Geodesic
Useful Four-Valued Extension of the Temporal Logic KtT4
Bulletin of the Section of Logic, Tome 47 (2018) no. 1.

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The temporal logic KtT4 is the modal logic obtained from the minimal temporal logic Kt by requiring the accessibility relation to be reflexive (which corresponds to the axiom T) and transitive (which corresponds to the axiom 4). This article aims, firstly, at providing both a model-theoretic and a proof-theoretic characterisation of a four-valued extension of the temporal logic KtT4 and, secondly, at identifying some of the most useful properties of this extension in the context of partial and paraconsistent logics.
Keywords: temporal logic, many-valued logic, bi-intuitionistic logic, paraconsistent logic, sequent calculus, duality, cut-redundancy 
@article{BSL_2018_47_1_a4,
     author = {Degauquier, Vincent},
     title = {Useful {Four-Valued} {Extension} of the {Temporal} {Logic} {KtT4}},
     journal = {Bulletin of the Section of Logic},
     publisher = {mathdoc},
     volume = {47},
     number = {1},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BSL_2018_47_1_a4/}
}
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Degauquier, Vincent. Useful Four-Valued Extension of the Temporal Logic KtT4. Bulletin of the Section of Logic, Tome 47 (2018) no. 1. http://geodesic.mathdoc.fr/item/BSL_2018_47_1_a4/