The paper builds on previous work on perfect paradefinite algebras and their associated logics of formal inconsistency and undeterminedness. The authors explore different approaches to adding an implication connective to these logics:
They first consider logics with a classical-like implication, but these fail to be self-extensional.
They then focus on expanding the perfect paradefinite algebra with a Heyting-style implication, based on the relative pseudo-complement. This leads to self-extensional SET-SET and SET-FMLA logics, which are shown to be closely related to Moisil's symmetric modal logic.
The authors provide detailed axiomatizations for these new implicative logics, study their algebraic semantics, and investigate properties like interpolation and amalgamation.
The main contribution is the systematic investigation of implicative expansions of the logics of perfect paradefinite algebras, while ensuring the resulting logics are self-extensional.
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