Friendliness and Sympathy in Logic

  • David Makinson


We define and examine a notion of logical friendliness, which is a broadening of the familiar notion of classical consequence. The concept is studied first in its simplest form, and then in a syntax-independent version, which we call sympathy. We also draw attention to the surprising number of familiar notions and operations with which it makes contact, providing a new light in which they may be seen.


Classical Logic Classical Consequence Propositional Formula Conservative Extension Paraconsistent Logician 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [Beth,1953]
    Beth, Evert W. 1953. On Padoa’s method in the theory of definition, Nederl. Akad. Wetensch. Proc. Ser. A 56: 330–339; also Indagationes Mathematicae 15: 330–339.Google Scholar
  2. [Boole,1847]
    Boole, George. 1847. The Mathematical Analysis of Logic. Cambridge: Macmillan.Google Scholar
  3. [Boole,1854]
    Boole, George. 1854. An Investigation into the Laws of Thought. London: Walton.Google Scholar
  4. [de Bouvère,1959]
    de Bouvère, K.L. 1959. A Method in Proofs of Undefinability. Amsterdam: North Holland.MATHGoogle Scholar
  5. [Dunn,1976]
    Dunn, J.M. 1976. Intuitive semantics for first-degree entailments and coupled trees, Philosophical Studies, 29, 149–168.CrossRefGoogle Scholar
  6. [Jeffrey,1967]
    Jeffrey, R.C. 1967. Formal Logic: Its Scope and Limits (second edition 1981). New York: McGraw-Hill.Google Scholar
  7. [Lang, 2003]
    Lang, J., P. Liberatore, P. Marquis. 2003. Propositional independence: formula-variable independence and forgetting, Journal of Artificial Intelligence Reseach, 18: 391–443.MATHGoogle Scholar
  8. [Leśniewski,1931]
    Leśniewski, S. 1931. Über definitionen in der sogennanten Theorie der Deduktion. Comptes Rendus des Séances de la Société des Sciences et des Lettres de Varsovie, Classe 3, XXIV: 300–302.Google Scholar
  9. [Lin and Reiter,1994]
    Lin, F. and R. Reiter (1994). Forget it!. In R. Greiner and D. Subramanian, eds. Working Notes on AAAI Fall Symposium on Relevance. Menlo Park: AAAI Press.Google Scholar
  10. [Makinson,2005]
    Makinson, David. 2005. Bridges from Classical to Nonmonotonic Logic. London: College Publications. Series: Texts in Computing, vol 5.MATHGoogle Scholar
  11. [Makinson,2005a]
    Makinson, David. 2005. Friendliness for logicians. In Sergei N. Artemov, Howard Barringer, Artur S. d’Avila Garcez, Luis C. Lamb, and John Woods, editors, We Will Show Them! Essays in Honour of Dov Gabbay, Volume Two, pages 259–292. College Publications, 2005.Google Scholar
  12. [Padoa,1901]
    Padoa, A. 1901. Essai d’une théorie algébrique des nombres entiers, précédé d’une introduction logique à une théorie deductive quelconque. Bibliothèque du Congrès International de Philosophie, Paris 1900, vol 3: 309–365. Paris: Armand Colin.Google Scholar
  13. [Parikh,1999]
    Parikh, R. 1999. Beliefs, belief revision, and splitting languages. Pages 266–278 of L. Moss et al eds, Logic, Language and Computation, vol 2. CSLI Lecture Notes no 96: 266–278. California: CSLI Publications.Google Scholar
  14. [Pietruszczak,2004]
    Pietruszczak, A. 2004. The consequence relation preserving logical information, Logic and Logical Philosophy 13: 89–120.Google Scholar
  15. [Ramsey,1931]
    Ramsey, F.P. 1931. The Foundations of Mathematics and Other Logical Essays ed. R.B. Braithwaite. London: Kegan Paul, Trench, Trubner.Google Scholar
  16. [Rantala,1991]
    Rantala, V. 1991. Definitions and definability, pages 135–159 of James H. Fetzer et al Definitions and Definability: Philosophical Perspectives. Dordrecht: Kluwer.Google Scholar
  17. [Sneed,1971]
    Sneed, J.D. 1971. The Logical Structure of Mathematical Physics. Dordrecht: Reidel.Google Scholar
  18. [Suppes,1957]
    Suppes, P. 1957. Introduction to Logic. Princeton: Van Nostrand.MATHGoogle Scholar
  19. [van Benthem,1978]
    Van Benthem, J.F.A.K. 1978. Ramsey eliminability, Studia Logica 37: 321–336.MATHCrossRefGoogle Scholar
  20. [Weber,1987]
    Weber, A. 1987. Updating propositional formulae, pages 487–500 in L. Kerschberg, ed. Proceedings of the First Conference on Expert Data Systems. Benjamin Cummings.Google Scholar

Copyright information

© Birkhäuser Verlag Basel/Switzerland 2007

Authors and Affiliations

  • David Makinson
    • 1
  1. 1.Dept. of Philosophy, Logic & Scientific MethodLondon School of EconomicsLondonUK

Personalised recommendations