A Coalgebraic Perspective on Logical Interpretations
Studia Logica
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Throughout this paper we consider data structures as sorted algebras endowed with a designated subset of their visible part, which represents the set of truth values. The originality of our approach is the application of the standard abstract algebraic logic theory of deductive systems to the hidden heterogeneous case. We generalize the well-known equivalence relation between finite automata, which relies on the Nerode equivalence relation between states, to k-data structures. This is obtained via the Leibniz congruence, which can be viewed as a generalization of the Nerode equivalence in automata theory.