General domain circumscription and its first-order reduction.
Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab
Linköping University, The Institute of Technology
Conference paper (Refereed)
Proceedings of the 1st International Conference on Formal and Applied Practical Reasoning (FAPR)
Dov Gabbay, Hans Olbach
Lecture Notes in Computer Science, ISSN 0302-9743; 1085
We first define general domain circumscription (GDC) and provide it with a semantics. GDC subsumes existing domain circumscription proposals in that it allows varying of arbitrary predicates, functions, or constants, to maximize the minimization of the domain of a theory We then show that for the class of semi-universal theories without function symbols, that the domain circumscription of such theories can be constructively reduced to logically equivalent first-order theories by using an extension of the DLS algorithm, previously proposed by the authors for reducing second-order formulas. We also isolate a class of domain circumscribed theories, such that any arbitrary second-order circumscription policy applied to these theories is guaranteed to be reducible to a logically equivalent first-order theory. In the case of semi-universal theories with functions and arbitrary theories which are not separated, we provide additional results, which although not guaranteed to provide reductions in all cases, do provide reductions in some cases. These results are based on the use of fixpoint reductions.