Hypertableau Reasoning for Description Logics

We present a novel reasoning calculus for the description logic SHOIQ^+---a knowledge representation formalism with applications in areas such as the Semantic Web. Unnecessary nondeterminism and the construction of large models are two primary sources of inefficiency in the tableau-based reasoning calculi used in state-of-the-art reasoners. In order to reduce nondeterminism, we base our calculus on hypertableau and hyperresolution calculi, which we extend with a blocking condition to ensure termination. In order to reduce the size of the constructed models, we introduce anywhere pairwise blocking. We also present an improved nominal introduction rule that ensures termination in the presence of nominals, inverse roles, and number restrictions---a combination of DL constructs that has proven notoriously difficult to handle. Our implementation shows significant performance improvements over state-of-the-art reasoners on several well-known ontologies

A Semantic Importing Approach to Reusing Knowledge from Multiple Autonomous Ontology Modules

We present the syntax and semantics of a modular ontology language \logic{SHOIQP} to accomplish knowledge integration from multiple ontologies and knowledge reuse from context-specific points of view. Specifically, a \logic{SHOIQP} ontology consists of multiple ontology modules (each of which can be viewed as a \logic{SHOIQ} ontology) and concept, role and nominal names can be shared by ``importing\u27\u27 relations among modules. The proposed language supports contextualized interpretation, i.e., interpretation from the point of view of a specific package. We establish the necessary and sufficient constraints on domain relations (i.e., the relations between individuals in different local domains) to preserve the satisfiability of concept formulae, monotonicity of inference, and transitive reuse of knowledge

Unions of conjunctive queries in SHOQ

Conjunctive queries play an important role as an expressive query language in Description Logics (DLs). Decision procedures for expressive Description Logics are, however, only recently emerging and it is still an open question whether answering conjunctive queries is decidable for the DL SHOIQ that underlies the OWL DL standard. In fact, no decision procedure was known for expressive DLs that contain nominals. In this paper, we close this gap by providing a decision procedure for entailment of unions of conjunctive queries in SHOQ. Our algorithm runs in deterministic time single exponential in the size of the knowledge base and double exponential in the size of the query, which is the same as for SHIQ. Our procedure also shows that SHOQ knowledge base consistency is indeed ExpTime-complete, which was, to the best of our knowledge, always conjectured but never proved

An Abstract Tableau Calculus for the Description Logic SHOI Using UnrestrictedBlocking and Rewriting

Abstract This paper presents an abstract tableau calculus for the description logic SHOI. SHOI is the extension of ALC with singleton concepts, role inverse, transitive roles and role inclusion axioms. The presented tableau calculus is inspired by a recently introduced tableau synthesis framework. Termination is achieved by a variation of the unrestricted blocking mechanism that immediately rewrites terms with respect to the conjectured equalities. This approach leads to reduced search space for decision procedures based on the calculus. We also discuss restrictions of the application of the blocking rule by means of additional side conditions and/or additional premises.

Automated Synthesis of Tableau Calculi

This paper presents a method for synthesising sound and complete tableau calculi. Given a specification of the formal semantics of a logic, the method generates a set of tableau inference rules that can then be used to reason within the logic. The method guarantees that the generated rules form a calculus which is sound and constructively complete. If the logic can be shown to admit finite filtration with respect to a well-defined first-order semantics then adding a general blocking mechanism provides a terminating tableau calculus. The process of generating tableau rules can be completely automated and produces, together with the blocking mechanism, an automated procedure for generating tableau decision procedures. For illustration we show the workability of the approach for a description logic with transitive roles and propositional intuitionistic logic.Comment: 32 page