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Towards an Ontological Modelling of Preference Relations

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AI*IA 2018 – Advances in Artificial Intelligence (AI*IA 2018)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 11298))

Abstract

Preference relations are intensively studied in Economics, but they are also approached in AI, Knowledge Representation, and Conceptual Modelling, as they provide a key concept in a variety of domains of application. In this paper, we propose an ontological foundation of preference relations to formalise their essential aspects across domains. Firstly, we shall discuss what is the ontological status of the relata of a preference relation. Secondly, we investigate the place of preference relations within a rich taxonomy of relations (e.g. we ask whether they are internal or external, essential or contingent, descriptive or non-descriptive relations). Finally, we provide an ontological modelling of preference relation as a module of a foundational (or upper) ontology (viz. OntoUML).

The aim of this paper is to provide a sharable foundational theory of preference relation that foster interoperability across the heterogeneous domains of application of preference relations.

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Notes

  1. 1.

    We do not have space here to provide an exhaustive view of the separation of objects. We simply say that two objects are separated if they are existentially independent, cf. [9].

  2. 2.

    This is the definition provided by Russell [25]. A stronger definition is the one proposed by Moore [14], which views an internal relation as a relation the holds merely in virtue of the existence of the relata. This second view of internal relation is what we term here essential, following the terminology of [7].

  3. 3.

    For an ontological theory of roles, we refer to [9] and [13].

  4. 4.

    This simplification amounts to assuming that in a preference statement only one dimension of choice is involved [15, 19]. That is, the value of a for i does not depend on any further conditions. To extend this modelling, one may assume that the value of a for i may depend on a number of parameters; e.g. “the value of a for i given that i already has a certain amount of a” may capture the marginal value for i of getting a further a.

  5. 5.

    A specification of this category, and what types of metric spaces is associated to it, is left for future work and for dedicated application of specific views of preferences. We shall also discuss this point in the next section, when we approach the distinction between cardinal and ordinal preferences.

  6. 6.

    This is the way qualities and quality values are related for instance in DOLCE, cf. [2].

  7. 7.

    The relation of derivation connects a descriptive relation with its truthmaker. In OntoUML, derivation is represented by a dashed line with a black circle in the end connected to the truthmaker type [9].

  8. 8.

    Unfortunately, in English, there seems to be no exact term to refer to the non-preferred entity of a preference relation. In Portuguese, for instance, there exist in the lexicon both the term Preferido (to refer to the preferred entity) as well as the term Preterido (to refer to the non-preferred one).

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Authors and Affiliations

  1. Free University of Bozen-Bolzano, Bolzano, Italy

    Daniele Porello & Giancarlo Guizzardi

Authors
  1. Daniele Porello
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  2. Giancarlo Guizzardi
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Correspondence to Daniele Porello .

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Editors and Affiliations

  1. Fondazione Bruno Kessler, Povo (TN), Italy

    Chiara Ghidini

  2. Fondazione Bruno Kessler, Povo (TN), Italy

    Bernardo Magnini

  3. University of Trento, Povo (TN), Italy

    Andrea Passerini

  4. Fondazione Bruno Kessler, Povo (TN), Italy

    Paolo Traverso

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Porello, D., Guizzardi, G. (2018). Towards an Ontological Modelling of Preference Relations. In: Ghidini, C., Magnini, B., Passerini, A., Traverso, P. (eds) AI*IA 2018 – Advances in Artificial Intelligence. AI*IA 2018. Lecture Notes in Computer Science(), vol 11298. Springer, Cham. https://doi.org/10.1007/978-3-030-03840-3_12

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  • DOI: https://doi.org/10.1007/978-3-030-03840-3_12

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