Dependence
The dependence atom =(x,y) was introduced in [11]. Here x and y are finite sets of attributes (or variables) and the intuitive meaning of =(x,y) is that the attributes x completely (functionally) determine the attributes y. One may wonder, whether the dependence atom is truly an atom or whether it has further constituents. My very pleasant co-operation with Samson Abramsky led to the breaking of this atom, with hitherto unforeseen consequences. Here is the story.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Abramsky, S.: Relational hidden variables and non-locality. Studia Logica, arXiv:1007.2754 (2013), doi: 10.1007/s11225-013-9477-4
Abramsky, S., Väänänen, J.: From IF to BI: a tale of dependence and separation. Synthese 167(2, Knowledge, Rationality & Action), 207–230 (2009)
Armstrong, W.W.: Dependency structures of data base relationships. In: IFIP Congress, pp. 580–583 (1974)
Galliani, P.: The dynamics of imperfect information. Doctoral Thesis, University of Amsterdam (2012)
Galliani, P.: Inclusion and exclusion dependencies in team semantics—on some logics of imperfect information. Ann. Pure Appl. Logic 163(1), 68–84 (2012)
Geiger, D., Paz, A., Pearl, J.: Axioms and algorithms for inferences involving probabilistic independence. Inform. and Comput. 91(1), 128–141 (1991)
Grädel, E., Väänänen, J.: Dependence and independence. Studia Logica, arXiv:1208.5268 (2013), doi: 10.1007/s11225-013-9479-2
Henkin, L.: Some remarks on infinitely long formulas. In: Infinitistic Methods (Proc. Sympos. Foundations of Math., Warsaw, 1959), pp. 167–183. Pergamon, Oxford (1961)
Hodges, W.: Some strange quantifiers. In: Mycielski, J., Rozenberg, G., Salomaa, A. (eds.) Structures in Logic and Computer Science. LNCS, vol. 1261, pp. 51–65. Springer, Heidelberg (1997)
Kontinen, J., Väänänen, J.: Axiomatizing first order consequences in dependence logic. Annals of Pure and Applied Logic (to appear)
Väänänen, J.: Dependence logic. London Mathematical Society Student Texts, vol. 70. Cambridge University Press, Cambridge (2007)
Väänänen, J.A.: Second-order logic and foundations of mathematics. Bulletin of Symbolic Logic 7(4), 504–520 (2001)
Yang, F.: Expressing second-order sentences in intuitionistic dependence logic. Studia Logica, arXiv:1302.2279 (2013), doi: 10.1007/s11225-013-9476-5
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Väänänen, J. (2013). Breaking the Atom with Samson. In: Coecke, B., Ong, L., Panangaden, P. (eds) Computation, Logic, Games, and Quantum Foundations. The Many Facets of Samson Abramsky. Lecture Notes in Computer Science, vol 7860. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38164-5_22
Download citation
DOI: https://doi.org/10.1007/978-3-642-38164-5_22
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-38163-8
Online ISBN: 978-3-642-38164-5
eBook Packages: Computer ScienceComputer Science (R0)