Reasoning with Inconsistencies in Hybrid MKNF Knowledge Bases

This article is concerned with the handling of inconsistencies occurring in the combination of description logics and rules, especially in hybrid MKNF knowledge bases. More precisely, we present a paraconsistent semantics for hybrid MKNF knowledge bases (called para-MKNF knowledge bases) based on four-valued logic as proposed by Belnap. We also reduce this paraconsistent semantics to the stable model semantics via a linear transformation operator, which shows the relationship between the two semantics and indicates that the data complexity in our paradigm is not higher than that of classical reasoning. Moreover, we provide fixpoint operators to compute paraconsistent MKNF models, each suitable to different kinds of rules. At last we present the data complexity of instance checking in different para-MKNF knowledge bases

Ontology-based knowledge representation and semantic search information retrieval: case study of the underutilized crops domain

The aim of using semantic technologies in domain knowledge modeling is to introduce the semantic meaning of concepts in knowledge bases, such that they are both human-readable as well as machine-understandable. Due to their powerful knowledge representation formalism and associated inference mechanisms, ontology-based approaches have been increasingly adopted to formally represent domain knowledge. The primary objective of this thesis work has been to use semantic technologies in advancing knowledge-sharing of Underutilized crops as a domain and investigate the integration of underlying ontologies developed in OWL (Web Ontology Language) with augmented SWRL (Semantic Web Rule Language) rules for added expressiveness. The work further investigated generating ontologies from existing data sources and proposed the reverse-engineering approach of generating domain specific conceptualization through competency questions posed from possible ontology users and domain experts. For utilization, a semantic search engine (the Onto-CropBase) has been developed to serve as a Web-based access point for the Underutilized crops ontology model. Relevant linked-data in Resource Description Framework Schema (RDFS) were added for comprehensiveness in generating federated queries. While the OWL/SWRL combination offers a highly expressive ontology language for modeling knowledge domains, the combination is found to be lacking supplementary descriptive constructs to model complex real-life scenarios, a necessary requirement for a successful Semantic Web application. To this end, the common logic programming formalisms for extending Description Logic (DL)-based ontologies were explored and the state of the art in SWRL expressiveness extensions determined with a view to extending the SWRL formalism. Subsequently, a novel fuzzy temporal extension to the Semantic Web Rule Language (FT-SWRL), which combines SWRL with fuzzy logic theories based on the valid-time temporal model, has been proposed to allow modeling imprecise temporal expressions in domain ontologies

A Language for Inconsistency-Tolerant Ontology Mapping

Ontology alignment plays a key role in enabling interoperability among various data sources present in the web. The nature of the world is such, that the same concepts differ in meaning, often so slightly, which makes it difficult to relate these concepts. It is the omni-present heterogeneity that is at the core of the web. The research work presented in this dissertation, is driven by the goal of providing a robust ontology alignment language for the semantic web, as we show that description logics based alignment languages are not suitable for aligning ontologies. The adoption of the semantic web technologies has been consistently on the rise over the past decade, and it continues to show promise. The core component of the semantic web is the set of knowledge representation languages -- mainly the W3C (World Wide Web Consortium) standards Web Ontology Language (OWL), Resource Description Framework (RDF), and Rule Interchange Format (RIF). While these languages have been designed in order to be suitable for the openness and extensibility of the web, they lack certain features which we try to address in this dissertation. One such missing component is the lack of non-monotonic features, in the knowledge representation languages, that enable us to perform common sense reasoning. For example, OWL supports the open world assumption (OWA), which means that knowledge about everything is assumed to be possibly incomplete at any point of time. However, experience has shown that there are situations that require us to assume that certain parts of the knowledge base are complete. Employing the Closed World Assumption (CWA) helps us achieve this. Circumscription is a very well-known approach towards CWA, which provides closed world semantics by employing the idea of minimal models with respect to certain predicates which are closed. We provide the formal semantics of the notion of Grounded Circumscription, which is an extension of circumscription with desirable properties like decidability. We also provide a tableaux calculus to reason over knowledge bases under the notion of grounded circumscription. Another form of common sense logic, is default logic. Default logic provides a way to specify rules that, by default, hold in most cases but not necessarily in all cases. The classic example of such a rule is: If something is a bird then it flies. The power of defaults comes from the ability of the logic to handle exceptions to the default rules. For example, a bird will be assumed to fly by default unless it is an exception, i.e. it belongs to a class of birds that do not fly, like penguins. Interestingly, this property of defaults can be utilized to create mappings between concepts of different ontologies (knowledge bases). We provide a new semantics for the integration of defaults in description logics and show that it improves upon previously known results in literature. In this study, we give various examples to show the utility and advantages of using a default logic based ontology alignment language. We provide the semantics and decidability results of a default based mapping language for tractable fragments of description logics (or OWL). Furthermore, we provide a proof of concept system and qualitative analysis of the results obtained from the system when compared to that of traditional mapping repair techniques

Ontology-based knowledge representation and semantic search information retrieval: case study of the underutilized crops domain

The aim of using semantic technologies in domain knowledge modeling is to introduce the semantic meaning of concepts in knowledge bases, such that they are both human-readable as well as machine-understandable. Due to their powerful knowledge representation formalism and associated inference mechanisms, ontology-based approaches have been increasingly adopted to formally represent domain knowledge. The primary objective of this thesis work has been to use semantic technologies in advancing knowledge-sharing of Underutilized crops as a domain and investigate the integration of underlying ontologies developed in OWL (Web Ontology Language) with augmented SWRL (Semantic Web Rule Language) rules for added expressiveness. The work further investigated generating ontologies from existing data sources and proposed the reverse-engineering approach of generating domain specific conceptualization through competency questions posed from possible ontology users and domain experts. For utilization, a semantic search engine (the Onto-CropBase) has been developed to serve as a Web-based access point for the Underutilized crops ontology model. Relevant linked-data in Resource Description Framework Schema (RDFS) were added for comprehensiveness in generating federated queries. While the OWL/SWRL combination offers a highly expressive ontology language for modeling knowledge domains, the combination is found to be lacking supplementary descriptive constructs to model complex real-life scenarios, a necessary requirement for a successful Semantic Web application. To this end, the common logic programming formalisms for extending Description Logic (DL)-based ontologies were explored and the state of the art in SWRL expressiveness extensions determined with a view to extending the SWRL formalism. Subsequently, a novel fuzzy temporal extension to the Semantic Web Rule Language (FT-SWRL), which combines SWRL with fuzzy logic theories based on the valid-time temporal model, has been proposed to allow modeling imprecise temporal expressions in domain ontologies

A Lightweight Defeasible Description Logic in Depth: Quantification in Rational Reasoning and Beyond

Description Logics (DLs) are increasingly successful knowledge representation formalisms, useful for any application requiring implicit derivation of knowledge from explicitly known facts. A prominent example domain benefiting from these formalisms since the 1990s is the biomedical field. This area contributes an intangible amount of facts and relations between low- and high-level concepts such as the constitution of cells or interactions between studied illnesses, their symptoms and remedies. DLs are well-suited for handling large formal knowledge repositories and computing inferable coherences throughout such data, relying on their well-founded first-order semantics. In particular, DLs of reduced expressivity have proven a tremendous worth for handling large ontologies due to their computational tractability. In spite of these assets and prevailing influence, classical DLs are not well-suited to adequately model some of the most intuitive forms of reasoning. The capability for abductive reasoning is imperative for any field subjected to incomplete knowledge and the motivation to complete it with typical expectations. When such default expectations receive contradicting evidence, an abductive formalism is able to retract previously drawn, conflicting conclusions. Common examples often include human reasoning or a default characterisation of properties in biology, such as the normal arrangement of organs in the human body. Treatment of such defeasible knowledge must be aware of exceptional cases - such as a human suffering from the congenital condition situs inversus - and therefore accommodate for the ability to retract defeasible conclusions in a non-monotonic fashion. Specifically tailored non-monotonic semantics have been continuously investigated for DLs in the past 30 years. A particularly promising approach, is rooted in the research by Kraus, Lehmann and Magidor for preferential (propositional) logics and Rational Closure (RC). The biggest advantages of RC are its well-behaviour in terms of formal inference postulates and the efficient computation of defeasible entailments, by relying on a tractable reduction to classical reasoning in the underlying formalism. A major contribution of this work is a reorganisation of the core of this reasoning method, into an abstract framework formalisation. This framework is then easily instantiated to provide the reduction method for RC in DLs as well as more advanced closure operators, such as Relevant or Lexicographic Closure. In spite of their practical aptitude, we discovered that all reduction approaches fail to provide any defeasible conclusions for elements that only occur in the relational neighbourhood of the inspected elements. More explicitly, a distinguishing advantage of DLs over propositional logic is the capability to model binary relations and describe aspects of a related concept in terms of existential and universal quantification. Previous approaches to RC (and more advanced closures) are not able to derive typical behaviour for the concepts that occur within such quantification. The main contribution of this work is to introduce stronger semantics for the lightweight DL EL_bot with the capability to infer the expected entailments, while maintaining a close relation to the reduction method. We achieve this by introducing a new kind of first-order interpretation that allocates defeasible information on its elements directly. This allows to compare the level of typicality of such interpretations in terms of defeasible information satisfied at elements in the relational neighbourhood. A typicality preference relation then provides the means to single out those sets of models with maximal typicality. Based on this notion, we introduce two types of nested rational semantics, a sceptical and a selective variant, each capable of deriving the missing entailments under RC for arbitrarily nested quantified concepts. As a proof of versatility for our new semantics, we also show that the stronger Relevant Closure, can be imbued with typical information in the successors of binary relations. An extensive investigation into the computational complexity of our new semantics shows that the sceptical nested variant comes at considerable additional effort, while the selective semantics reside in the complexity of classical reasoning in the underlying DL, which remains tractable in our case