rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Advanced Łukasiewicz calculus and MV-algebras
  name:
    name part: Mundici, D.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: ne
    date issued: 2011
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XVIII, 258 p. online resource.
  abstract: In recent years, the discovery of the relationships between formulas in Łukasiewicz logic and rational polyhedra, Chang MV-algebras and lattice-ordered abelian roups, MV-algebraic states and coherent de Finetti’s assessments of continuous events, has changed the study and practice of many-valued logic. This book is intended as an up-to-date monograph on inﬁnite-valued Łukasiewicz logic and MV-algebras. Each chapter features a combination of classical and re¬cent results, well beyond the traditional domain of algebraic logic: among others, a comprehensive account is given of many eﬀective procedures that have been re¬cently developed for the algebraic and geometric objects represented by formulas in Łukasiewicz logic. The book embodies the viewpoint that modern Łukasiewicz logic and MV-algebras provide a benchmark for the study of several deep mathematical prob¬lems, such as Rényi conditionals of continuously valued events, the many-valued generalization of Carathéodory algebraic probability theory, morphisms and invari¬ant measures of rational polyhedra, bases and Schauder bases as jointly reﬁnable partitions of unity, and ﬁrst-order logic with [0,1]-valued identity on Hilbert space. Complete versions are given of a compact body of recent results and techniques, proving virtually everything that is used throughout, so that the book can be used both for individual study and as a source of reference for the more advanced reader.
  table of contents: Preface -- Chapter 1. Prologue: de Finetti coherence criterion and Łukasiewicz logic -- Chapter 2. Rational polyhedra, Interpolation, Amalgamation -- Chapter 3. The Galois connection (Mod, Th) in Ł∞ 21 -- Chapter 4. The spectral and the maximal spectral space -- Chapter 5. De Concini-Procesi theorem and Schauder bases -- Chapter 6. Bases and ﬁnitely presented MV-algebras -- Chapter 7. The free product of MV-algebras -- The construction of free products -- Chapter 8. Direct limits, conﬂuence and multisets -- Chapter 9. Tensors -- Chapter 10. States and the Kroupa-Panti Theorem -- Chapter 11. The MV-algebraic Loomis-Sikorski theorem.- Chapter 12. The MV-algebraic Stone-von Neumann theorem -- Chapter 13. Recurrence, probability, measure -- Chapter 14. Measuring polyhedra and averaging truth-values -- Chapter 15. A Rényi conditional in Łukasiewicz logic -- Chapter 16. The Lebesgue state and the completion of FREEn -- Chapter 17. Finitely generated projective MV-algebras -- Chapter 18. Eﬀective procedures for Ł∞ and MV-algebras -- Chapter 19. A ﬁrst-order Łukasiewicz logic with [0, 1]-identity -- Chapter 20. Applications, further reading, selected problems -- Chapter 21. Background results -- Special Bibliography. References. Index.
  note: by D. Mundici.
  subject:
    topic: Mathematics
  subject:
    topic: Mathematical logic
  subject:
    topic: Mathematics
  subject:
    topic: Mathematical Logic and Foundations
  classification: QA8.9-10.3
  classification: 511.3
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Trends in Logic ; 35
  identifier: 9789400708402
  identifier: http://dx.doi.org/10.1007/978-94-007-0840-2
  record info:
    record creation date: 110621
    record change date: 20151125232017.0
    record identifier: 978-94-007-0840-2