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On dual programs in co-logic programming. (English) Zbl 1362.68057
Falaschi, Moreno (ed.), Logic-based program synthesis and transformation. 25th international symposium, LOPSTR 2015, Siena, Italy, July 13–15, 2015. Revised selected papers. Cham: Springer (ISBN 978-3-319-27435-5/pbk; 978-3-319-27436-2/ebook). Lecture Notes in Computer Science 9527, 21-35 (2015).
Summary: Co-logic programming is an extension of the conventional logic programming language, by allowing each predicate to be annotated as either inductive or coinductive. To define its procedural semantics as well as an alternating fixpoint semantics, the stratification restriction, a condition on predicate dependency in programs, has been imposed on co-logic programs (co-LPs). In this paper, we first consider dual programs in co-logic programming: given a program \(P\), its dual program \(P^{*}\) is a program such that it defines the “complement” of \(P\), i.e., for any ground atom \(p(\overline{t})\), it computes its negation \(\lnot p(\overline{t})\). When we consider co-LPs with negation, we show that the stratification restriction becomes too restrictive in general, and that the Horn \(\mu\)-calculus by Charatonik et al. can be used as an extension of co-logic programming for handling “non-stratified” co-LPs. We then consider some applications of non-stratified co-LPs to answer set programming (ASP) and the well-founded semantics (WFS). In particular, we give new iterated fixpoint characterizations of answer sets as well as the WFS via dual programs. We also discuss some applications of non-stratified co-LPs to program transformation such as partial deduction, and a proof procedure for the WFS.
For the entire collection see [Zbl 1326.68017].
MSC:
68N30 Mathematical aspects of software engineering (specification, verification, metrics, requirements, etc.)
03B70 Logic in computer science
68N17 Logic programming
Software:
Smodels; SWI-Prolog
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