Archive for Mathematical Logic

, Volume 56, Issue 5–6, pp 585–605 | Cite as

A predicate extension of real valued logic

  • Stefano BaratellaEmail author


We study a predicate extension of an unbounded real valued propositional logic that has been recently introduced. The latter, in turn, can be regarded as an extension of both the abelian logic and of the propositional continuous logic. Among other results, we prove that our predicate extension satisfies the property of weak completeness (the equivalence between satisfiability and consistency) and, under an additional assumption on the set of premisses, the property of strong completeness (the equivalence between logical consequence and provability). Eventually we discuss some topological properties of the space of types in our logic.


Many-valued logic Unbounded truth values Real-valued logic Abelian logic Continuous logic 

Mathematics Subject Classification



Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Aliprantis, C.D., Burkinshaw, O.: Positive Operators. Springer, Berlin (2006)CrossRefzbMATHGoogle Scholar
  2. 2.
    Baratella, S., Zambella, D.: The real truth. Math. Log. Q. 61–1(2), 32–44 (2015)CrossRefzbMATHGoogle Scholar
  3. 3.
    Ben Yaacov, I.: Positive model theory and compact abstract theories. J. Math. Log. 3–1, 85–118 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Ben Yaacov, I.: Uncountable dense categoricity in cats. J. Symb. Log. 70–3, 829–860 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Ben Yaacov, I., et al.: Model theory for metric structures. In: Model Theory with Applications to Algebra and Analysis, vol. 2, pp. 315–427. London Mathematical Society Lecture Note Series, vol. 350. Cambridge Univ. Press, Cambridge (2008)Google Scholar
  6. 6.
    Ben Yaacov, I., Pedersen, A.P.: A proof of completeness for continuous first-order logic. J. Symb. Log. 75–1, 168–190 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Hewitt, E., Stromberg, K.: Real and Abstract Analysis, 3rd edn. Springer, Berlin (1975)zbMATHGoogle Scholar
  8. 8.
    Kelley, J.L.: General Topology. Springer, Berlin (1985)zbMATHGoogle Scholar
  9. 9.
    Luxemburg, W.A.J., Zaanen, A.C.: Riesz Spaces I. North-Holland, Amsterdam (1971)zbMATHGoogle Scholar
  10. 10.
    Meyer, R.K., Slaney, J.K.: Abelian logic from A to Z. In: Priest, G., et al. (eds.) Paraconsistent Logic: Essays on the Inconsistent, pp. 245–288. Philosophia, München (1989)Google Scholar
  11. 11.
    Pavelka, J.: On fuzzy logic III. Zeitschrift für Mathematische Logik und Grundlagen der Mathematik 25–5, 447–464 (1979)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Dipartimento di MatematicaUniversità di TrentoPovoItaly

Personalised recommendations