On the relation between default and autoepistemic logic
Readings in nonmonotonic reasoning
On the relation between default and autoepistemic logic
Artificial Intelligence
Journal of the ACM (JACM)
Fixpoint 3-valued semantics for autoepistemic logic
AAAI '98/IAAI '98 Proceedings of the fifteenth national/tenth conference on Artificial intelligence/Innovative applications of artificial intelligence
Approximations, stable operators, well-founded fixpoints and applications in nonmonotonic reasoning
Logic-based artificial intelligence
Epistemic Logic for AI and Computer Science
Epistemic Logic for AI and Computer Science
Uniform semantic treatment of default and autoepistemic logics
Artificial Intelligence
Predicate Introduction for Logics with a Fixpoint Semantics. Part I: Logic Programming
Fundamenta Informaticae
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We study the transformation of "predicate introduction" in non-monotonic logics. By this, we mean the act of replacing a complex formula by a newly defined predicate. From a knowledge representation perspective, such transformations can be used to eliminate redundancy or to simplify a theory. From a more practical point of view, they can also be used to transform a theory into a normal form imposed by certain inference programs or theorems. In a companion paper, we developed an algebraic theory that considers predicate introduction within the framework of "approximation theory", a fixpoint theory for non-monotone operators that generalizes all main semantics of various non-monotonic logics, including logic programming, default logic and autoepistemic logic. We then used these results to show that certain logic programming transformations are equivalence preserving under, among others, both the stable and well-founded semantics. In this paper, we now apply the same algebraic results to autoepistemic logic and prove that a transformation to reduce the nesting depth of modal operators is equivalence preserving under a family of semantics for this logic. This not only provides useful theorems for autoepistemic logic, but also demonstrates that our algebraic theory does indeed capture the essence of predicate introduction in a generally applicable way.