We show how to interoperate, semantically and inferentially, between the leading Semantic Web approaches to rules (RuleML Logic Programs) and ontologies (OWL/DAML+OIL Description Logic) via analyzing their expressive intersection. To do so, we define a new intermediate knowledge representation (KR) contained within this intersection: Description Logic Programs (DLP), and the closely related Description Horn Logic (DHL) which is an expressive fragment of first-order logic (FOL). DLP provides a significant degree of expressiveness, substantially greater than the RDFSchema fragment of Description Logic.

Both OWL-DL and function-free Horn rules are decidable fragments of first-order logic with interesting, yet orthogonal expressive power. A combination of OWL-DL and rules is desirable for the Semantic Web; however, it might easily lead to the undecidability of interesting reasoning problems. Here, we present a decidable such combination where rules are required to be DL-safe: each variable in the rule is required to occur in a non-DL-atom in the rule body. We discuss the expressive power of such a combination and present an algorithm for query answering in the related logic SHIQ extended with DL-safe rules, based on a reduction to disjunctive programs.

OWL DL, a new W3C ontology language recommendation, is based on the expressive description logic SHOIN. Although the ontology consistency problem for SHOIN is known to be decidable, up to now there has been no known “practical ” decision procedure, i.e., a goal directed procedure that is likely to perform well with realistic ontology derived problems. We present such a decision procedure (for SHOIQ, a slightly more expressive logic than SHOIN), extending the well known algorithm for SHIQ,

Guarded fragments of first-order logic were recently introduced by Andr'eka, van Benthem and N'emeti; they consist of relational first-order formulae whose quantifiers are appropriately relativized by atoms. These fragments are interesting because they extend in a natural way many propositional modal logics, because they have useful model-theoretic properties and especially because they are decidable classes that avoid the usual syntactic restrictions (on the arity of relation symbols, the quantifier pattern or the number of variables) of almost all other known decidable fragments of first-order logic. Here, we investigate the computational complexity of these fragments. We prove that the satisfiability problems for the guarded fragment (GF) and the loosely guarded fragment (LGF) of first-order logic are complete for deterministic double exponential time. For the subfragments that have only a bounded number of variables or only relation symbols of bounded arity, satisfiability is EXPTI...

Conjunctive queries play an important role as an expressive query language for Description Logics (DLs). Although modern DLs usually provide for transitive roles, it was an open problem whether conjunctive query answering over DL knowledge bases is decidable if transitive roles are admitted in the query. In this paper, we consider conjunctive queries over knowledge bases formulated in the popular DL SHIQ and allow transitive roles in both the query and the knowledge base. We show that query answering is decidable and establish the following complexity bounds: regarding combined complexity, we devise a deterministic algorithm for query answering that needs time single exponential in the size of the KB and double exponential in the size of the query. Regarding data complexity, we prove co-NP-completeness. 1

) Glenn Bruns and Patrice Godefroid Bell Laboratories, Lucent Technologies fgrb,godg@bell-labs.com Abstract. We address the problem of relating the result of model checking a partial state space of a system to the properties actually possessed by the system. We represent incomplete state spaces as partial Kripke structures, and give a 3-valued interpretation to modal logic formulas on these structures. The third truth value ? means "unknown whether true or false". We define a preorder on partial Kripke structures that reflects their degree of completeness. We then provide a logical characterization of this preorder. This characterization thus relates properties of less complete structures to properties of more complete structures. We present similar results for labeled transition systems and show a connection to intuitionistic modal logic. We also present a 3-valued CTL model checking algorithm, which returns ? only when the partial state space lacks information needed ...

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We discuss the problem of model checking temporal properties on partial Kripke structures, which were used in [BG99] to represent incomplete state spaces. We first extend the results of [BG99] by showing that the model-checking problem for any 3-valued temporal logic can be reduced to two model-checking problems for the corresponding 2-valued temporal logic. We then introduce a new semantics for 3-valued temporal logics that can give more definite answers than the previous one. With this semantics, the evaluation of a formula OE on a partial Kripke structure M returns the third truth value? (read "unknown") only if there exist Kripke structures M1 and M2 that both complete M and such that M1 satisfies OE while M2 violates OE, hence making the value of OE on M truly unknown. The partial Kripke structure M can thus be viewed as a partial solution to the satisfiability problem which reduces the solution space to complete Kripke structures that are more complete than M wit...

Abstract. We give two sufficient conditions on XPath like languages for having first order expressivity, meaning that every first order definable set of paths in an ordered node-labeled tree is definable in that XPath language. They are phrased in terms of expansions of navigational (sometimes called “Core”) XPath. Adding either complementation, or the more elegant conditional paths is sufficient. A conditional path is an axis relation of the form (one step axis::n[F]) +, denoting the transitive closure of the relation expressed by one step axis::n[F]. As neither is expressible in navigational XPath we also give characterizations in terms of first order logic of the answer sets and the sets of paths navigational XPath can define. The first in terms of a suitable two variable fragment, the second in terms of unions of conjunctive queries. 1

Abstract. XPath 1.0 is a variable free language designed to specify paths between nodes in XML documents. Such paths can alternatively be specified in first-order logic. The logical abstraction of XPath 1.0, usually called Navigational or Core XPath, is not powerful enough to express every first-order definable path. In this paper we show that there exists a natural expansion of Core XPath in which every first-order definable path in XML document trees is expressible. This expansion is called Conditional XPath. It contains additional axis relations of the form (child::n[F])+, denoting the transitive closure of the path expressed by child::n[F]. The difference with XPath’s descendant::n[F] is that the path (child::n[F])+ is conditional on the fact that all nodes in between should be labeled by n and should make the predicate F true. This result can be viewed as the XPath analogue of the expressive completeness of the relational algebra with respect to first-order logic. 1