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Towards a Logic of Epistemic Theory of Measurement

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Modeling and Using Context (CONTEXT 2019)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 11939))

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Abstract

We propose a logic to reason about data collected by a number of measurement systems. The semantic of this logic is grounded on the epistemic theory of measurement that gives a central role to measurement devices and calibration. In this perspective, the lack of evidences (in the available data) for the truth or falsehood of a proposition requires the introduction of a third truth-value (the undetermined). Moreover, the data collected by a given source are here represented by means of a possible world, which provide a contextual view on the objects in the domain. We approach (possibly) conflicting data coming from different sources in a social choice theoretic fashion: we investigate viable operators to aggregate data and we represent them in our logic by means of suitable (minimal) modal operators.

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Notes

  1. 1.

    MSs are “provided with instructions specifying how such interaction must be performed and interpreted” [9].

  2. 2.

    Notice that \(\mathcal{E}\) refers to potential interactions with objects, i.e., by abstracting from specific objects, it depends only on the (physical) structure of d.

  3. 3.

    Differently from RMT, \(\mathcal{S}\) is not necessarily a numerical structure.

  4. 4.

    See [16] for the formal details.

  5. 5.

    In terms of the theory of conceptual spaces [10], single classification systems correspond to the domains of a conceptual space (e.g., color, taste, shape, temperature, etc.), while the whole space requires the composition of several systems.

  6. 6.

    It is possible to extend the notion of MB to allow to have different MSs relative to the same classification system, e.g., different scales, different thermometers, etc.

  7. 7.

    A treatment for a larger class of aggregators in social choice is presented in [23]. The motivation for the present treatment is that it easily allows for viewing aggregators as modalities. An overview of functions used to aggregated data is discussed in [4].

  8. 8.

    The majority rule is generalized by quota rules that specify a threshold for acceptance of a certain truth-value. In this case, to define F as a function, we have to separately define quota rules for true, false, and undetermined.

  9. 9.

    See https://www.w3.org/TR/prov-overview.

  10. 10.

    Note that an analogous argument applies to the determined majority rule.

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Authors and Affiliations

  1. Laboratory for Applied Ontology, ISTC -CNR, Trento, Italy

    Claudio Masolo & Daniele Porello

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  1. Claudio Masolo
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  2. Daniele Porello
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Correspondence to Daniele Porello .

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Editors and Affiliations

  1. University of Trento, Trento, Italy

    Gábor Bella

  2. University of Trento, Trento, Italy

    Paolo Bouquet

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Masolo, C., Porello, D. (2019). Towards a Logic of Epistemic Theory of Measurement. In: Bella, G., Bouquet, P. (eds) Modeling and Using Context. CONTEXT 2019. Lecture Notes in Computer Science(), vol 11939. Springer, Cham. https://doi.org/10.1007/978-3-030-34974-5_15

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  • DOI: https://doi.org/10.1007/978-3-030-34974-5_15

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