Areas of Mathematics

Edited by Nemi Boris Pelgrom (Ludwig Maximilians Universität, München)
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  1. Towards a Computational Ontology for the Philosophy of Wittgenstein: Representing Aspects of the Tractarian Philosophy of Mathematics.Jakub Gomułka - 2023 - Analiza I Egzystencja 63:27-54.
    The present paper concerns the Wittgenstein ontology project: an attempt to create a Semantic Web representation of Ludwig Wittgenstein’s philosophy. The project has been in development since 2006, and its current state enables users to search for information about Wittgenstein-related documents and the documents themselves. However, the developers have much more ambitious goals: they attempt to provide a philosophical subject matter knowledge base that would comprise the claims and concepts formulated by the philosopher. The current knowledge representation technology is not (...)
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  2. Algorithm theory - SWAT 2014: 14th Scandinavian Symposium and Workshops, Copenhagen, Denmark, July 2-4, 2014: proceedings.R. Ravi & Inge Li Gørtz (eds.) - 2014 - New York: Springer.
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  3. Die Struktur formalisierter Sprachen.Herbert Pilch (ed.) - 1965 - Darmstadt,: Deutsches Rechenzentrum.
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  4. Reduktionstypen der Prädikatenlogik.Dieter Rödding - 1970 - Münster i.: W., Westfälische Wilhelms-Universität Münster, Institut für Mathematische Logik und Grundlagenforschung.
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  5. Boolesche Funktionen und Postsche Klassen.Sergeĭ Vsevolodovich I︠A︡blonskiĭ - 1970 - Basel,: C. F. Winter. Edited by Gavrilov, Gariĭ Petrovich, [From Old Catalog], Kudri︠a︡vt︠s︡ev & Valeriĭ Borisovich.
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  6. Aspectos de la lógica modal.David Makinson - 1971 - Bahía Blanca,: Universidad Nacional del Sur, Instituto de Matemática.
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  7. Logica simbolică.Gheorghe Enescu - 1971 - București,: Editura știinţifică.
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  8. Notions de logique.Jean Drabbe - unknown - Bruxelles,: Centre belge de pédagogie de la mathématique, av. Albert.
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  9. Modelltheorie.Georg Kreisel - 1972 - Berlin,: Springer. Edited by J. L. Krivine.
    Wir betrachten hier jenen Teil der Grundlagenforschung, der die "intui­ tive" oder "inhaltliche" Mathematik, d. h. das, was ein gew6hnlicher Mathematiker unter Mathematik versteht, systematisch beschreibt und analysiert. Im deskriptiven Teil wird die informale Mathematik in einer formal en Sprache (z. B. der der Mengenlehre) neu formuliert. Eine solche Sprache hat, verglichen mit der Sprache der informalen Mathematik, ein sehr eingeschr~nktes Vokabular und eine vollkommen exakte Grammatik; dadurch wird naturlich die Pr~zision erh6ht und der Blick von Unwesentlichem befreit. Im Gegensatz (...)
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  10. Infinitary logic: in memoriam Carol Karp: a collection of papers by various authors.Carol Karp & D. W. Kueker (eds.) - 1975 - New York: Springer Verlag.
    López-Escobar, E. G. K. Introduction.--Kueker, D. W. Back-and-forth arguments and infinitary logics.--Green, J. Consistency properties for finite quantifier languages.--Cunningham, E. Chain models.--Gregory, J. On a finiteness condition for infinitary languages.
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  11. Las paradojas de la lógica.Evert Willem Beth - 1975 - [Valencia]: Departamento de Lógica y Filosofía de la Ciencia, Universidad de Valencia.
  12. Introduzione alle logiche polivalenti.Michele Marsonet - 1976 - Roma: Abete.
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  13. Logik, Mengen, Relationen: Praxis d. math. Beweisens.H. Freund - 1976 - Stuttgart: Teubner. Edited by Peter Sorger.
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  14. Systemy nonsense-logics.Krystyna Piróg-Rzepecka - 1977 - Wrocław: Państwowe Wydawn. Naukowe.
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  15. Algoritmy vokrug nas.N. A. Krinit︠s︡kiĭ - 1977 - Moskva: Nauka.
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  16. Logikkalküle.Michael M. Richter - 1978 - Stuttgart: Teubner.
    In diesem Buch werden Aspekte der Aussagenlogik und der Prädikaten­ logik der ersten Stufe behandelt. Eine Mathematisierung und Kalkü­ lisierung der Logik kann natürlich ganz verschieden ausfallen, je nach dem, von welchen Motiven man sich primär leiten läßt. Wir stellen drei Gesichtspunkte, die uns auch als die wesentlichsten erscheinen, in den Vordergrund: Die Formalisierung des Wahrheits­ begriffes, die Formalisierung des Beweisbarkeitsbegriffes und das Problem des Suchens nach Beweisen. Diese drei Aspekte führen zu drei verschiedenen Arten von Kalkülen. Die Betonung des (...)
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  17. Kvantumlogika.Gyula Fáy - 1978 - Budapest: Gondolat. Edited by Róbert Tőrös.
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  18. Klassische und nichtklassische Aussagenlogik.Wolfgang Rautenberg - 1979 - Wiesbaden: Vieweg.
    Der Fortschritt der Aussagenlogik in jungster Zeit HiBt es sinnvoll erscheinen, einen breiteren Leserkreis mit dieser Entwicklung bekannt zu machen. Obwohl vorliegendes Buch als Lehrbuch, nicht als Monographie fUr einen engeren Spezialistenkreis konzipiert wurde, soli es in einigen Themen einen tieferen Einblick in den aktuellen Stand der Dinge vermitteln. Kap. lund ein Tei! von Kap. II befassen sich mit der zweiwertigen Aussagenlogik und sind fUr Leser gedacht, die an Logik interessiert sind, doch noch nicht niiher mit ihr befaBt waren. Die (...)
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  19. Recursion theory: its generalisations and applications: proceedings of Logic Colloquium '79, Leeds, August 1979.F. R. Drake & S. S. Wainer (eds.) - 1980 - New York: Cambridge University Press.
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  20. Prädikatenlogik ohne gebundene Variablen.Jürgen Bartnick - 1980 - Frankfurt am Main: P. Lang.
    Wenn es eine Aufgabe der Philosophie ist, die Herrschaft des Wortes über den menschlichen Geist zu brechen (Frege), dann ist zu fragen, ob die Prädikatenlogik die Wörter «für alle» und «es gibt» angemessen formalisiert. Übersetzt man «alle Menschen sind sterblich» mit «für alle x : wenn x ein Mensch ist, dann ist x sterblich», so hat man zwar die Syllogistik des Aristoteles überwunden, dafür tritt jetzt aber eine Variable x auf, die in der Aussage vorher nicht vorkam.
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  21. Constructive Type Theory, an appetizer.Laura Crosilla - forthcoming - In Peter Fritz & Nicholas K. Jones (eds.), Higher-Order Metaphysics. Oxford University Press.
    Recent debates in metaphysics have highlighted the significance of type theories, such as Simple Type Theory (STT), for our philosophical analysis. In this chapter, I present the salient features of a constructive type theory in the style of Martin-Löf, termed CTT. My principal aim is to convey the flavour of this rich, flexible and sophisticated theory and compare it with STT. I especially focus on the forms of quantification which are available in CTT. A further aim is to argue that (...)
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  22. V.A. Yankov on Non-Classical Logics, History and Philosophy of Mathematics.Alex Citkin & Ioannis M. Vandoulakis (eds.) - 2022 - Springer, Outstanding Contributions To Logic (volume 24).
    This book is dedicated to V.A. Yankov’s seminal contributions to the theory of propositional logics. His papers, published in the 1960s, are highly cited even today. The Yankov characteristic formulas have become a very useful tool in propositional, modal and algebraic logic. The papers contributed to this book provide the new results on different generalizations and applications of characteristic formulas in propositional, modal and algebraic logics. In particular, an exposition of Yankov’s results and their applications in algebraic logic, the theory (...)
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  23. Nichtklassische Logik: eine Einführung.Lothar Kreiser, Siegfried Gottwald & Werner Stelzner (eds.) - 1988 - Berlin: Akademie Verlag.
  24. Estudios de lógica borrosa y sus aplicaciones.Alejandro Sobrino E. Senén Barro (ed.) - 1993 - [Santiago de Compostela]: Universidad de Santiago de Compostela.
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  25. Einführung in die Fuzzy-Logik.Dirk H. Traeger - 1994 - Stuttgart: Teubner.
  26. Louis Couturat--Traité de logique algorithmique.Louis Couturat - 2010 - [Basel?]: Birkhäuser. Edited by Oliver Schlaudt & Mohsen Sakhri.
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  27. La logique, un aiguillon pour la pensée.Jean-Paul Delahaye - 2012 - Paris: Belin: Pour la science.
    Ce livre est un recueil des articles que l'auteur a publiés dans la rubrique Logique et Calcul du magazine Pour la Science. La sélection a pour thème la logique dans toute sa diversité. Par exemple, elle peut concerner les mathématiques pures : L'infini est-il paradoxal en mathématiques, Libre arbitre et mécanique quantique ou Les limites logiques des mathématiques. Mais on la trouve aussi au coeur d'applications concrètes. Ainsi, L'étonnante loi de Benford, selon laquelle un nombre pris au hasard, par exemple (...)
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  28. Type theory and formal proof: an introduction.R. P. Nederpelt - 2014 - New York: Cambridge University Press. Edited by Herman Geuvers.
    Type theory is a fast-evolving field at the crossroads of logic, computer science and mathematics. This gentle step-by-step introduction is ideal for graduate students and researchers who need to understand the ins and outs of the mathematical machinery, the role of logical rules therein, the essential contribution of definitions and the decisive nature of well-structured proofs. The authors begin with untyped lambda calculus and proceed to several fundamental type systems culminating in the well-known and powerful Calculus of Constructions. The book (...)
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  29. Soft computing applications for renewable energy and energy efficiency.Garcia Cascales & Maria del Socorro (eds.) - 2015 - Hershey, PA: Information Science Reference.
    This book brings together the latest technological research in computational intelligence and fuzzy logic as a way to care for our environment, highlighting current advances and future trends in environmental sustainability using the principles of soft computing.
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  30. Penser l'épistémologie non classique des mathématiques chez Imré Lakatos.Fabrice Moussiessi - 2016 - Paris: L'Harmattan. Edited by Marcel Nguimbi.
    L'ouvrage invite à penser l'épistémologie non classique des mathématiques comme une construction épistémique des mathématiques quasi empirique qu'Imré Lakatos a réalisé au moyen des présupposés ontologiques (comme la redécouverte du temps, le passage du déterminisme à l'indéterminisme, etc.) et qu'il réussit grâce à l'implémentation du principe de complexité dialectique de l'esprit mathématique. L'auteur étudie la thèse selon laquelle, depuis le début du XXe siècle, la science est aussi bien objective que subjective. Et c'est à partir de celle-ci que le principe (...)
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  31. Fuzzy logic theory and applications: Part I and Part II.Lotfi A. Zadeh - 2018 - New Jersey: World Scientific. Edited by R. A. Aliev.
    part 1. Fuzzy logic theory 1 -- part 2. Applications and advanced topics of fuzzy logic.
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  32. The digital and the real world: computational foundations of mathematics, science, technology, and philosophy.Klaus Mainzer - 2018 - [Hackensack,] New Jersey: World Scientific.
  33. Propositional logics of logical truth.A. C. Paseau & Owen Griffiths - 2021 - In Gil Sagi & Jack Woods (eds.), The Semantic Conception of Logic : Essays on Consequence, Invariance, and Meaning. Cambridge University Press.
  34. There might be a paradox of logical validity after all.Roy Cook - 2021 - In Gil Sagi & Jack Woods (eds.), The Semantic Conception of Logic : Essays on Consequence, Invariance, and Meaning. Cambridge University Press.
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  35. Introduction: The semantic conception of logic : problems and prospects.Gil Sagi & Jack Woods - 2021 - In Gil Sagi & Jack Woods (eds.), The Semantic Conception of Logic : Essays on Consequence, Invariance, and Meaning. Cambridge University Press.
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  36. An Introduction to Many-valued Logics.Robert John Ackermann - 1967 - New York,: Routledge.
    Originally published in 1967. An introduction to the literature of nonstandard logic, in particular to those nonstandard logics known as many-valued logics. Part I expounds and discusses implicational calculi, modal logics and many-valued logics and their associated calculi. Part II considers the detailed development of various many-valued calculi, and some of the important metathereoms which have been proved for them. Applications of the calculi to problems in the philosophy are also surveyed. This work combines criticism with exposition to form a (...)
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  37. Fuzzy Logic and Mathematics: A Historical Perspective.Radim Bělohlávek, Joseph W. Dauben & George J. Klir - 2017 - Oxford, England and New York, NY, USA: Oxford University Press. Edited by Joseph Warren Dauben & George J. Klir.
    The term "fuzzy logic," as it is understood in this book, stands for all aspects of representing and manipulating knowledge based on the rejection of the most fundamental principle of classical logic---the principle of bivalence. According to this principle, each declarative sentence is required to be either true or false. In fuzzy logic, these classical truth values are not abandoned. However, additional, intermediate truth values between true and false are allowed, which are interpreted as degrees of truth. This opens a (...)
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  38. The Semantic Conception of Logic : Essays on Consequence, Invariance, and Meaning.Gil Sagi & Jack Woods (eds.) - 2021 - New York, NY: Cambridge University Press.
    This collection of new essays presents cutting-edge research on the semantic conception of logic, the invariance criteria of logicality, grammaticality, and logical truth. Contributors explore the history of the semantic tradition, starting with Tarski, and its historical applications, while central criticisms of the tradition, and especially the use of invariance criteria to explain logicality, are revisited by the original participants in that debate. Other essays discuss more recent criticism of the approach, and researchers from mathematics and linguistics weigh in on (...)
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  39. Are They Class-names?J. M. Hinton - 1982 - Philosophy 57 (219):27-50.
    We often, in effect, take it for granted that some word or phrase is what is called ‘the name of a class, be that class empty or non-empty’. We do so whenever in effect we either wonder about, or mean to be taking a view on, the number of members a certain suppositious class has, on the ultrasimple number scale: ‘None, more than none’.
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  40. Real Numbers, Generalizations of the Reals and Theories of Continua.Philip Ehrlich - 1996 - British Journal for the Philosophy of Science 47 (2):320-324.
  41. Review of Real Numbers, Generalizations of the Reals, & Theories of Continua by Philip Ehrlich. [REVIEW]Colin McLarty - 1999 - Philosophy of Science 66 (3):500-501.
  42. Belief, construction, and language: Philosophical lenses on issues of understanding and cognition in mathematics.Bradley Thomas Baker - unknown
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  43. The Emergence of Meaning.Stephen Crain - 2012 - Cambridge University Press.
    Over the past forty years, scientists have developed models of human reasoning based on the principle that human languages and classical logic involve fundamentally different concepts and different methods of interpretation. In The Emergence of Meaning Stephen Crain challenges this view, arguing that a common logical nativism underpins human language and logical reasoning. The approach which Crain takes is twofold. Firstly, he uncovers the underlying meanings of logical expressions and logical principles that appear in typologically different languages - English and (...)
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  44. On Numerations of a Formal System.Hidehisa Sakai - 1974 - Annals of the Japan Association for Philosophy of Science 4 (4):227-230.
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  45. A System of Simple Type Theory with Type Variables.Sh^|^Ocirc Maehara & Ji - 1969 - Annals of the Japan Association for Philosophy of Science 3 (4):131-137.
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  46. An Extension of the Craig-Sch^|^uuml;tte Interpolation Theorem.Takashi Nagashima - 1966 - Annals of the Japan Association for Philosophy of Science 3 (1):12-18.
  47. A Note on Constructive Ordinals.Akiko Kino - 1964 - Annals of the Japan Association for Philosophy of Science 2 (4):189-198.
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  48. La fonction propositionelle de Principia Mathematica.Akira Oide - 1958 - Annals of the Japan Association for Philosophy of Science 1 (3):171-186.
  49. On the Formal Theory of the Ordinal Diagrams.Gaisi Takeuti - 1958 - Annals of the Japan Association for Philosophy of Science 1 (3):151-170.
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  50. A combinatorial version of the Svenonius theorem on definability.A. L. Semenov & S. F. Soprunov - 2015 - Logic Journal of the IGPL 23 (6):966-975.
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