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Two axiomatic characterizations for the system of spheres-based (and the Epistemic Entrenchment-based) multiple contractions

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Abstract

In some recent works (Reis 2011, Fermé and Reis, J. Philos. Log. 41, 29–52, 2012, Fermé and Reis, Rev. Symb. Log. 6, 460–487, 2013) two new kinds of multiple contraction functions have been proposed, namely the system of spheres-based multiple contractions and the epistemic entrenchment-based multiple contractions, as generalizations (to the case of multiple contraction) of the well-known classes of systems of spheres-based and of epistemic entrenchment-based (singleton) contractions. Additionally, a representation theorem for the class of epistemic entrenchment-based multiple contraction has been proposed, and it has been shown that the two newly proposed constructions are equivalent, in the sense that a multiple contraction function is a system of spheres-based multiple contraction if and only if it is an epistemic entrenchment-based multiple contraction. In this paper we present two axiomatic characterizations for those multiple contraction functions which differ from the one mentioned above and, in particular, make use of some more intuitive postulates.

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Authors and Affiliations

  1. Universidade da Madeira, Campus Universitário da Penteada, 9020-105, Funchal, Portugal

    Maurício D. L. Reis & Eduardo Fermé

  2. NOVA Laboratory for Computer Science and Informatics (NOVA LINCS), Universidade Nova de Lisboa, Lisboa, Portugal

    Maurício D. L. Reis & Eduardo Fermé

  3. Department of Business Administration, University of Patras, 265 00, Patras, Greece

    Pavlos Peppas

  4. QCIS, Faculty of Engineering and IT, University of Technology, Sydney, NSW 2007, Australia

    Pavlos Peppas

Authors
  1. Maurício D. L. Reis
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  2. Pavlos Peppas
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  3. Eduardo Fermé
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Correspondence to Maurício D. L. Reis.

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Reis, M.D.L., Peppas, P. & Fermé, E. Two axiomatic characterizations for the system of spheres-based (and the Epistemic Entrenchment-based) multiple contractions. Ann Math Artif Intell 78, 181–203 (2016). https://doi.org/10.1007/s10472-015-9454-x

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  • DOI: https://doi.org/10.1007/s10472-015-9454-x

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