8 research outputs found
Equality-friendly well-founded semantics and applications to description logics
We tackle the problem of deïŹning a well-founded semantics (WFS) for Datalog rules with existentially quantiïŹed variables in their heads and nega- tions in their bodies. In particular, we provide a WFS for the recent Datalog± family of ontology languages, which covers several important description logics (DLs). To do so, we generalize Datalog± by non-stratiïŹed nonmonotonic nega- tion in rule bodies, and we deïŹne a WFS for this generalization via guarded ïŹxed point logic. We refer to this approach as equality-friendly WFS, since it has the advantage that it does not make the unique name assumption (UNA); this brings it close to OWL and its proïŹles as well as typical DLs, which also do not make the UNA. We prove that for guarded Datalog± with negation under the equality- friendly WFS, conjunctive query answering is decidable, and we provide precise complexity results for this problem. From these results, we obtain precise deïŹ- nitions of the standard WFS extensions of EL and of members of the DL-Lite family, as well as corresponding complexity results for query answering
Saturation-based decision procedures for extensions of the guarded fragment
We apply the framework of Bachmair and Ganzinger for saturation-based theorem proving to derive a range of decision procedures for logical formalisms, starting with a simple terminological language EL, which allows for conjunction and existential restrictions only, and ending with extensions of the guarded fragment with equality, constants, functionality, number restrictions and compositional axioms of form S ◦ T ⊆ H. Our procedures are derived in a uniform way using standard saturation-based calculi enhanced with simplification rules based on the general notion of redundancy. We argue that such decision procedures can be applied for reasoning in expressive description logics, where they have certain advantages over traditionally used tableau procedures, such as optimal worst-case complexity and direct correctness proofs.Wir wenden das Framework von Bachmair und Ganzinger fĂŒr saturierungsbasiertes Theorembeweisen an, um eine Reihe von Entscheidungsverfahren fĂŒr logische Formalismen abzuleiten, angefangen von einer simplen terminologischen Sprache EL, die nur Konjunktionen und existentielle Restriktionen erlaubt, bis zu Erweiterungen des Guarded Fragment mit Gleichheit, Konstanten, FunktionalitĂ€t, Zahlenrestriktionen und Kompositionsaxiomen der Form S ◦ T ⊆ H. Unsere Verfahren sind einheitlich abgeleitet unter Benutzung herkömmlicher saturierungsbasierter KalkĂŒle, verbessert durch Simplifikationsregeln, die auf dem Konzept der Redundanz basieren. Wir argumentieren, daĂ solche Entscheidungsprozeduren fĂŒr das Beweisen in ausdrucksvollen Beschreibungslogiken angewendet werden können, wo sie gewisse Vorteile gegenĂŒber traditionell benutzten Tableauverfahren besitzen, wie z.B. optimale worst-case KomplexitĂ€t und direkte Korrektheitsbeweise
Guarded fragments with constants
We prove ExpTime-membership of the satisfiability problem for loosely 00-guarded first-order formulas with a bounded number of variables and an unbounded number of constants. Guarded fragments with constants are interesting by themselves and because of their connection to hybrid logic
Structure of Flagellar Motor Proteins in Complex Allows for Insights into Motor Structure and Switching
Abstract. We prove ExpTime-membership of the satisfiability problem for loosely â-guarded first-order formulas with a bounded number of variables and an unbounded number of constants. Guarded fragments with constants are interesting by themselves and because of their connection to hybrid logic