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Equivalence in Abductive Logic

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Katsumi Inoue and Chiaki Sakama

* Proceedings of the 19th International Joint Conference
on Artificial Intelligence (IJCAI-05), pages 472-477, Morgan Kaufmann Publishers, 2005.
*
## Abstract

We consider the problem of identifying equivalence of two knowledge
bases which are capable of abductive reasoning.
Here, a knowledge base is written in either first-order logic or
nonmonotonic logic programming. In this work, we will give two definitions
of abductive equivalence. The first one, *explainable equivalence*,
requires that two abductive programs have the same explainability
for any observation. Another one, *explanatory equivalence*, guarantees
that any observation has exactly the same explanations in each
abductive framework.
Explanatory equivalence is a stronger notion than explainable equivalence.
In first-order abduction, explainable equivalence can be verified by
the notion of extensional equivalence in default theories.
In nonmonotonic logic programs, explanatory equivalence can be checked
by means of the notion of relative strong equivalence.
We also show the complexity results for abductive equivalence.

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