Experimenting with Consistency

Part of the Synthese Library book series (SYLI, volume 387)


This paper discusses logical accounts of the notions of consistency and negation, and in particular explores some potential means of defining consistency and negation when expressed in modal terms. Although this can be done with interesting consequences when starting from classical normal modal logics, some intriguing cases arise when starting from paraconsistent modalities and negations, as in the hierarchy of the so-called cathodic modal paraconsistent systems (cf. Bueno-Soler, Log Univers 4(1):137–160, 2010). The paper also takes some first steps in exploring the philosophical significance of such logical tools, comparing the notions of consistency and negation modally defined with the primitive notions of consistency and negation in the family of Logics of Formal Inconsistency (LFIs), suggesting some experiments on their expressive power.


Modal logics Paraconsistency Contradiction Consistency Logics of formal inconsistency 



Both authors acknowledge support from FAPESP Thematic Project LogCons 2010/51038-0, Brazil, and the second author thanks a research grant from The National Council for Scientific and Technological Development (CNPq), Brazil. We are indebted to David Gilbert, Raymundo Morado, and Peter Verdee for discussions that helped to improve this paper.


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Authors and Affiliations

  1. 1.School of TechnologyState University of Campinas – UNICAMPCampinasBrazil
  2. 2.Centre for Logic, Epistemology and the History of Science and Department of PhilosophyState University of Campinas – UNICAMPCampinasBrazil

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