Hegel’s idealism to demonstrate that his critique of Kant’s dichotomy between form and content or concept and intuition does not commit him to the view that human cognition is materially creative of its content in the manner of a God-like or intuitive intellect—does not, in other words, signify a return to a pre-Critical metaphysics. This is the interpretative stance I adopt here as well, in hope of giving defenders of Kant reasons for taking Hegel more seriously. (shrink)

This volume presents the proceedings from the Eleventh Brazilian Logic Conference on Mathematical Logic held by the Brazilian Logic Society in Salvador, Bahia, Brazil. The conference and the volume are dedicated to the memory of professor Mario Tourasse Teixeira, an educator and researcher who contributed to the formation of several generations of Brazilian logicians. Contributions were made from leading Brazilian logicians and their Latin-American and European colleagues. All papers were selected by a careful refereeing processs and were revised and updated (...) by their authors for publication in this volume. There are three sections: Advances in Logic, Advances in Theoretical Computer Science, and Advances in Philosophical Logic. Well-known specialists present original research on several aspects of model theory, proof theory, algebraic logic, category theory, connections between logic and computer science, and topics of philosophical logic of current interest. Topics interweave proof-theoretical, semantical, foundational, and philosophical aspects with algorithmic and algebraic views, offering lively high-level research results. (shrink)

The Joint International Conference on Logic Programming, sponsored by the Association for Logic Programming, is a major forum for presentations of research, applications, and implementations in this important area of computer science. Logic programming is one of the most promising steps toward declarative programming and forms the theoretical basis of the programming language Prolog and its various extensions. Logic programming is also fundamental to work in artificial intelligence, where it has been used for nonmonotonic and commonsense reasoning, expert systems (...) implementation, deductive databases, and applications such as computer-aided manufacturing. Krzysztof R. Apt is project leader at the Centre for Mathematics and Computer Science in Amsterdam and part-time Professor in Computer Science at the University of Amsterdam. Topics covered: Theory Foundations. Programming Languages. Implementation. Programming Methodologies and Tools. Applications. Deductive Databases. Artificial Intelligence. Parallelism. (shrink)

Logic has pride of place in mathematics and its 20th century offshoot, computer science. Modern symbolic logic was developed, in part, as a way to provide a formal framework for mathematics: Frege, Peano, Whitehead and Russell, as well as Hilbert developed systems of logic to formalize mathematics. These systems were meant to serve either as themselves foundational, or at least as formal analogs of mathematical reasoning amenable to mathematical study, e.g., in Hilbert’s consistency program. Similar efforts continue, but have (...) been expanded by the development of sophisticated methods to study the properties of such systems using proof and model theory. In parallel with this evolution of logical formalisms as tools for articulating mathematical theories (broadly speaking), much progress has been made in the quest for a mechanization of logical inference and the investigation of its theoretical limits, culminating recently in the development of new foundational frameworks for mathematics with sophisticated computer-assisted proof systems. In addition, logical formalisms developed by logicians in mathematical and philosophical contexts have proved immensely useful in describing theories and systems of interest to computer scientists, and to some degree, vice versa. Three examples of the influence of logic in computer science are automated reasoning, computer verification, and type systems for programming languages. (shrink)

Major figures of twentieth-century philosophy were enthralled by the revolution in formal logic, and many of their arguments are based on novel mathematical discoveries. Hilary Putnam claimed that the Löwenheim-Skølem theorem refutes the existence of an objective, observer-independent world; Bas van Fraassen claimed that arguments against empiricism in philosophy of science are ineffective against a semantic approach to scientific theories; W. V. O. Quine claimed that the distinction between analytic and synthetic truths is trivialized by the fact that any (...) theory can be reduced to one in which all truths are analytic. This book dissects these and other arguments through in-depth investigation of the mathematical facts undergirding them. It presents a systematic, mathematically rigorous account of the key notions arising from such debates, including theory, equivalence, translation, reduction, and model. The result is a far-reaching reconceptualization of the role of formal methods in answering philosophical questions. (shrink)

This is a personal, incomplete, and very informal take on the role of logic in general philosophy of science, which is aimed at a broader audience. We defend and advertise the application of logical methods in philosophy of science, starting with the beginnings in the Vienna Circle and ending with some more recent logical developments.

Logical theory codifies rules of correct inferences. On the other hand, logical reasoning is typically considered as one of the most fundamental cognitive activities. Thus, cognitive science is a natural meeting-point for investigations about the place of logic in human cognition. Investigations in this perspective strongly depend on a possible understanding of logic. This paper focuses on logic in the strict sense; that is, the theory of deductive inferences. Two problems are taken into account, namely: do humans apply logical (...) rules in ordinary reasoning?; the genesis of logic. The second issue is analyzed from the naturalistic point of view. (shrink)

A useful logic in which to specify normative system behaviour, deontic logic has a broad spectrum of possible applications within the field: from legal expert systems to natural language processing, database integrity to electronic contracting and the specification of fault-tolerant software.

This book is a collection of rare material regarding logical and analytic-philosophical traditions in Central and Eastern European countries, covering the period from the late nineteenth century to the early twenty-first century. An encyclopedic feature covers the history of logic and analytic philosophy in all European post-Socialist countries.

According to a brief and very general definition Cognitive Science is an interdisciplinary scientific study of how information is represented and transformed in a human nervous system. “Information”, “representation” and “transformation” are keywords here. Many disciplines bring considerable contribution to Cognitive Science. Logic is one of them. Logic investigates these rules which allow us to recognize valid reasonings and distinguish them from those that fail to fulfill the condition of valid- ity. Thus logic investigates some representation (or representations) (...) of reasoning. Significant part of information transformed in nervous system is related to reasoning and inference. This fact opens special perspectives on applying Logic in Cognitive Science both in representing as well as in transforming information. Any formal logical system constitutes a kind of representation of a class of propositions considered as sentence content. In this way each logical system provides a representation of a broad class of belief states. At the same time any inference relation, related to a given logical system, represents a transformation of some type of information. As a consequence it would be hard to find logical investigations which could not be applied in Cognitive Science. Such an idea guided us while we were preparing the present volume. (shrink)

Linear Logic is a branch of proof theory which provides refined tools for the study of the computational aspects of proofs. These tools include a duality-based categorical semantics, an intrinsic graphical representation of proofs, the introduction of well-behaved non-commutative logical connectives, and the concepts of polarity and focalisation. These various aspects are illustrated here through introductory tutorials as well as more specialised contributions, with a particular emphasis on applications to computer science: denotational semantics, lambda-calculus, logic programming and concurrency theory. (...) The volume is rounded-off by two invited contributions on new topics rooted in recent developments of linear logic. The book derives from a summer school that was the climax of the EU Training and Mobility of Researchers project 'Linear Logic in Computer Science'. It is an excellent introduction to some of the most active research topics in the area. (shrink)

The Logic in Philosophy of Science, by HalvorsonHans. Cambridge: Cambridge University Press, 2019. Pp. viii + 296.

Il naturale senso della logica in relazione alla scienza è quello di fornire un linguaggio alle acquisizioni epistemologiche: tale sembra essere il senso assegnatogli anche da Avicenna in al-Mantiq. La questione in realtà è molto più profonda: quale relazione c'è fra gli universali predicabili e gli oggetti della scienza? Attraverso l'esame della questione quale è delineata nel Madkhal, in particolare in merito al genere e alla differenza, e il loro ruolo nelle scienze in alcuni passaggi del Kitab al-Burhan, l'A. verifica (...) l'applicazione delle considerazioni teoretiche in un problema fisico pratico affrontato nel Kitab-al-Tabi'iyat. (shrink)

This paper surveys applications of logical methods in the cognitive sciences. Special attention is paid to non-monotonic logics and complexity theory. We argue that these particular tools have been useful in clarifying the debate between symbolic and connectionist models of cognition.

The role of classical logic as the base of formalized scientific theories seems to be unshakable. Yet legitimate doubts about its universal applicability in science have resulted in the development of alternative systems, among which constructive and modal logic are discussed in syntactic and semantic terms.

The role of classical logic as the base of formalized scientific theories seems to be unshakable. Yet legitimate doubts about its universal applicability in science have resulted in the development of alternative systems, among which constructive and modal logic are discussed in syntactic and semantic terms.

The difference between Hermann Cohen’s systematic philosophy and his philosophy of religion can be determined via the logical “Judgment of Contradiction,” viewed as an “Authority of Annihilation.” In Cohen’s Logic of Pure Knowledge the “Judgment of Contradiction” acts as a “means of protection” against “falsifications” that may have arisen on the pathway through the previous judgments of “origin” and “identity.” Cohen thematizes these operations in his Religion of Reason Out of the Sources of Judaism, too. However, there they do not (...) form the grounding for natural science but rather for the knowledge of nature as creation in a strict correlation to God’s uniqueness. Any admixture between God and nature is the falseness that must be excluded via the “Authority of Annihilation.” The Being of God places the world over against the possibility of its own radical Non-Being. Yet at the same time, a second mode of Negation, a relative Nothing providing continuity for the world’s being-there, grounded in the “Logic of Origin,” retains its validity. In Cohen’s view a Creation “in the beginning” stands side by side with a continuous “renewal of the world”. (shrink)

This book gives a state-of-the-art survey of current research in logic and philosophy of science, as viewed by invited speakers selected by the most prestigious international organization in the field. In particular, it gives a coherent picture of foundational research into the various sciences, both natural and social. In addition, it has special interest items such as symposia on interfaces between logic and methodology, semantics and semiotics, as well as updates on the current state of the field in Eastern (...) Europe and the Far East. (shrink)

This book gives a state-of-the-art survey of current research in logic and philosophy of science, as viewed by invited speakers selected by the most prestigious international organization in the field. In particular, it gives a coherent picture of foundational research into the various sciences, both natural and social. In addition, it has special interest items such as symposia on interfaces between logic and methodology, semantics and semiotics, as well as updates on the current state of the field in Eastern (...) Europe and the Far East. (shrink)

This paper grapples with two objections against Max Weber’s methodology that arise because Weber borrows some ideas from Heinrich Rickert’s neo-Kantian philosophical system. The first objection (“the contradiction argument”) is raised by Julius J. Schaaf who disagrees with Weber’s claim that historical objects are constituted through retrospectively and hypothetically applied selections of value relations and that we can understand these objects. Weber’s idea that the relating ideal type constructions are also non-arbitrary—i.e., not merely subjective—and can be rectified, Schaaf maintains, contradicts (...) his own characterization of historical objects and reality. The second objection (“the incom¬patibility argument”) was made by Gerhard Wagner and Heinz Zipprian. It focuses on the conception of objective possibility. According to this, counter¬factual chains of historical events are contrived to figure out the relevant set of causes by which a certain event can be said to necessarily occur. The critics claim that it is only based on the ontological assumption of a preexisting real object that this thought-experiment can operate. That is, the pre-emptive assumption of realism is indis¬pensable for explaining the historical individual. To refute these two objections, I clarify some foundational notions and ideas of Weber’s methodology. (shrink)

In their work McCulloch and Pitts describe an idea of representing all of nervous activity in terms of propositional logic. This idea was quickly challenged. One of reasons for this challenge was rising believe that logic is unable to describe most of human cognitive processes. In this paper we will analyse premises of original McCulloch and Pitts proposition. Following that, we will ask about ability of symbolic systems to represent human cognition. We will finish by analysing relation between symbolic and (...) subsymbolic computing, in hope of bridging the gap between the two. (shrink)

This book is a collection of rare material regarding logical and analytic-philosophical traditions in Central and Eastern European countries, covering the period from the late nineteenth century to the early twenty-first century. An encyclopedic feature covers the history of logic and analytic philosophy in all European post-Socialist countries.

The logical pattern underlying twentieth century science is strikingly uniform from physics through biology and psychology to social science. Our purpose will be to analyze and illustrate this pattern, to trace its development, especially from the Middle Ages to the present time, and to suggest some possible consequences for the future.

The concept of the subject, of what Hegel calls absolute negativity, already appears early in the logic of being.1 Absolute negativity, negation of the negation, occurs throughout the logic as identity in difference understood as self-identification under different descriptions. First, the subject refers to itself merely under an incomplete description. Secondly, it refers to something other than itself under a second description which is logically required by the first. (For example, the description of being in general requires some determinate description (...) of being in particular). But this second description is dialectically excluded by the assumption that the first description is complete. Thirdly, the subject negates its negation of the other. It discovers itself in the other, under the other description, and thus comes to refer to itself less incompletely. This is Hegel in the analytic mode. (shrink)

QUINE'S DOCTRINE of the indeterminacy of translation is made possible by the principle of substitution characteristic of extensional logic. The same characteristic makes it impossible, in philosophy of science, to choose among theoretical models no one of which is obviously best suited to explain the facts. Hilary Putnam achieved a sort of closure to the problem of reference in philosophy of science, when he pointed out the implications of the Skolem-Löwenheim theorem. He said that besides the facts a (...) theory is designed to explain, there are any number of unintended interpretations of the same theory that assign the correct truth values to all sentences of the theory. There can be no sound basis for deciding upon the sole interpretation for a theory. Following Putnam, some philosophers have abandoned the problem of reference in the context of axiomatic systems. Ian Hacking, for instance, prefers a notion of reference "that is not tied by any specific, binding theory about what is referred to." He has turned to the study of approximations and practical models, spurred on by the difficulty of reconciling axiomatic systems to scientific practice. (shrink)

As far as the history of logic is concerned, late nineteenth and twentieth century Central and Eastern Europe seem oddly obscure. The work of several influential individuals or national schools is...

This Handbook is a combination of authoritative exposition, comprehensive survey, and fundamental research exploring the underlying unifying themes in the various areas. The intended audience is graduate students and researchers in the areas of computing and logic, as well as other people interested in the subject. We assume as background some mathematical sophistication. Much of the material will also be of interest to logicians and mathematicians.

The work is the presentation of a logical theory - Logic in Reality (LIR) - and of applications of that theory in natural science and philosophy, including ...

Carl Hempel introduced what he called "Craig's theorem" into the philosophy of science in a famous discussion of the "problem of theoretical terms." Beginning with Hempel's use of 'Craig's theorem," I shall bring out some of the key differences between Hempel's treatment of the "problem of theoretical terms" and Carnap's in order to illuminate the peculiar function of Wissenschaftslogik in Carnap's mature philosophy. Carnap's treatment, in particular, is fundamentally antimetaphysical—he aims to use the tools of mathematical logic to dissolve (...) rather solve traditional philosophical problems—and it is precisely this point that is missed by his logically-minded contemporaries such as Hempel and Quine. (shrink)