Advertisement

Rasiowa-Sikorski Style Relational Elementary Set Theory

  • Eugenio Omodeo
  • Ewa Orłowska
  • Alberto Policriti
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3051)

Abstract

A Rasiowa-Sikorski proof system is presented for an elementary set theory which can act as a target language for translating propositional modal logics. The proposed system permits a modular analysis of (modal) axioms in terms of deductive rules for the relational apparatus. Such an analysis is possible even in the case when the starting modal logic does not possess a first-order correspondent. Moreover, the formalism enables a fine-tunable and uniform analysis of modal deductions in a simple and purely set-theoretic language.

Keywords

Modal logic relational systems translation methods 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [BDMP97]
    van Benthem, J.F.A.K., D’Agostino, G., Montanari, A., Policriti, A.: Modal deduction in second-order logic and set theory-I. Journal of Logic and Computation 7(2), 251–265 (1997)zbMATHCrossRefMathSciNetGoogle Scholar
  2. [COP01]
    Cantone, D., Omodeo, E.G., Policriti, A.: Set theory for computing. from decision procedures to declarative programming with sets. Monographs in Computer Science. Springer, Heidelberg (2001)zbMATHGoogle Scholar
  3. [DMP95]
    D’Agostino, G., Montanari, A., Policriti, A.: A set-theoretic translation method for polymodal logics. Journal of Automated Reasoning 3(15), 317–337 (1995)CrossRefMathSciNetGoogle Scholar
  4. [DO00]
    Düntsch, I., Orłowska, E.: A proof system for contact relation algebras. Journal of Philosophical Logic (29), 241–262 (2000)Google Scholar
  5. [FO95]
    Frias, M., Orłowska, E.: A proof system for fork algebras and its applications to reasoning in logics based on intuitionism. Logique et Analyse (150-151-152), 239–284 (1995)Google Scholar
  6. [FO98]
    Frias, M., Orłowska, E.: Equational reasoning in nonclassical logics. Journal of Applied Non-Classical Logics 8(1-2), 27–66 (1998)zbMATHMathSciNetGoogle Scholar
  7. [FOP03]
    Formisano, A., Omodeo, E.G., Policriti, A.: Three-variable statements of set-pairing (2003) (submitted)Google Scholar
  8. [Jec78]
    Jech, T.J.: Set theory. Springer, New York (1978)Google Scholar
  9. [MO02]
    MacCaull, W., Orłowska, E.: Correspondence results for relational proof systems with application to the Lambek calculus. Studia Logica 71, 279–304 (2002)CrossRefGoogle Scholar
  10. [RS63]
    Rasiowa, H., Sikorski, R.: The mathematics of metamathematics. Polish Scientific Publishers, Warsaw (1963)zbMATHGoogle Scholar
  11. [SO96]
    Demri, S., Orłowska, E.: Logical analysis of demonic nondeterministic programs. Theoretical Computer Science (166), 173–202 (1996)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Eugenio Omodeo
    • 1
  • Ewa Orłowska
    • 2
  • Alberto Policriti
    • 3
  1. 1.Dipartimento di InformaticaUniversità di L’AquilaItaly
  2. 2.Institute of TelecommunicationsWarsawPoland
  3. 3.Dipartimento di Matematica e InformaticaUniversità di UdineItaly

Personalised recommendations