Journal of Logic, Language and Information

, Volume 24, Issue 3, pp 307–322 | Cite as

A Logic for Trial and Error Classifiers

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Abstract

Trial and error classifiers, corresponding to concepts which change their extensions over time, are introduced and briefly philosophically motivated. A fragment of the language of classical first-order logic is given a new semantics, using \(\omega \)-sequences of classical models, in order to interpret the basic predicates as classifiers of this kind. It turns out that we can use a natural deduction proof system which differs from classical logic only in the conditions for application of existential elimination. Soundness and completeness theorems are proved for this system.

Keywords

Classifiers Completeness Experimental logic Trial and error 

Notes

Acknowledgments

As usual, I am deep in intellectual debt to my collegues in the logic group at my department at the University of Gothenburg, and special mention goes to Christian Bennet and Fredrik Engström for outstanding generosity with their time. Valuable comments from two anonymous reviewers have been most helpful in revising the paper. Most ideas which underlie, or eventually became part of, this paper have previously been presented in different contexts, and I would in particular like to thank the Logic and Language group at ILLC, Amsterdam, for inviting me to give a talk at their colloquium on this subject. The work on this paper was partly funded by the foundation Kungliga och Hvitfeldtska stiftelsen.

References

  1. Jeroslow, R. (1975). Experimental logics and \({\varDelta }^0_2\)-theories. Journal of Philosophical Logic, 4, 253–267.CrossRefGoogle Scholar
  2. McCarthy, T., & Shapiro, S. (1987). Turing projectability. Notre Dame Journal of Formal Logic, 28(4), 520–535.CrossRefGoogle Scholar
  3. Peirce, C. S. (1877). The fixation of belief. In The essential Peirce: Selected philosophical writings (1867–1893) (Vol. 1, pp. 109–123), Indiana University Press.Google Scholar
  4. Putnam, H. (1965). Trial and error predicates and the solution to a problem of Mostowski. The Journal of Symbolic Logic, 30(1), 49–57.CrossRefGoogle Scholar
  5. van Benthem, J. (2010). Modal logic for open minds. Stanford: CSLI Publications.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Department of Philosophy, Linguistics and Theory of ScienceUniversity of GothenburgGothenburgSweden

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