The work Parameterized simplification logic I: reasoning with implications and classes of closure operators has been published in International Journal of General Systems vol 49 (7), pp. 724 – 746.
Abstract:
In this paper, we present a general inference system for reasoning with if-then rules. They are defined using general lattice-theoretic notions and their semantics is defined using particular closure operators parameterized by systems of isotone Galois connections. In this general setting, we introduce a simplification logic, show its sound and complete axiomatization, and deal with related issues. The presented results can be seen as forming parameterized framework for dealing with if-then rules that allows to focus on particular dependencies obtained by choices of parameterizations.
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