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A family of genuine and non-algebraisable C-systems
Ist Teil von
Journal of applied non-classical logics, 2021-01, Vol.31 (1), p.56-84
Ort / Verlag
Taylor & Francis
Erscheinungsjahr
2021
Link zum Volltext
Quelle
Taylor & Francis Journals Auto-Holdings Collection
Beschreibungen/Notizen
In 2016, Béziau introduced the notion of genuine paraconsistent logic as logic that does not verify the principle of non-contradiction; as an important example, he presented the genuine paraconsistent logic
in terms of three connectives
,
, and
. In this paper, we show that
is an axiomatic extension of
through the introduction of a non-primitive deductive implication. Furthermore, we prove that
is an algebraisable logic with Blok-Pigozzi's method. From the proof that
is non-algebraisable logic, we are able to see that
is not algebraisable logic and studying the borders of algebrisabilty, we can give an enumerable family of new genuine, paraconsistent and non-algebraisable logics, extensions of
. Finally, we introduced n-valued (
) and infinite-valued
logic and show that they are genuine and non-algebraisable paraconsistent ones; in addition, we present semantics for this extensions of
by means of Fidel's structures.