Abstract
This paper develops and compares two tableaux-style proof systems for Peirce algebras. One is a tableau refutation proof system, the other is a proof system in the style of Rasiowa-Sikorski.
This work was supported by EU COST Action 274, and research grants GR/M88761 and GR/R92035 from the UK Engineering and Physical Sciences Research Council. Part of the work by the first author was done while on sabbatical leave at the Max-Planck-Institut für Informatik, Germany, in 2002.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Brink, C.: Boolean modules. J. Algebra 71(2), 291–313 (1981)
Brink, C., Britz, K., Schmidt, R.A.: Peirce algebras. Formal Aspects of Computing 6(3), 339–358 (1994)
Britz, K.: Relations and programs. Master’s thesis, Univ. Stellenbosch, South Africa (1988)
Dawson, J., Goré, R.: A mechanised proof system for relation algebra using display logic. In: Dix, J., Fariñas del Cerro, L., Furbach, U. (eds.) JELIA 1998. LNCS (LNAI), vol. 1489, pp. 264–278. Springer, Heidelberg (1998)
de Rijke, M.: Extending Modal Logic. PhD thesis, Univ. Amsterdam (1993)
Düntsch, I., Orlowska, E.: A proof system for contact relation algebras. J. Philos. Logic 29, 241–262 (2000)
Fitting, M.: First-Order Logic and Automated Theorem Proving. Texts and Monographs in Computer Science. Springer, Heidelberg (1990)
Gargov, G., Passy, S.: A note on Boolean modal logic. In: Petkov, P.P. (ed.) Mathematical Logic: Proc. 1988 Heyting Summerschool, pp. 299–309. Plenum Press, New York (1990)
Goré, R.: Cut-free display calculi for relation algebras. In: van Dalen, D., Bezem, M. (eds.) CSL 1996. LNCS, vol. 1258, pp. 198–210. Springer, Heidelberg (1997)
Hennessy, M.C.B.: A proof-system for the first-order relational calculus. J. Computer and System Sci. 20, 96–110 (1980)
Hustadt, U., Schmidt, R.A.: MSPASS: Modal reasoning by translation and first-order resolution. In: Dyckhoff, R. (ed.) TABLEAUX 2000. LNCS (LNAI), vol. 1847, pp. 67–71. Springer, Heidelberg (2000)
Lyndon, R.C.: The representation of relational algebras. Ann. Math. 51, 707–729 (1950)
MacCaull, W., Orlowska, E.: Correspondence results for relational proof systems with applications to the Lambek calculus. Studia Logica 71, 279–304 (2002)
Maddux, R.D.: A sequent calculus for relation algebras. Ann. Pure Applied Logic 25, 73–101 (1983)
Monk, J.D.: On representable relation algebras. Michigan Math. J. 11, 207–210 (1964)
Nellas, K.: Reasoning about sets and relations: A tableaux-based automated theorem prover for Peirce logic. Master’s thesis, Univ. Manchester, UK (2001)
Orlowska, E.: Relational formalisation of nonclassical logics. In: Brink, C., Kahl, W., Schmidt, G. (eds.) Relational Methods in Computer Science, Advances in Computing, pp. 90–105. Springer, Wien (1997)
Rasiowa, H., Sikorski, R.: The Mathematics of Metamathematics. Polish Scientific Publ., Warsaw (1963)
Schmidt, R.A.: Algebraic terminological representation. Master’s thesis, Univ. Cape Town, South Africa (1991); Available as Technical Report MPI-I- 91-216, Max-Planck-Institut für Informatik, Saarbrücken, Germany
Schmidt, R.A.: Relational grammars for knowledge representation. In: Böttner, M., Thümmel, W. (eds.) Variable-Free Semantics. Artikulation und Sprache, vol. 3, pp. 162–180. Secolo Verlag, Osnabrück (2000)
Schmidt, R.A., Hustadt, U.: Mechanised reasoning and model generation for extended modal logics. In: de Swart, H., Orłowska, E., Schmidt, G., Roubens, M. (eds.) Theory and Applications of Relational Structures as Knowledge Instruments. LNCS, vol. 2929, pp. 38–67. Springer, Heidelberg (2003) (to appear)
Schönfeld, W.: Upper bounds for a proof-search in a sequent calculus for relational equations. Z. Math. Logik Grundlagen Math. 28, 239–246 (1982)
Smullyan, R.M.: First Order Logic. Springer, Berlin (1971)
Tarski, A.: On the calculus of relations. J. Symbolic Logic 6(3), 73–89 (1941)
Wadge, W.W.: A complete natural deduction system for the relational calculus. Theory of Computation Report 5, Univ. Warwick (1975)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Schmidt, R.A., Orłowska, E., Hustadt, U. (2004). Two Proof Systems for Peirce Algebras. In: Berghammer, R., Möller, B., Struth, G. (eds) Relational and Kleene-Algebraic Methods in Computer Science. RelMiCS 2003. Lecture Notes in Computer Science, vol 3051. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24771-5_21
Download citation
DOI: https://doi.org/10.1007/978-3-540-24771-5_21
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-22145-6
Online ISBN: 978-3-540-24771-5
eBook Packages: Springer Book Archive