26,423 research outputs found
Adding DL-Lite TBoxes to Proper Knowledge Bases
Levesque’s proper knowledge bases (proper KBs) correspond to infinite sets of ground positive and negative facts, with the notable property that for FOL formulas in a certain normal form, which includes conjunctive queries and positive queries possibly extended with a controlled form of negation, entailment reduces to formula evaluation. However proper KBs represent extensional knowledge only. In description logic terms, they correspond to ABoxes. In this paper, we augment them with DL-Lite TBoxes, expressing intensional knowledge (i.e., the ontology of the domain). DL-Lite has the notable property that conjunctive query answering over TBoxes and standard description logic ABoxes is re- ducible to formula evaluation over the ABox only. Here, we investigate whether such a property extends to ABoxes consisting of proper KBs. Specifically, we consider two DL-Lite variants: DL-Literdfs , roughly corresponding to RDFS, and DL-Lite_core , roughly corresponding to OWL 2 QL. We show that when a DL- Lite_rdfs TBox is coupled with a proper KB, the TBox can be compiled away, reducing query answering to evaluation on the proper KB alone. But this reduction is no longer possible when we associate proper KBs with DL-Lite_core TBoxes. Indeed, we show that in the latter case, query answering even for conjunctive queries becomes coNP-hard in data complexity
Decidable Reasoning in Terminological Knowledge Representation Systems
Terminological knowledge representation systems (TKRSs) are tools for
designing and using knowledge bases that make use of terminological languages
(or concept languages). We analyze from a theoretical point of view a TKRS
whose capabilities go beyond the ones of presently available TKRSs. The new
features studied, often required in practical applications, can be summarized
in three main points. First, we consider a highly expressive terminological
language, called ALCNR, including general complements of concepts, number
restrictions and role conjunction. Second, we allow to express inclusion
statements between general concepts, and terminological cycles as a particular
case. Third, we prove the decidability of a number of desirable TKRS-deduction
services (like satisfiability, subsumption and instance checking) through a
sound, complete and terminating calculus for reasoning in ALCNR-knowledge
bases. Our calculus extends the general technique of constraint systems. As a
byproduct of the proof, we get also the result that inclusion statements in
ALCNR can be simulated by terminological cycles, if descriptive semantics is
adopted.Comment: See http://www.jair.org/ for any accompanying file
Constrained Query Answering
Traditional answering methods evaluate queries only against positive
and definite knowledge expressed by means of facts and deduction rules. They do
not make use of negative, disjunctive or existential information. Negative or indefinite
knowledge is however often available in knowledge base systems, either as
design requirements, or as observed properties. Such knowledge can serve to rule out
unproductive subexpressions during query answering. In this article, we propose an
approach for constraining any conventional query answering procedure with general,
possibly negative or indefinite formulas, so as to discard impossible cases and to
avoid redundant evaluations. This approach does not impose additional conditions
on the positive and definite knowledge, nor does it assume any particular semantics
for negation. It adopts that of the conventional query answering procedure it
constrains. This is achieved by relying on meta-interpretation for specifying the
constraining process. The soundness, completeness, and termination of the underlying
query answering procedure are not compromised. Constrained query answering
can be applied for answering queries more efficiently as well as for generating more
informative, intensional answers
Elimination of Cuts in First-order Finite-valued Logics
A uniform construction for sequent calculi for finite-valued first-order logics with distribution quantifiers is exhibited. Completeness, cut-elimination and midsequent theorems are established. As an application, an analog of Herbrand’s theorem for the four-valued knowledge-representation logic of Belnap and Ginsberg is presented. It is indicated how this theorem can be used for reasoning about knowledge bases with incomplete and inconsistent information
Possibilistic Boolean games: strategic reasoning under incomplete information
Boolean games offer a compact alternative to normal-form games, by encoding the goal of each agent as a propositional formula. In this paper, we show how this framework can be naturally extended to model situations in which agents are uncertain about other agents' goals. We first use uncertainty measures from possibility theory to semantically define (solution concepts to) Boolean games with incomplete information. Then we present a syntactic characterization of these semantics, which can readily be implemented, and we characterize the computational complexity
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