On dual programs in co-logic programming and the Horn μ-calculus

Abstract

Abstract We consider some extensions of co-logic programming and study its relationship with the Horn μ -calculus by Charatonik et al. We first consider negation elimination (NE) , a familiar technique of program transformation, for co-logic programs. Given a program P , NE derives its dual program P * which defines the “complement” of P . When we apply NE to co-logic programs with negation, we show that the stratification restriction, a syntactic condition imposed on co-logic programs, becomes too restrictive in general, and that the Horn μ -calculus can be used as an extension of co-logic programming for handling “non-stratified” co-logic programs. We then consider some applications of non-stratified co-logic programs to the well-founded semantics (WFS) and Answer Set Programming. In particular, we give new iterated fixpoint characterizations of the WFS as well as answer sets via dual programs. We also discuss some applications of non-stratified co-logic programs to program transformation such as partial deduction, and a proof procedure for the WFS.