## Notre Dame Journal of Formal Logic

### A Remark on Negation in Dependence Logic

#### Abstract

We show that for any pair $\phi$ and $\psi$ of contradictory formulas of dependence logic there is a formula $\theta$ of the same logic such that $\phi\equiv\theta$ and $\psi\equiv\neg\theta$. This generalizes a result of Burgess.

#### Article information

Source
Notre Dame J. Formal Logic, Volume 52, Number 1 (2011), 55-65.

Dates
First available in Project Euclid: 13 December 2010

https://projecteuclid.org/euclid.ndjfl/1292249610

Digital Object Identifier
doi:10.1215/00294527-2010-036

Mathematical Reviews number (MathSciNet)
MR2747162

Zentralblatt MATH identifier
1216.03048

#### Citation

Kontinen, Juha; Väänänen, Jouko. A Remark on Negation in Dependence Logic. Notre Dame J. Formal Logic 52 (2011), no. 1, 55--65. doi:10.1215/00294527-2010-036. https://projecteuclid.org/euclid.ndjfl/1292249610

#### References

• [1] Armstrong, W. W., "Dependency structures of data base relationships", pp. 580--83 in Information Processing 74 (Proceedings of the IFIP Congress, Stockholm, 1974), North-Holland, Amsterdam, 1974.
• [2] Burgess, J. P., "A remark on Henkin sentences and their contraries", Notre Dame Journal of Formal Logic, vol. 44 (2003), pp. 185--88.
• [3] Cameron, P., and W. Hodges, "Some combinatorics of imperfect information", The Journal of Symbolic Logic, vol. 66 (2001), pp. 673--84.
• [4] Craig, W., "Linear reasoning. A new form of the Herbrand-Gentzen theorem", The Journal of Symbolic Logic, vol. 22 (1957), pp. 250--68.
• [5] Enderton, H. B., "Finite partially-ordered quantifiers", Zeitschrift für mathematische Logik und Grundlagen der Mathematik, vol. 16 (1970), pp. 393--97.
• [6] Henkin, L., "Some remarks on infinitely long formulas", pp. 167--83 in Infinitistic Methods (Proceedings of the Symposium on the Foundations of Mathematics, Warsaw, 1959), Pergamon, Oxford, 1961.
• [7] Hodges, W., "Compositional semantics for a language of imperfect information", Logic Journal of the IGPL, vol. 5 (1997), pp. 539--63.
• [8] Hodges, W., "Some strange quantifiers", pp. 51--65 in Structures in Logic and Computer Science, vol. 1261 of Lecture Notes in Computer Science, Springer, Berlin, 1997.
• [9] Kontinen, J., and J. Väänänen, "On definability in dependence logic", Journal of Logic, Language and Information, vol. 18 (2009), pp. 317--32.
• [10] Kontinen, J., and J. Väänänen, Erratum: On definability in dependence logic,'' To appear in Journal of Logic, Language and Information. DOI: 10.1007/s10849-010-9125-6.
• [11] Väänänen, J., "A remark on nondeterminacy in IF" logic, Acta Philosophica Fennica, vol. 78 (2006), pp. 71--77.
• [12] Väänänen, J., Dependence Logic: A New Approach to Independence Friendly Logic, vol. 70 of London Mathematical Society Student Texts, Cambridge University Press, Cambridge, 2007.
• [13] Walkoe, W. J., Jr., "Finite partially-ordered quantification", The Journal of Symbolic Logic, vol. 35 (1970), pp. 535--55.