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Negation: Two Points of View

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Book cover What is Negation?

Part of the book series: Applied Logic Series ((APLS,volume 13))

Abstract

In this paper we look at negation from two different points of view: a syntactical one and a semantical one. Accordingly, we identify two different types of negation. The same connective of a given logic might be of both types, but this might not always be the case.

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References

  1. O. Arieli and A. Avron. Logical Bilattices and Inconsistent Data, Proceedings of the 9th IEEE Annual Symp. on Logic in Computer Science, pp. 468-476. IEEE Press, 1994.

    Google Scholar 

  2. O. Arieli and A. Avron. Reasoning with Logical Bilattices. Journal of Logic, Language and Information, 5, 25 – 63, 1996.

    Article  Google Scholar 

  3. A. R. Anderson and N. D. Belnap. Entailment. Vol. 1. Princeton University Press, Princeton, NJ, 1975.

    Google Scholar 

  4. A. R. Anderson and N. D. Belnap. Entailment. Vol. 2. Princeton University Press, Princeton, NJ, 1992.

    Google Scholar 

  5. A. Almukdad and D. Nelson. Constructible falsity and inexact predicates. Journal of Symbolic Logic, 49, 231 – 333, 1984.

    Article  Google Scholar 

  6. A. Avron. On an implication connective of RM. Notre Dame Journal of Formal Logic, 27, 201 – 209, 1986.

    Article  Google Scholar 

  7. A. Avron. The semantics and proof theory of linear logic. Journal of Theoretical Computer Science, 57, 161 – 184, 1988.

    Article  Google Scholar 

  8. A. Avron. Relevance and paraconsistency - a new approach. Journal of Symbolic Logic, 55, 707 – 732, 1990.

    Article  Google Scholar 

  9. A. Avron. Relevance and paraconsistency - a new approach. Part II: the formal systems. Notre Dame Journal of Formal Logic, 31, 169 – 202, 1990.

    Article  Google Scholar 

  10. A. Avron. Simple consequence relations. Information and Computation, 92, 105 – 139, 1991.

    Article  Google Scholar 

  11. A. Avron. Natural 3-valued logics—characterization and proof theory. Journal of Symbolic Logic, 56, 276 – 294, 1991.

    Article  Google Scholar 

  12. A. Avron. On negation, consistency and completeness. To appear in the second edition of the Handbook of Philosophical Logic, D. M. Gabbay and F. Guenthner, eds. Kluwer Academic Publishers.

    Google Scholar 

  13. A. Avron. What is a logical system?. In What is a Logical System? D. Gabbay, ed. Oxford Science Publications, Clarendon Press, Oxford, 1994.

    Google Scholar 

  14. H. Barringer, J. H. Cheng and C. B. Jones. A logic covering undefiness in program proofs. Acta Informatica, 21, 251 – 269, 1984.

    Article  Google Scholar 

  15. J. P. Cleave. A Study of Logics. Oxford Logic Guides, Clarendon Press, Oxford, 1991.

    Google Scholar 

  16. N. C. A. da-Costa. Theory of inconsistent formal systems. Notre Dame Journal of Formal Logic, 15, 497 – 510, 1974.

    Article  Google Scholar 

  17. I. M. L. D’Ottaviano. The completeness and compactness of a three-valued first-order logic. Re-vista Colombiana de Matematicas, XIX, 31 – 42, 1985.

    Google Scholar 

  18. J. M. Dunn. Relevant logic and entailment. In Handbook of Philosophical Logic, Vol III. D. M. Gabbay and F. Guenthner, eds. Reidel, Dordrecht, 1986.

    Google Scholar 

  19. R. L. Epstein. The Semantic Foundations of Logic. Vol. 1: Propositional Logics, 2nd Edition, Oxford University Press, 1995.

    Google Scholar 

  20. R. Fagin, J. Y. Halpern and Y. Vardi. What is an inference rule? Journal of Symbolic Logic, 57, 1017 – 1045, 1992.

    Article  Google Scholar 

  21. D. M. Gabbay. Semantical Investigations in Heyting’s Intuitionistic Logic. Reidel, Dordrecht, 1981.

    Google Scholar 

  22. D. M. Gabbay, ed. What is a Logical System? Oxford Science Publications, Clarendon Press, Oxford, 1994.

    Google Scholar 

  23. J. Y. Girard. Linear logic. Theoretical Computer Science, 50, 1 – 101, 1987.

    Article  Google Scholar 

  24. I. Hacking. What is logic? The Journal of Philosophy, 76, 285–318, 1979. Reprinted in [22].

    Google Scholar 

  25. C. B. Jones. Systematic software development using VDM, Journal of Symbolic Logic, 24, 324, 1959.

    Google Scholar 

  26. F. von Kutschera. Ein verallgemeinerter Widerlegungsbegriff für Gentzenkalkule. Archiv für Mathematische Logik and Grundlagenforschung, 12, 104 – 118, 1969.

    Article  Google Scholar 

  27. H. Ono and Y. Komori. Logics without the contraction rule. The Journal of Symbolic Logic, 50, 169 – 201, 1985.

    Article  Google Scholar 

  28. L. I. Rozonoer. On interpretation of inconsistent theories. Information Sciences, 47, 243 – 266, 1989.

    Article  Google Scholar 

  29. D. Scott. Rules and derived rules. In Logical Theory and Semantical Analysis, S. Stenlund, ed. pp. 147 – 161. Reidel, Dordrecht, 1974.

    Google Scholar 

  30. D. Scott. Completeness and axiomatizability in many-valued logic. In Proceeding of the Tarski Symposium, Proceeding of Symposia in Pure Mathematics, Vol. XXV, pp. 411 – 435. American Mathematical Society, Rhode Island, 1974.

    Google Scholar 

  31. R. Schroeder-Heister and K. Dosen, eds. Substructural Logics. Oxford Science Publications, Clarendon Press, Oxford, 1993.

    Google Scholar 

  32. B. Sobocinski. Axiomatization of partial system of three-valued calculus of propositions. The Journal of Computing Systems, 11, 23 – 55, 1952.

    Google Scholar 

  33. A. Urquhart. Many-valued logic. In Handbook of Philosophical Logic, Vol III. D. M. Gabbay and F. Guenthner, eds. Reidel, Dordrecht, 1984.

    Google Scholar 

  34. H. Wansing. The Logic of Information Structures. LNAI 681, Springer-Verlag, 1993

    Google Scholar 

  35. R. Wojcicki. Theory of Logical Calculi, Synthese Library, Vol. 199, Kluwer Academic Publishers, 1988.

    Google Scholar 

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© 1999 Springer Science+Business Media Dordrecht

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Avron, A. (1999). Negation: Two Points of View. In: Gabbay, D.M., Wansing, H. (eds) What is Negation?. Applied Logic Series, vol 13. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9309-0_1

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  • DOI: https://doi.org/10.1007/978-94-015-9309-0_1

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-5169-1

  • Online ISBN: 978-94-015-9309-0

  • eBook Packages: Springer Book Archive

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