28 research outputs found
Stable Models of Formulas with Generalized Quantifiers (Preliminary Report)
Applications of answer set programming motivated various extensions of the stable model semantics, for instance, to allow aggregates or to facilitate interface with external ontology descriptions. We present a uniform, reductive view on these extensions by viewing them as special cases of formulas with generalized quantifiers. This is done by extending the first-order stable model semantics by Ferraris, Lee and Lifschitz to account for generalized quantifiers and then by reducing the individual extensions to this formalism
Stable Models of Formulas with Generalized Quantifiers (Preliminary Report)
Applications of answer set programming motivated various extensions of the stable model semantics, for instance, to allow aggregates or to facilitate interface with external ontology descriptions. We present a uniform, reductive view on these extensions by viewing them as special cases of formulas with generalized quantifiers. This is done by extending the first-order stable model semantics by Ferraris, Lee and Lifschitz to account for generalized quantifiers and then by reducing the individual extensions to this formalism
On Loop Formulas with Variables
Recently Ferraris, Lee and Lifschitz proposed a new definition of stable
models that does not refer to grounding, which applies to the syntax of
arbitrary first-order sentences. We show its relation to the idea of loop
formulas with variables by Chen, Lin, Wang and Zhang, and generalize their loop
formulas to disjunctive programs and to arbitrary first-order sentences. We
also extend the syntax of logic programs to allow explicit quantifiers, and
define its semantics as a subclass of the new language of stable models by
Ferraris et al. Such programs inherit from the general language the ability to
handle nonmonotonic reasoning under the stable model semantics even in the
absence of the unique name and the domain closure assumptions, while yielding
more succinct loop formulas than the general language due to the restricted
syntax. We also show certain syntactic conditions under which query answering
for an extended program can be reduced to entailment checking in first-order
logic, providing a way to apply first-order theorem provers to reasoning about
non-Herbrand stable models.Comment: 10 pages. In Proc. Eleventh International Conference on Principles of
Knowledge Representation and Reasoning (KR 2008), pages 444-453. arXiv admin
note: text overlap with arXiv:1401.389