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An Approach to Inconsistency-Tolerant Reasoning About Probability Based on Łukasiewicz Logic

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Scalable Uncertainty Management (SUM 2022)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 13562))

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Abstract

In this paper we consider the probability logic over Łukasiewicz logic with rational truth-constants, denoted FP(RPL), and we explore a possible approach to reason from inconsistent FP(RPL) theories in a non-trivial way. It basically consists of suitably weakening the formulas in an inconsistent theory T, depending on the degree of inconsistency of T. We show that such a logical approach is in accordance with other proposals in the literature based on distance-based and violation-based inconsistency measures.

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Notes

  1. 1.

    Although we are using the same symbols \(\wedge , \lnot , \vee , \rightarrow \) as in Łukasiewicz logic to denote the conjunction, negation, disjunction and implication, the context will help in avoiding any confusion. In particular classical logic connectives will appear only under the scope of the operator P, see below.

  2. 2.

    An equivalent formulation of (FP3) is \(P(\varphi \vee \psi ) \equiv P\varphi \oplus (P\psi \ominus P(\varphi \wedge \psi ))\).

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Acknowledgments

The authors are grateful to the anonymous reviewers for their helpful comments. The authors also acknowledge partial support by the MOSAIC project (EU H2020- MSCA-RISE-2020 Project 101007627). Flaminio and Godo also acknowledge support by the Spanish project ISINC (PID2019-111544GB-C21) funded by MCIN/AEI/10.13039/501100011033, while Ugolini also acknowledges the Marie Sklodowska-Curie grant agreement No. 890616 (H2020-MSCA-IF-2019).

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Authors and Affiliations

  1. IIIA - CSIC, 08193, Bellaterra, Spain

    Tommaso Flaminio, Lluis Godo & Sara Ugolini

Authors
  1. Tommaso Flaminio
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  2. Lluis Godo
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  3. Sara Ugolini
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Correspondence to Lluis Godo .

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Editors and Affiliations

  1. IRIT-Université Toulouse, Toulouse, France

    Florence Dupin de Saint-Cyr

  2. Université Paris-Dauphine - PSL, Paris, France

    Meltem Öztürk-Escoffier

  3. Imperial College London, London, UK

    Nico Potyka

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Flaminio, T., Godo, L., Ugolini, S. (2022). An Approach to Inconsistency-Tolerant Reasoning About Probability Based on Łukasiewicz Logic. In: Dupin de Saint-Cyr, F., Öztürk-Escoffier, M., Potyka, N. (eds) Scalable Uncertainty Management. SUM 2022. Lecture Notes in Computer Science(), vol 13562. Springer, Cham. https://doi.org/10.1007/978-3-031-18843-5_9

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  • DOI: https://doi.org/10.1007/978-3-031-18843-5_9

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