Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-23T03:47:06.605Z Has data issue: false hasContentIssue false
  • English
  • Français

ON THE TERMINATION OF RUSSELL’S DESCRIPTION ELIMINATION ALGORITHM

Published online by Cambridge University Press:  21 September 2011

CLEMENS GRABMAYER ,
JOOP LEO ,
VINCENT VAN OOSTROM  and
ALBERT VISSER
CLEMENS GRABMAYER*
Affiliation:
Department of Philosophy, Utrecht University
JOOP LEO*
Affiliation:
Department of Philosophy, Utrecht University
VINCENT VAN OOSTROM*
Affiliation:
Department of Philosophy, Utrecht University
ALBERT VISSER*
Affiliation:
Department of Philosophy, Utrecht University
*
*DEPARTMENT OF PHILOSOPHY, UTRECHT UNIVERSITY, JANSKERKHOF 13A, UTRECHT, THE NETHERLANDS. E-mail:[email protected]
†DEPARTMENT OF PHILOSOPHY, UTRECHT UNIVERSITY, JANSKERKHOF 13A, UTRECHT, THE NETHERLANDS. E-mail:[email protected]
‡DEPARTMENT OF PHILOSOPHY, UTRECHT UNIVERSITY, JANSKERKHOF 13A, UTRECHT, THE NETHERLANDS. E-mail:[email protected]
§DEPARTMENT OF PHILOSOPHY, UTRECHT UNIVERSITY, JANSKERKHOF 13A, UTRECHT, THE NETHERLANDS. E-mail:[email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper we study the termination behavior of Russell’s description elimination rewrite system. We discuss certain claims made by Kripke (2005) in his paper concerning the possible nontermination of elimination of descriptions.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 4 , Issue 3 , September 2011 , pp. 367 - 393
Copyright
Copyright © Association for Symbolic Logic 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

BIBLIOGRAPHY

Church, A. (1940). A formulation of the simple theory of types. Journal of Symbolic Logic, 5, 56–68.CrossRefGoogle Scholar
Fleischer, R. (2007). Die another day. In Crescenzi, P., Prencipe, G., and Pucci, G., editors. FUN, volume 4475 of Lecture Notes in Computer Science. New York: Springer, pp. 146–155.Google Scholar
Gödel, K. (1944).Russell’s mathematical logic.In Schilpp, P. A., editor. The Philosophy of Bertrand Russell, volume 5 of The Library of Living Philosophers. Chicago, IL: Northwestern University Press, pp. 123–153.Google Scholar
Khasidashvili, Z. (1994). On higher order recursive program schemes. In Sophie, T., editor. Trees in Algebra and Programming, 19th International Colloquium, CAAP’94, Edinburgh, UK, April 1113, 1994, volume 787 of Lecture Notes in Computer Science. New York: Springer, pp. 172–186.Google Scholar
Korp, M., Sternagel, C., Zankl, H., & Middeldorp, A. (2009). Tyrolean termination tool 2. In Proceedings of the 20th International Conference on Rewriting Techniques and Applications, volume 5595 of Lecture Notes in Computer Science. Berlin: Brasília, pp. 295–304.Google Scholar
Kripke, S. (2005). Russell’s notion of scope. Mind, 114, 1005–1037.CrossRefGoogle Scholar
Levy, J., & Villaret, M. (2000). Linear second-order unification and context unification with tree-regular constraints. In Leo, B., editor. Rewriting Techniques and Applications, 11th International Conference, RTA 2000, Norwich, UK, July 10-12, 2000, Proceedings, volume 1833 of Lecture Notes in Computer Science. Berlin: Springer, pp. 156–171.Google Scholar
Mayr, R., & Nipkow, T. (1998). Higher-order rewrite systems and their confluence. Theoretical Computer Science, 192(1), 3–29.CrossRefGoogle Scholar
Moser, G. (2009). The Hydra battle and Cichon’s principle. Applicable Algebra in Engineering, Communication and Computing, 20(2), 133–158.CrossRefGoogle Scholar
Neale, S. (1990). Descriptions. Cambridge, MA: MIT Press.Google Scholar
Quine, W. V. O. (1937). New foundations for mathematical logic. American Mathematical Monthly, 44, 70–80.CrossRefGoogle Scholar
Quine, W. V. O. (1996). Mathematical Logic. Cambridge, MA: Harvard University Press.Google Scholar
Russell, R. (1905). On denoting. Mind, 14, 479–493.CrossRefGoogle Scholar
Russell, B., & Whitehead, A. N. (1970). Principia Mathematica to * 56. London: Cambridge University Press.Google Scholar
Terese. (2003). Term Rewriting Systems, volume 55 of Cambridge Tracts in Theoretical Computer Science. Cambridge: Cambridge University Press.Google Scholar
van Oostrom, V. (1997). Finite family developments. In Proceedings of the 8th International Conference on Rewriting Techniques and Applications, volume 1232 of Lecture Notes in Computer Science. Berlin: Springer, pp. 308–322.Google Scholar
Wolfram, D. A. (1993). The Clausal Theory of Types, volume 21 of Cambridge Tracts in Theoretical Computer Science. Cambridge: Cambridge University Press.CrossRefGoogle Scholar