Logica Universalis 11 (3):345-382 (2017)

Joao Marcos
Universidade Federal do Rio Grande do Norte
Non-classical negations may fail to be contradictory-forming operators in more than one way, and they often fail also to respect fundamental meta-logical properties such as the replacement property. Such drawbacks are witnessed by intricate semantics and proof systems, whose philosophical interpretations and computational properties are found wanting. In this paper we investigate congruential non-classical negations that live inside very natural systems of normal modal logics over complete distributive lattices; these logics are further enriched by adjustment connectives that may be used for handling reasoning under uncertainty caused by inconsistency or undeterminedness. Using such straightforward semantics, we study the classes of frames characterized by seriality, reflexivity, functionality, symmetry, transitivity, and some combinations thereof, and discuss what they reveal about sub-classical properties of negation. To the logics thereby characterized we apply a general mechanism that allows one to endow them with analytic ordinary sequent systems, most of which are even cut-free. We also investigate the exact circumstances that allow for classical negation to be explicitly defined inside our logics.
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DOI 10.1007/s11787-017-0175-2
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References found in this work BETA

An Essay in Classical Modal Logic.Krister Segerberg - 1971 - Uppsala, Filosofiska Föreningen Och Filosofiska Institutionen Vid Uppsala Universitet.
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Citations of this work BETA

Sequent Systems for Negative Modalities.Ori Lahav, João Marcos & Yoni Zohar - 2017 - Logica Universalis 11 (3):345-382.
Compositional Meaning in Logic.Carlos Caleiro & Luca Viganò - 2017 - Logica Universalis 11 (3):283-295.

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