11,873 research outputs found
Graph theoretical structures in logic programs and default theories
In this paper we present a graph representation of logic programs and default theories. We show that many of the semantics proposed for logic programs can be expressed in terms of notions emerging from graph theory, establishing in this way a link between the fields. Namely the stable models, the partial stable models, and the well-founded semantics correspond respectively to the kernels, semikernels and the initial acyclic part of the associated graph. This link allows us to consider both theoretical problems (existence, uniqueness) and computational problems (tractability, algorithms, approximations) from a more abstract and rather combinatorial point of view. It also provides a clear and intuitive understanding about how conflicts between rules are resolved within the different semantics. Furthermore, we extend the basic framework developed for logic programs to the case of Default Logic by introducing the notions of partial, deterministic and well-founded extensions for default theories. These semantics capture different ways of reasoning with a default theory
Super Logic Programs
The Autoepistemic Logic of Knowledge and Belief (AELB) is a powerful
nonmonotic formalism introduced by Teodor Przymusinski in 1994. In this paper,
we specialize it to a class of theories called `super logic programs'. We argue
that these programs form a natural generalization of standard logic programs.
In particular, they allow disjunctions and default negation of arbibrary
positive objective formulas.
Our main results are two new and powerful characterizations of the static
semant ics of these programs, one syntactic, and one model-theoretic. The
syntactic fixed point characterization is much simpler than the fixed point
construction of the static semantics for arbitrary AELB theories. The
model-theoretic characterization via Kripke models allows one to construct
finite representations of the inherently infinite static expansions.
Both characterizations can be used as the basis of algorithms for query
answering under the static semantics. We describe a query-answering interpreter
for super programs which we developed based on the model-theoretic
characterization and which is available on the web.Comment: 47 pages, revised version of the paper submitted 10/200
Ultimate approximations in nonmonotonic knowledge representation systems
We study fixpoints of operators on lattices. To this end we introduce the
notion of an approximation of an operator. We order approximations by means of
a precision ordering. We show that each lattice operator O has a unique most
precise or ultimate approximation. We demonstrate that fixpoints of this
ultimate approximation provide useful insights into fixpoints of the operator
O.
We apply our theory to logic programming and introduce the ultimate
Kripke-Kleene, well-founded and stable semantics. We show that the ultimate
Kripke-Kleene and well-founded semantics are more precise then their standard
counterparts We argue that ultimate semantics for logic programming have
attractive epistemological properties and that, while in general they are
computationally more complex than the standard semantics, for many classes of
theories, their complexity is no worse.Comment: This paper was published in Principles of Knowledge Representation
and Reasoning, Proceedings of the Eighth International Conference (KR2002
Embedding Non-Ground Logic Programs into Autoepistemic Logic for Knowledge Base Combination
In the context of the Semantic Web, several approaches to the combination of
ontologies, given in terms of theories of classical first-order logic and rule
bases, have been proposed. They either cast rules into classical logic or limit
the interaction between rules and ontologies. Autoepistemic logic (AEL) is an
attractive formalism which allows to overcome these limitations, by serving as
a uniform host language to embed ontologies and nonmonotonic logic programs
into it. For the latter, so far only the propositional setting has been
considered. In this paper, we present three embeddings of normal and three
embeddings of disjunctive non-ground logic programs under the stable model
semantics into first-order AEL. While the embeddings all correspond with
respect to objective ground atoms, differences arise when considering
non-atomic formulas and combinations with first-order theories. We compare the
embeddings with respect to stable expansions and autoepistemic consequences,
considering the embeddings by themselves, as well as combinations with
classical theories. Our results reveal differences and correspondences of the
embeddings and provide useful guidance in the choice of a particular embedding
for knowledge combination.Comment: 52 pages, submitte
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