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Consistency of Variable Splitting in Free Variable Systems of First-Order Logic

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 3702))

Abstract

We prove consistency of a sequent calculus for classical logic with explicit splitting of free variables by means of a semantical soundness argument. The free variable system is a mature formulation of the system proposed at TABLEAUX 2003 [1]. We also identify some challenging and interesting open research problems.

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References

  1. Waaler, A., Antonsen, R.: A free variable sequent calculus with uniform variable splitting. In: Cialdea Mayer, M., Pirri, F. (eds.) TABLEAUX 2003, vol. 2796, pp. 214–229. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  2. Bibel, W.: Automated Theorem Proving, 2nd edn. Vieweg Verlag (1987)

    Google Scholar 

  3. Antonsen, R.: Uniform variable splitting. In: Contributions to the Doctoral Programme of the Second International Joint Conference on Automated Reasoning (IJCAR 2004). CEUR Workshop Proceedings, Cork, Ireland, July 04-July 08, 2004. Vol. 106, pp. 1–5 (2004), Online: http://ceur-ws.org/Vol-106/01-antonsen.pdf

  4. Wallen, L.A.: Automated deduction in nonclassical logics. MIT Press, Cambridge (1990)

    Google Scholar 

  5. Hähnle, R.: Tableaux and related methods. In: Robinson, A., Voronkov, A. (eds.) Handbook of Automated Reasoning, vol. I, pp. 100–178. Elsevier Science, Amsterdam (2001)

    Google Scholar 

  6. Letz, R.: Clausal tableaux. In: Bibel, W., Schmidt, P.H. (eds.) Automated Deduction: A Basis for Applications. Foundations: Calculi and Methods, vol. I. Kluwer Academic Publishers, Dordrecht (1998)

    Google Scholar 

  7. Letz, R., Stenz, G.: Universal variables in disconnection tableaux. In: Cialdea Mayer, M., Pirri, F. (eds.) TABLEAUX 2003, vol. 2796, pp. 117–133. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  8. Giese, M.: Incremental Closure of Free Variable Tableaux. In: Goré, R.P., Leitsch, A., Nipkow, T. (eds.) IJCAR 2001. LNCS, vol. 2083, pp. 545–560. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  9. Hansen, C.M.: Incremental Proof Search in the Splitting Calculus. Master’s thesis, Dept. of Informatics, University of Oslo (2004)

    Google Scholar 

  10. Antonsen, R.: Free variable sequent calculi. Master’s thesis, University of Oslo, Language, Logic and Information, Department of Linguistics (2003)

    Google Scholar 

  11. Smullyan, R.M.: First-Order Logic. Ergebnisse der Mathematik und ihrer Grenzgebiete, vol. 43. Springer, Heidelberg (1968)

    MATH  Google Scholar 

  12. Waaler, A.: Connections in nonclassical logics. In: Robinson, A., Voronkov, A. (eds.) Handbook of Automated Reasoning, vol. II, pp. 1487–1578. Elsevier Science, Amsterdam (2001)

    Chapter  Google Scholar 

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© 2005 Springer-Verlag Berlin Heidelberg

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Antonsen, R., Waaler, A. (2005). Consistency of Variable Splitting in Free Variable Systems of First-Order Logic. In: Beckert, B. (eds) Automated Reasoning with Analytic Tableaux and Related Methods. TABLEAUX 2005. Lecture Notes in Computer Science(), vol 3702. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11554554_5

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  • DOI: https://doi.org/10.1007/11554554_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-28931-9

  • Online ISBN: 978-3-540-31822-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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