284 research outputs found
Incremental Recompilation of Knowledge
Approximating a general formula from above and below by Horn formulas (its
Horn envelope and Horn core, respectively) was proposed by Selman and Kautz
(1991, 1996) as a form of ``knowledge compilation,'' supporting rapid
approximate reasoning; on the negative side, this scheme is static in that it
supports no updates, and has certain complexity drawbacks pointed out by
Kavvadias, Papadimitriou and Sideri (1993). On the other hand, the many
frameworks and schemes proposed in the literature for theory update and
revision are plagued by serious complexity-theoretic impediments, even in the
Horn case, as was pointed out by Eiter and Gottlob (1992), and is further
demonstrated in the present paper. More fundamentally, these schemes are not
inductive, in that they may lose in a single update any positive properties of
the represented sets of formulas (small size, Horn structure, etc.). In this
paper we propose a new scheme, incremental recompilation, which combines Horn
approximation and model-based updates; this scheme is inductive and very
efficient, free of the problems facing its constituents. A set of formulas is
represented by an upper and lower Horn approximation. To update, we replace the
upper Horn formula by the Horn envelope of its minimum-change update, and
similarly the lower one by the Horn core of its update; the key fact which
enables this scheme is that Horn envelopes and cores are easy to compute when
the underlying formula is the result of a minimum-change update of a Horn
formula by a clause. We conjecture that efficient algorithms are possible for
more complex updates.Comment: See http://www.jair.org/ for any accompanying file
Reason Maintenance - State of the Art
This paper describes state of the art in reason maintenance with a focus on its future usage in the KiWi project. To give a bigger picture of the field, it also mentions closely related issues such as non-monotonic logic and paraconsistency. The paper is organized as follows: first, two motivating scenarios referring to semantic wikis are presented which are then used to introduce the different reason maintenance techniques
Space Efficiency of Propositional Knowledge Representation Formalisms
We investigate the space efficiency of a Propositional Knowledge
Representation (PKR) formalism. Intuitively, the space efficiency of a
formalism F in representing a certain piece of knowledge A, is the size of the
shortest formula of F that represents A. In this paper we assume that knowledge
is either a set of propositional interpretations (models) or a set of
propositional formulae (theorems). We provide a formal way of talking about the
relative ability of PKR formalisms to compactly represent a set of models or a
set of theorems. We introduce two new compactness measures, the corresponding
classes, and show that the relative space efficiency of a PKR formalism in
representing models/theorems is directly related to such classes. In
particular, we consider formalisms for nonmonotonic reasoning, such as
circumscription and default logic, as well as belief revision operators and the
stable model semantics for logic programs with negation. One interesting result
is that formalisms with the same time complexity do not necessarily belong to
the same space efficiency class
Updating DL-Lite ontologies through first-order queries
In this paper we study instance-level update in DL-LiteA, the description logic underlying the OWL 2 QL standard. In particular we focus on formula-based approaches to ABox insertion and deletion. We show that DL-LiteA, which is well-known for enjoying first-order rewritability of query answering, enjoys a first-order rewritability property also for updates. That is, every update can be reformulated into a set of insertion and deletion instructions computable through a nonrecursive datalog program. Such a program is readily translatable into a first-order query over the ABox considered as a database, and hence into SQL. By exploiting this result, we implement an update component for DLLiteA-based systems and perform some experiments showing that the approach works in practice.Peer ReviewedPostprint (author's final draft
On Properties of Update Sequences Based on Causal Rejection
We consider an approach to update nonmonotonic knowledge bases represented as
extended logic programs under answer set semantics. New information is
incorporated into the current knowledge base subject to a causal rejection
principle enforcing that, in case of conflicts, more recent rules are preferred
and older rules are overridden. Such a rejection principle is also exploited in
other approaches to update logic programs, e.g., in dynamic logic programming
by Alferes et al. We give a thorough analysis of properties of our approach, to
get a better understanding of the causal rejection principle. We review
postulates for update and revision operators from the area of theory change and
nonmonotonic reasoning, and some new properties are considered as well. We then
consider refinements of our semantics which incorporate a notion of minimality
of change. As well, we investigate the relationship to other approaches,
showing that our approach is semantically equivalent to inheritance programs by
Buccafurri et al. and that it coincides with certain classes of dynamic logic
programs, for which we provide characterizations in terms of graph conditions.
Therefore, most of our results about properties of causal rejection principle
apply to these approaches as well. Finally, we deal with computational
complexity of our approach, and outline how the update semantics and its
refinements can be implemented on top of existing logic programming engines.Comment: 59 pages, 2 figures, 3 tables, to be published in "Theory and
Practice of Logic Programming
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