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The Lvov-Warsaw School. Past and Present pp 485–497Cite as

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Variations on Jaśkowski’s Discursive Logic

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Part of the book series: Studies in Universal Logic ((SUL))

Abstract

Stanisław Jaśkowski, in his 1948–1949 papers on propositional calculus for contradictory deductive systems, proposed discursive logic D2. The main motivation behind D2 is the need to properly deal with contradictions that naturally appear in many areas of philosophy and discourse. The intuitive justification of this logic reflects knowledge fusion occurring when “the theses advanced by several participants in a discourse are combined into a single system.” This point of view was seminal in the mid twentieth century and remains visionary nowadays.

In contemporary autonomous systems operating in dynamic, unpredictable information-rich environments, distributed reasoning routinely takes place. This explains the key role of knowledge fusion, among others, in Distributed Artificial Intelligence. Therefore, different types of modern knowledge and belief bases become primarily concerned with inconsistent or lacking information. This requirement leads to recent approaches to paraconsistent and paracomplete reasoning, where nonmonotonic techniques for disambiguating inconsistencies and completing missing knowledge can be applied.

In this chapter we remind Jaśkowski’s seminal, pioneering work on paraconsistent reasoning and indicate some of its relations to contemporary research on reasoning in Distributed AI.

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Notes

  1. 1.

    For open-source interpreters of 4QL, see 4ql.org.

  2. 2.

    Note that epistemic profiles of [17, 18] are functions of the sort \(\mbox{\textsc {Fin}}(\ensuremath {\mathbb C} ) \longrightarrow \ensuremath {\mathbb C} \). That is, they basically are deterministic epistemic profiles with \(\ensuremath {\mathbb F} \) consisting of one consequent.

  3. 3.

    Note that, in the simplest case, \(\ensuremath {\mathbb B} _1^{\ensuremath {\mathbb E}} \) and \(\ensuremath {\mathbb B} _2^{\ensuremath {\mathbb E}} \) can be identical.

  4. 4.

    Observe that the property of consistency of beliefs requires beliefs to exclude only falsity f. On the other hand, beliefs can contain contradictory claims.

  5. 5.

    Of course, one should take into considerations rich theories developed outside of logical formalisms, in particular in the case of negotiations.

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Acknowledgements

Supported by the Polish National Science Centre grants 2015/19/B/ST6/02589 and 2015/17/N/ST6/03642.

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Authors and Affiliations

  1. Institute of Informatics, University of Warsaw, Warsaw, Poland

    Barbara Dunin-Kęplicz & Andrzej Szałas

  2. (Formerly Alina Strachocka) Institute of Informatics, University of Warsaw, Warsaw, Poland

    Alina Powała

  3. Department of Computer and Information Science, Linköping University, Linköping, Sweden

    Andrzej Szałas

Authors
  1. Barbara Dunin-Kęplicz
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  2. Alina Powała
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  3. Andrzej Szałas
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Correspondence to Andrzej Szałas .

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Editors and Affiliations

  1. Department of Fundamental Mathematics, UNED, Madrid, Spain

    Ángel Garrido

  2. Cardinal Stefan Wyszyński University in Warsaw, Warsaw, Poland

    Urszula Wybraniec-Skardowska

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Dunin-Kęplicz, B., Powała, A., Szałas, A. (2018). Variations on Jaśkowski’s Discursive Logic. In: Garrido, Á., Wybraniec-Skardowska, U. (eds) The Lvov-Warsaw School. Past and Present. Studies in Universal Logic. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-65430-0_34

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