Relativised Equivalence in Equilibrium Logic and its Applications to Prediction and Explanation: Preliminary Report

For a given semantics, two nonmonotonic theories Π1 and Π2 can be said to be equivalent if they have the same intended models and strongly (resp., uniformly) equivalent if for any Σ, Π1∪Σ and Π2∪Σ are equivalent, where Σ is a set of sentences (resp., literals). In the general case, no restrictions are placed on the language (signature) of Σ. Relativised notions of strong and uniform equivalence are obtained by requiring that Σ belongs to a specified sublanguage L of the theories Π1 and Π2. For normal and disjunctive logic programs under stablemodel semantics, relativised strong and uniform equivalence have been defined and characterised in previous work by Woltran. Here, we extend these concepts to nonmonotonic theories in equilibrium logic and discuss applications in the context of prediction and explanation.

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