On Possibilistic Modal Logics Defined Over MTL-Chains

  • Félix Bou
  • Francesc Esteva
  • Lluís GodoEmail author
Part of the Outstanding Contributions to Logic book series (OCTR, volume 6)


In this chapter we revisit a 1994 chapter by Hájek et al. where a modal logic over a finitely-valued Łukasiewicz logic is defined to capture possibilistic reasoning. In this chapter we go further in two aspects: first, we generalize the approach in the sense of considering modal logics over an arbitrary finite MTL-chain, and second, we consider a different possibilistic semantics for the necessity and possibility modal operators. The main result is a completeness proof that exploits similar techniques to the ones involved in Hájek et al.’s previous work.


Possibitistic Logic Fuzzy Logic Many-valued Modal Logic 



The authors are deeply indebted to an anonymous reviewer for the useful comments that have helped to significantly improve the layout of this chapter. The authors also acknowledge partial support of the Spanish projects EdeTRI (TIN2012-39348-C02-01) and Agreement Technologies (CONSOLIDER CSD2007-0022, INGENIO 2010), and the grant 2009SGR-1433 from the Catalan Government. Initially they were also supported by the projects TASSAT (TIN2010-20967-C04-01) and 2009SGR-1434.


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© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Department of Probability, Logic and StatisticsUniversity of BarcelonaBarcelonaSpain
  2. 2.Artificial Intelligence Research InstituteIIIA-CSICBellaterraSpain

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