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)

Foundational questions in logic, mathematics, computer science and physics are constant sources of epistemological debate in contemporary philosophy. To what extent is the transfinite part of mathematics completely trustworthy? Why is there a general 'malaise' concerning the logical approach to the foundations of mathematics? What is the role of symmetry in physics? Is it possible to build a coherent worldview compatible with a macroobjectivistic position and based on the quantum picture of the world? What account can be given (...) of opinion change in the light of new evidence? These are some of the questions discussed in this volume, which collects 14 lectures on the foundations of science given at the School of Philosophy of Science, Trieste, October 1989. The volume will be of particular interest to any student or scholar engaged in interdisciplinary research into the foundations of science in the context of contemporary debates. (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)

The IOth International Congress of Logic, Methodology and Philosophy of Science, which took place in Florence in August 1995, offered a vivid and comprehensive picture of the present state of research in all directions of Logic and Philosophy of Science. The final program counted 51 invited lectures and around 700 contributed papers, distributed in 15 sections. Following the tradition of previous LMPS-meetings, some authors, whose papers aroused particular interest, were invited to submit their works for publication in a collection (...) of selected contributed papers. Due to the large number of interesting contributions, it was decided to split the collection into two distinct volumes: one covering the areas of Logic, Foundations of Mathematics and Computer Science, the other focusing on the general Philosophy of Science and the Foundations of Physics. As a leading choice criterion for the present volume, we tried to combine papers containing relevant technical results in pure and applied logic with papers devoted to conceptual analyses, deeply rooted in advanced present-day research. After all, we believe this is part of the genuine spirit underlying the whole enterprise of LMPS studies. (shrink)

This book constitutes the refereed proceedings of the Third International Symposium on Stochastic Algorithms: Foundations and Applications, SAGA 2005, held in Moscow, Russia in October 2005. The 14 revised full papers presented together with 5 invited papers were carefully reviewed and selected for inclusion in the book. The contributed papers included in this volume cover both theoretical as well as applied aspects of stochastic computations whith a special focus on new algorithmic ideas involving stochastic decisions and the (...) design and evaluation of stochastic algorithms within realistic scenarios. (shrink)

This collection of papers focuses on Philosophy as Metanoetics, the seminal work of the celebrated Japanese philosopher Tanabe Hajime (1885-1962).

This is a concise book that introduces students to the basics of logical thinking and important mathematical structures that are critical for a solid understanding of logical formalisms themselves as well as for building the necessary background to tackle other fields that are based on these logical principles. Despite its compact and small size, it includes many solved problems and quite a few end-of-section exercises that will help readers consolidate their understanding of the material. This textbook is essential reading (...) for anyone interested in the logical foundations of Informatics, Computer Science, Data Science, Artificial Intelligence, and other related areas. Written with undergraduate students in these disciplines in mind, this book can very well serve the needs of interested and curious readers who wish to get a grasp of the logical principles upon which these fields are built. This book does not require readers to possess math skills beyond those learned in high school. (shrink)

This edited work presents contemporary mathematical practice in the foundational mathematical theories, in particular set theory and the univalent foundations. It shares the work of significant scholars across the disciplines of mathematics, philosophy and computer science. Readers will discover systematic thought on criteria for a suitable foundation in mathematics and philosophical reflections around the mathematical perspectives. The first two sections focus on the two most prominent candidate theories for a foundation of mathematics. Readers may trace (...) current research in set theory, which has widely been assumed to serve as a framework for foundational issues, as well as new material elaborating on the univalent foundations, considering an approach based on homotopy type theory (HoTT). The further sections then build on this and are centred on philosophical questions connected to the foundations of mathematics. Here, the authors contribute to discussions on foundational criteria with more general thoughts on the foundations of mathematics which are not connected to particular theories. This book shares the work of some of the most important scholars in the fields of set theory (S. Friedman), non-classical logic (G. Priest) and the philosophy of mathematics (P. Maddy). The reader will become aware of the advantages of each theory and objections to it as a foundation, following the latest and best work across the disciplines and it is therefore a valuable read for anyone working on the foundations of mathematics or in the philosophy of mathematics. (shrink)

Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. This volume, the fifteenth publication in the Lecture Notes in Logic series, collects papers presented at the symposium 'Reflections on the Foundations of Mathematics' held in celebration of Solomon Feferman's 70th birthday (The 'Feferfest') at Stanford University, California (...) in 1988. Feferman has shaped the field of foundational research for nearly half a century. These papers reflect his broad interests as well as his approach to foundational research, which emphasizes the solution of mathematical and philosophical problems. There are four sections, covering proof theoretic analysis, logic and computation, applicative and self-applicative theories, and philosophy of modern mathematical and logic thought. (shrink)

The volume deals with the history of logic, the question of the nature of logic, the relation of logic and mathematics, modal or alternative logics (many-valued, relevant, paraconsistent logics) and their relations, including translatability, to classical logic in the Fregean and Russellian sense, and, more generally, the aim or aims of philosophy of logic and mathematics. Also explored are several problems concerning the concept of definition, non-designating terms, the interdependence of quantifiers, and the idea of an assertion sign. The contributions (...) concerned with Wittgenstein's investigations into the philosophy of logic and mathematics pursue issues relating to logical necessity, the undeniability of the law of the excluded middle, and the source of self-evidence, often characterized in the literature as the "rule-following considerations". Additionally, they examine Wittgenstein's attitudes towards the very idea of set-theory as a possible foundation for arithmetic. The volume also includes a number of contributions on specific issues concerning Wittgenstein's views on moral and religious judgements. (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)

Part 1 of this article exposed a tension between Poincaré’s views of arithmetic and geometry and argued that it could not be resolved by taking geometry to depend on arithmetic. Part 2 aims to resolve the tension by supposing not merely that intuition’s role is to justify induction on the natural numbers but rather that it also functions to acquaint us with the unity of orders and structures and show practices to fit or harmonize with experience. I argue that in (...) this manner, intuition serves the epistemological function of warranting generalizations and justifying practices. In particular, it justifies the application of group-theoretic notions in geometry but not the use of set-theoretic notions in arithmetic. (shrink)

This review essay analyzes the book by Giuseppe Primiero, On the foundations of computing. Oxford: Oxford University Press (ISBN 978-0-19-883564-6/hbk; 978-0-19-883565-3/pbk). xix, 296 p. (2020). It gives a critical view from the perspective of physical computing as a foundation of computing and argues that the neglected pillar of material computation (Stepney) should be brought centerstage and computing recognized as the fourth great domain of science (Denning).

This volume comprises a selection of papers that were contributed to the 7th International Congress of Logic, Methodology and Philosophy of Science, which was held in Salzburg from the 11th - 16th July, 1983. There were 14 sections in this congress: 1. proof theory and foundations of mathematics 2. model theory and its applica ti on 3. recursion theory and theory of computation 4. axiomatic set theory 5. philosophical logic 6. general methodology of science 7. foundations of (...) probability and induction 8. foundations and philosophy of the physical sciences 9. foundati ons and phi 1 osophy of biology 10. foundations and philosophy of psychology foundations and philosophy 11. of the social sciences 12. foundati ons and philosophy of linguistics 13. history of logic, methodology and philosophy of science 14. fundamental principles of the ethics of science In each section, three or four invited addresses were given, which will be published in the Congress Proceedings (Ruth Barcan Marcus, Georg J. W. Dorn and Paul Weingartner, eds. : Logic, Metho dology and Philosophy of Science VII. Proceedings of the Seventh International Congress of Logic, Methodology and Philosophy of v PREFACE Science, Salzburg, 1983. - Amsterdam, New York, Oxford: North-Holland Publishing 'Company, 1985. ) Every section with the exception of section 14 also contained contributed papers. (shrink)

This paper offers a review of Giuseppe Primero’s (2020) book “On the foundations of computing”_._ Mathematical, engineering, and experimental foundations of the science of computing are examined under the light of the notions of formal, physical, and experimental computational validity provided by the author. It is challenged the thesis that experimental computational validity can be defined only for the algorithmic method and not for the software development process. The notions of computational hypothesis and computational experiment provided by (...) Primiero (2020) are extended to the case of software development. Finally, it is highlighted how the hypothetical-deductive method is involved in the practice of using models to corroborate computational hypotheses in software testing. As a concluding remark, it is underlined how defining experimental computational validity in the context of software development offers a sound experimental foundation to the science of computing. (shrink)

Computing, today more than ever before, is a multi-faceted discipline which collates several methodologies, areas of interest, and approaches: mathematics, engineering, programming, and applications. Given its enormous impact on everyday life, it is essential that its debated origins are understood, and that its different foundations are explained. On the Foundations of Computing offers a comprehensive and critical overview of the birth and evolution of computing, and it presents some of the most important technical results and philosophical problems of (...) the discipline, combining both historical and systematic analyses. -/- The debates this text surveys are among the latest and most urgent ones: the crisis of foundations in mathematics and the birth of the decision problem, the nature of algorithms, the debates on computational artefacts and malfunctioning, and the analysis of computational experiments. By covering these topics, On the Foundations of Computing provides a much-needed resource to contextualize these foundational issues. -/- For practitioners, researchers, and students alike, a historical and philosophical approach such as what this volume offers becomes essential to understand the past of the discipline and to figure out the challenges of its future. (shrink)

Computational complexity theory is a branch of computer science dedicated to classifying computational problems in terms of their difficulty. While computability theory tells us what we can compute in principle, complexity theory informs us regarding our practical limits. In this chapter I argue that the science of \emph{quantum computing} illuminates complexity theory by emphasising that its fundamental concepts are not model-independent, but that this does not, as some suggest, force us to radically revise the foundations of the theory. (...) For model-independence never has been essential to those foundations. The fundamental aim of complexity theory is to describe what is achievable in practice under various models of computation for our various practical purposes. Reflecting on quantum computing illuminates complexity theory by reminding us of this, too often under-emphasised, fact. (shrink)

This volume presents essays by pioneering thinkers including Tyler Burge, Gregory Chaitin, Daniel Dennett, Barry Mazur, Nicholas Humphrey, John Searle and Ian Stewart. Together they illuminate the Map/Territory Distinction that underlies at the foundation of the scientific method, thought and the very reality itself. It is imperative to distinguish Map from the Territory while analyzing any subject but we often mistake map for the territory. Meaning for the Reference. Computational tool for what it computes. Representations are handy and tempting that (...) we often end up committing the category error of over-marrying the representation with what is represented, so much so that the distinction between the former and the latter is lost. This error that has its roots in the pedagogy often generates a plethora of paradoxes/confusions which hinder the proper understanding of the subject. What are wave functions? Fields? Forces? Numbers? Sets? Classes? Operators? Functions? Alphabets and Sentences? Are they a part of our map? Or do they actually belong to the territory? Researcher, like a cartographer, clothes the reality by stitching multitudes of maps that simultaneously co-exist. A simple apple, for example, can be analyzed from several viewpoints beginning with evolution and biology, all the way down its microscopic quantum mechanical components. Is there a reality out there apart from these maps? How do these various maps interact/intermingle with each other to produce a coherent reality that we interact with? Or do they not? Does our brain uses its own internal maps to facilitate “physicist/mathematician” in us to construct the maps about the external territories in turn? If so, what is the nature of these internal maps? Are there meta-maps? Evolution definitely fences our perception and thereby our ability to construct maps, revealing to us only those aspects beneficial for our survival. But the question is, to what extent? Is there a way out of the metaphorical Platonic cave erected around us by the nature? While “Map is not the territory” as Alfred Korzybski remarked, join us in this journey to know more, while we inquire on the nature and the reality of the maps which try to map the reality out there. The book also includes a foreword by Sir Roger Penrose and an afterword by Dagfinn Follesdal. (shrink)

This volume comprises seven of the eight addresses presented before the International Colloquium on Mathematical Logic and Foundations of Set theory held at the Acadmey Building in Jerusalem, Israel, On November 11-14, 1968.

Any attempt to conceptualize, categorize and constraint foundational issues in a living science, such as Computing, is bound to show its limitations and leave a number of open issues. Taking stock with some critical reviews of Primiero (On the foundations of computing, Oxford University Press, Oxford, 2019) published in this Journal, I overview potential new problems to be investigated by a foundational analysis of the science of computing.

The INBIOSA project brings together a group of experts across many disciplines who believe that science requires a revolutionary transformative step in order to address many of the vexing challenges presented by the world. It is INBIOSA’s purpose to enable the focused collaboration of an interdisciplinary community of original thinkers. This paper sets out the case for support for this effort. The focus of the transformative research program proposal is biology-centric. We admit that biology to date has been more fact-oriented (...) and less theoretical than physics. However, the key leverageable idea is that careful extension of the science of living systems can be more effectively applied to some of our most vexing modern problems than the prevailing scheme, derived from abstractions in physics. While these have some universal application and demonstrate computational advantages, they are not theoretically mandated for the living. A new set of mathematical abstractions derived from biology can now be similarly extended. This is made possible by leveraging new formal tools to understand abstraction and enable computability. [The latter has a much expanded meaning in our context from the one known and used in computer science and biology today, that is "by rote algorithmic means", since it is not known if a living system is computable in this sense (Mossio et al., 2009).] Two major challenges constitute the effort. The first challenge is to design an original general system of abstractions within the biological domain. The initial issue is descriptive leading to the explanatory. There has not yet been a serious formal examination of the abstractions of the biological domain. What is used today is an amalgam; much is inherited from physics (via the bridging abstractions of chemistry) and there are many new abstractions from advances in mathematics (incentivized by the need for more capable computational analyses). Interspersed are abstractions, concepts and underlying assumptions “native” to biology and distinct from the mechanical language of physics and computation as we know them. A pressing agenda should be to single out the most concrete and at the same time the most fundamental process-units in biology and to recruit them into the descriptive domain. Therefore, the first challenge is to build a coherent formal system of abstractions and operations that is truly native to living systems. Nothing will be thrown away, but many common methods will be philosophically recast, just as in physics relativity subsumed and reinterpreted Newtonian mechanics. -/- This step is required because we need a comprehensible, formal system to apply in many domains. Emphasis should be placed on the distinction between multi-perspective analysis and synthesis and on what could be the basic terms or tools needed. The second challenge is relatively simple: the actual application of this set of biology-centric ways and means to cross-disciplinary problems. In its early stages, this will seem to be a “new science”. This White Paper sets out the case of continuing support of Information and Communication Technology (ICT) for transformative research in biology and information processing centered on paradigm changes in the epistemological, ontological, mathematical and computational bases of the science of living systems. Today, curiously, living systems cannot be said to be anything more than dissipative structures organized internally by genetic information. There is not anything substantially different from abiotic systems other than the empirical nature of their robustness. We believe that there are other new and unique properties and patterns comprehensible at this bio-logical level. The report lays out a fundamental set of approaches to articulate these properties and patterns, and is composed as follows. -/- Sections 1 through 4 (preamble, introduction, motivation and major biomathematical problems) are incipient. Section 5 describes the issues affecting Integral Biomathics and Section 6 -- the aspects of the Grand Challenge we face with this project. Section 7 contemplates the effort to formalize a General Theory of Living Systems (GTLS) from what we have today. The goal is to have a formal system, equivalent to that which exists in the physics community. Here we define how to perceive the role of time in biology. Section 8 describes the initial efforts to apply this general theory of living systems in many domains, with special emphasis on crossdisciplinary problems and multiple domains spanning both “hard” and “soft” sciences. The expected result is a coherent collection of integrated mathematical techniques. Section 9 discusses the first two test cases, project proposals, of our approach. They are designed to demonstrate the ability of our approach to address “wicked problems” which span across physics, chemistry, biology, societies and societal dynamics. The solutions require integrated measurable results at multiple levels known as “grand challenges” to existing methods. Finally, Section 10 adheres to an appeal for action, advocating the necessity for further long-term support of the INBIOSA program. -/- The report is concluded with preliminary non-exclusive list of challenging research themes to address, as well as required administrative actions. The efforts described in the ten sections of this White Paper will proceed concurrently. Collectively, they describe a program that can be managed and measured as it progresses. (shrink)

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)

We argue that Wittgenstein’s philosophical perspective on Gödel’s most famous theorem is even more radical than has commonly been assumed. Wittgenstein shows in detail that there is no way that the Gödelian construct of a string of signs could be assigned a useful function within (ordinary) mathematics. — The focus is on Appendix III to Part I of Remarks on the Foundations of Mathematics. The present reading highlights the exceptional importance of this particular set of remarks and, more specifically, (...) emphasises its refined composition and rigorous internal structure. (shrink)

The Handbook of Computational Social Science is a comprehensive reference source for scholars across multiple disciplines. It outlines key debates in the field, showcasing novel statistical modeling and machine learning methods, and draws from specific case studies to demonstrate the opportunities and challenges in CSS approaches. The Handbook is divided into two volumes written by outstanding, internationally renowned scholars in the field. This first volume focuses on the scope of computational social science, ethics, and case studies. It covers a range (...) of key issues, including open science, formal modeling, and the social and behavioral sciences. This volume explores major debates, introduces digital trace data, reviews the changing survey landscape, and presents novel examples of computational social science research on sensing social interaction, social robots, bots, sentiment, manipulation, and extremism in social media. The volume not only makes major contributions to the consolidation of this growing research field, but also encourages growth into new directions. With its broad coverage of perspectives (theoretical, methodological, computational), international scope, and interdisciplinary approach, this important resource is integral reading for advanced undergraduates, postgraduates and researchers engaging with computational methods across the social sciences, as well as those within the scientific and engineering sectors. (shrink)

The computational view of mind rests on certain intuitions regarding the fundamental similarity between computation and cognition. We examine some of these intuitions and suggest that they derive from the fact that computers and human organisms are both physical systems whose behavior is correctly described as being governed by rules acting on symbolic representations. Some of the implications of this view are discussed. It is suggested that a fundamental hypothesis of this approach is that there is a natural domain of (...) human functioning that can be addressed exclusively in terms of a formal symbolic or algorithmic vocabulary or level of analysis. Much of the paper elaborates various conditions that need to be met if a literal view of mental activity as computation is to serve as the basis for explanatory theories. The coherence of such a view depends on there being a principled distinction between functions whose explanation requires that we posit internal representations and those that we can appropriately describe as merely instantiating causal physical or biological laws. In this paper the distinction is empirically grounded in a methodological criterion called the " cognitive impenetrability condition." Functions are said to be cognitively impenetrable if they cannot be influenced by such purely cognitive factors as goals, beliefs, inferences, tacit knowledge, and so on. Such a criterion makes it possible to empirically separate the fixed capacities of mind from the particular representations and algorithms used on specific occasions. In order for computational theories to avoid being ad hoc, they must deal effectively with the "degrees of freedom" problem by constraining the extent to which they can be arbitrarily adjusted post hoc to fit some particular set of observations. This in turn requires that the fixed architectural function and the algorithms be independently validated. It is argued that the architectural assumptions implicit in many contemporary models run afoul of the cognitive impenetrability condition, since the required fixed functions are demonstrably sensitive to tacit knowledge and goals. The paper concludes with some tactical suggestions for the development of computational cognitive theories. (shrink)

In computational complexity theory, decision problems are divided into complexity classes based on the amount of computational resources it takes for algorithms to solve them. In theoretical computer science, it is commonly accepted that only functions for solving problems in the complexity class P, solvable by a deterministic Turing machine in polynomial time, are considered to be tractable. In cognitive science and philosophy, this tractability result has been used to argue that only functions in P can feasibly work as (...) computational models of human cognitive capacities. One interesting area of computational complexity theory is descriptive complexity, which connects the expressive strength of systems of logic with the computational complexity classes. In descriptive complexity theory, it is established that only first-order systems are connected to P, or one of its subclasses. Consequently, second-order systems of logic are considered to be computationally intractable, and may therefore seem to be unfit to model human cognitive capacities. This would be problematic when we think of the role of logic as the foundations of mathematics. In order to express many important mathematical concepts and systematically prove theorems involving them, we need to have a system of logic stronger than classical first-order logic. But if such a system is considered to be intractable, it means that the logical foundation of mathematics can be prohibitively complex for human cognition. In this paper I will argue, however, that this problem is the result of an unjustified direct use of computational complexity classes in cognitive modelling. Placing my account in the recent literature on the topic, I argue that the problem can be solved by considering computational complexity for humanly relevant problem solving algorithms and input sizes. (shrink)