A Tableau Algorithm for the Clique Guarded

A Tableau Algorithm for the Clique

Finite conformal hypergraph covers and Gaifman cliques in finite structures

We provide a canonical construction of conformal covers for finite hypergraphs and present two immediate applications to the finite model theory of relational structures. In the setting of relational structures, conformal covers serve to construct guarded bisimilar companion structures that avoid all incidental Gaifman cliques – thus serving as a partial analogue in finite model theory for the ...

A Guarded negation

We consider restrictions of first-order logic and of fixpoint logic in which all occurrences of negation are required to be guarded by an atomic predicate. In terms of expressive power, the logics in question, called GNFO and GNFP, extend the guarded fragment of first-order logic and the guarded least fixpoint logic, respectively. They also extend the recently introduced unary negation fragment...

Extending Consequence-Based Reasoning to SHIQ

Description logics (DLs) [3] are a family of knowledge representation formalisms with numerous practical applications. SHIQ is a particularly important DL as it provides the formal underpinning for the Web Ontology Language (OWL). DLs model a domain of interest using concepts (i.e., unary predicate symbols) and roles (i.e., binary predicate symbols). DL applications often rely on subsumption—th...

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 a...