On Reasoning about Structural Equality in XML: A Description Logic Approach

Abstract

Abstract. We define a boolean complete description logic dialect called DLFDreg that can be used to reason about structural equality in semistructured ordered data in the presence of document type definitions. This application depends on the novel ability of DLFDreg to express functional dependencies over sets of possibly infinite feature paths defined by regular languages. We also present a decision procedure for the associated logical implication problem. The procedure underlies a mapping of such problems to satisfiability problems of Datalog ∨,¬ nS and in turn to the Ackermann case of the decision problem.

Undecidability of Finite Model Reasoning in DLFD

“…This note is an addendum to [4].In this note we show that the finite logical implication for description logics endowed with PFDs is undecidable. This result complements the decidability of the unrestricted problem that is complete for EXPTIME [2,3].…”

On Limited Conjunctions and Partial Features in Parameter-Tractable Feature Logics

“…Unfortunately, unrestricted use of the concept constructors in Fig. 1 leads to intractability of checking KB consistency and logical implication (Toman and Weddell 2005). As usual, to ensure PTIME complexity, one looks for additional restrictions on concept constructors.…”

Roughening the $\mathcal{EL}$ Envelope

“…If we restrict ρ to be reflexive, and include the role inclusion axioms ρ • ρ ρ (transitivity), and ρ −1 ρ (symmetry), then the concepts C and C are equivalent to the concepts ∃ρ.C and ∀ρ.C, respectively (see [22] for full details). However, although transitive roles are a feature of EL ++ , it is well known that extensions of classical EL ++ with either value restrictions or inverse roles are already intractable; in fact reasoning in these extensions is ExpTime-complete [1,2,24]. Applying this reduction directly, yields an ExpTime upper bound for the complexity of deciding subsumption of rough EL ++ concepts.…”