Automated Reasoning in Deontic Logic

Deontic logic is a very well researched branch of mathematical logic and philosophy. Various kinds of deontic logics are discussed for different application domains like argumentation theory, legal reasoning, and acts in multi-agent systems. In this paper, we show how standard deontic logic can be stepwise transformed into description logic and DL- clauses, such that it can be processed by Hyper, a high performance theorem prover which uses a hypertableau calculus. Two use cases, one from multi-agent research and one from the development of normative system are investigated

Converting Instance Checking to Subsumption: A Rethink for Object Queries over Practical Ontologies

Efficiently querying Description Logic (DL) ontologies is becoming a vital task in various data-intensive DL applications. Considered as a basic service for answering object queries over DL ontologies, instance checking can be realized by using the most specific concept (MSC) method, which converts instance checking into subsumption problems. This method, however, loses its simplicity and efficiency when applied to large and complex ontologies, as it tends to generate very large MSC's that could lead to intractable reasoning. In this paper, we propose a revision to this MSC method for DL SHI, allowing it to generate much simpler and smaller concepts that are specific-enough to answer a given query. With independence between computed MSC's, scalability for query answering can also be achieved by distributing and parallelizing the computations. An empirical evaluation shows the efficacy of our revised MSC method and the significant efficiency achieved when using it for answering object queries

Range-Restricted Interpolation through Clausal Tableaux

We show how variations of range-restriction and also the Horn property can be passed from inputs to outputs of Craig interpolation in first-order logic. The proof system is clausal tableaux, which stems from first-order ATP. Our results are induced by a restriction of the clausal tableau structure, which can be achieved in general by a proof transformation, also if the source proof is by resolution/paramodulation. Primarily addressed applications are query synthesis and reformulation with interpolation. Our methodical approach combines operations on proof structures with the immediate perspective of feasible implementation through incorporating highly optimized first-order provers

Consistency in Fuzzy Description Logics over Residuated De Morgan Lattices

Fuzzy description logics can be used to model vague knowledge in application domains. This paper analyses the consistency and satisfiability problems in the description logic SHI with semantics based on a complete residuated De Morgan lattice. The problems are undecidable in the general case, but can be decided by a tableau algorithm when restricted to finite lattices. For some sublogics of SHI, we provide upper complexity bounds that match the complexity of crisp reasoning

Logical Gene Ontology Annotations (GOAL): exploring gene ontology annotations with OWL

MOTIVATION: Ontologies such as the Gene Ontology (GO) and their use in annotations make cross species comparisons of genes possible, along with a wide range of other analytical activities. The bio-ontologies community, in particular the Open Biomedical Ontologies (OBO) community, have provided many other ontologies and an increasingly large volume of annotations of gene products that can be exploited in query and analysis. As many annotations with different ontologies centre upon gene products, there is a possibility to explore gene products through multiple ontological perspectives at the same time. Questions could be asked that link a gene product’s function, process, cellular location, phenotype and disease. Current tools, such as AmiGO, allow exploration of genes based on their GO annotations, but not through multiple ontological perspectives. In addition, the semantics of these ontology’s representations should be able to, through automated reasoning, afford richer query opportunities of the gene product annotations than is currently possible. RESULTS: To do this multi-perspective, richer querying of gene product annotations, we have created the Logical Gene Ontology, or GOAL ontology, in OWL that combines the Gene Ontology, Human Disease Ontology and the Mammalian Phenotype Ontology, together with classes that represent the annotations with these ontologies for mouse gene products. Each mouse gene product is represented as a class, with the appropriate relationships to the GO aspects, phenotype and disease with which it has been annotated. We then use defined classes to query these protein classes through automated reasoning, and to build a complex hierarchy of gene products. We have presented this through a Web interface that allows arbitrary queries to be constructed and the results displayed. CONCLUSION: This standard use of OWL affords a rich interaction with Gene Ontology, Human Disease Ontology and Mammalian Phenotype Ontology annotations for the mouse, to give a fine partitioning of the gene products in the GOAL ontology. OWL in combination with automated reasoning can be effectively used to query across ontologies to ask biologically rich questions. We have demonstrated that automated reasoning can be used to deliver practical on-line querying support for the ontology annotations available for the mouse. AVAILABILITY: The GOAL Web page is to be found at http://owl.cs.manchester.ac.uk/goal

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