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Implicational (semilinear) logics III: completeness properties

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Abstract

This paper presents an abstract study of completeness properties of non-classical logics with respect to matricial semantics. Given a class of reduced matrix models we define three completeness properties of increasing strength and characterize them in several useful ways. Some of these characterizations hold in absolute generality and others are for logics with generalized implication or disjunction connectives, as considered in the previous papers. Finally, we consider completeness with respect to matrices with a linear dense order and characterize it in terms of an extension property and a syntactical metarule. This is the final part of the investigation started and developed in the papers (Cintula and Noguera in Arch Math Logic 49(4):417–446, 2010; Arch Math Logic 53(3):353–372, 2016).

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Authors and Affiliations

  1. Institute of Computer Science, Czech Academy of Sciences, Pod Vodárenskou věží 2, 182 07, Prague, Czechia

    Petr Cintula

  2. Institute of Information Theory and Automation, Czech Academy of Sciences, Pod Vodárenskou věží 4, 182 08, Prague, Czechia

    Carles Noguera

Authors
  1. Petr Cintula
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  2. Carles Noguera
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Correspondence to Carles Noguera.

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Cintula, P., Noguera, C. Implicational (semilinear) logics III: completeness properties. Arch. Math. Logic 57, 391–420 (2018). https://doi.org/10.1007/s00153-017-0577-0

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  • DOI: https://doi.org/10.1007/s00153-017-0577-0

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