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Complementary lemmas in the theory of binary relations

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Abstract

This paper presents a metatheorem with the following property: Given a proven axiom-free lemma, which interrelates some of the elementary properties of a binary relation, the metatheorem mechanically transforms this lemma into its uniquely corresponding complementary lemma. Therefore, the metatheorem nearly doubles our knowledge about the elementary properties of binary relations, for application to statistical decision theory. At present we do not know whether there exists a nontrivial axiom-free lemma that is its own complementary lemma.

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Bibliography

  1. Burros, R. H., ‘Complementary Properties of Binary Relations’, Theory and Decision 6 (1975), 177–183.

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  2. Fishburn, P. C., Mathematics of Decision Theory, Mouton, The Hague, 1972.

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Authors and Affiliations

  1. Research and Development Division, Engineering Dept., The Port Authority of New York and New Jersey, USA

    Raymond H. Burros

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  1. Raymond H. Burros
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Burros, R.H. Complementary lemmas in the theory of binary relations. Theor Decis 8, 299–303 (1977). https://doi.org/10.1007/BF00133449

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  • DOI: https://doi.org/10.1007/BF00133449

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