2 research outputs found
Beyond NP: Quantifying over Answer Sets
Answer Set Programming (ASP) is a logic programming paradigm featuring a
purely declarative language with comparatively high modeling capabilities.
Indeed, ASP can model problems in NP in a compact and elegant way. However,
modeling problems beyond NP with ASP is known to be complicated, on the one
hand, and limited to problems in {\Sigma}^P_2 on the other. Inspired by the way
Quantified Boolean Formulas extend SAT formulas to model problems beyond NP, we
propose an extension of ASP that introduces quantifiers over stable models of
programs. We name the new language ASP with Quantifiers (ASP(Q)). In the paper
we identify computational properties of ASP(Q); we highlight its modeling
capabilities by reporting natural encodings of several complex problems with
applications in artificial intelligence and number theory; and we compare
ASP(Q) with related languages. Arguably, ASP(Q) allows one to model problems in
the Polynomial Hierarchy in a direct way, providing an elegant expansion of ASP
beyond the class NP. Under consideration for acceptance in TPLP.Comment: Paper presented at the 35th International Conference on Logic
Programming (ICLP 2019), Las Cruces, New Mexico, USA, 20-25 September 2019,
16 page
Technical Report: Inconsistency in Answer Set Programs and Extensions
Answer Set Programming (ASP) is a well-known problem solving approach based
on nonmonotonic logic programs. HEX-programs extend ASP with external atoms for
accessing arbitrary external information, which can introduce values that do
not appear in the input program. In this work we consider inconsistent ASP- and
HEX-programs, i.e., programs without answer sets. We study characterizations of
inconsistency, introduce a novel notion for explaining inconsistencies in terms
of input facts, analyze the complexity of reasoning tasks in context of
inconsistency analysis, and present techniques for computing inconsistency
reasons. This theoretical work is motivated by two concrete applications, which
we also present. The first one is the new modeling technique of query answering
over subprograms as a convenient alternative to the well-known saturation
technique. The second application is a new evaluation algorithm for
HEX-programs based on conflict-driven learning for programs with multiple
components: while for certain program classes previous techniques suffer an
evaluation bottleneck, the new approach shows significant, potentially
exponential speedup in our experiments. Since well-known ASP extensions such as
constraint ASP and DL-programs correspond to special cases of HEX, all
presented results are interesting beyond the specific formalism