Philip H. P. Nguyen

A basic mathematical framework for conceptual graphs

Based on the original idea of Sowa on conceptual graph and a recent formalism by Corbett on ontology, this paper presents a rigorous mathematization of basic concepts encountered in the conceptual structure theory, including canon, ontology, conceptual graph, projection, and canonical formation operations, with the aim of deriving their mathematical properties and applying them to future research and development on knowledge representation. Our proposed formalism enhances the conceptual structure theory and enables it to compare favorably with other alternative methods such as the formal concept analysis theory.

Building corporate knowledge through ontology integration

This paper presents an approach for building corporate knowledge, defined as the total knowledge acquired by an enterprise in its business dealings, through integration of its existing ontologies. We propose to represent corporate knowledge as the final merged ontology, defined under our formalism, in which a canon, or common ontology, is used as the standard under which all other ontologies are aligned. The canon is also enriched with knowledge gained during each ontology merging exercise. Our method ensures that all resulting ontologies are semantically consistent, compact and complete, as well as mathematically sound, so that formal reasoning could be conducted.

An Ontology Formalization of Relation Type Hierarchy in Conceptual Structure Theory

This paper presents an enhancement to ontology formalization, combining previous work in Conceptual Structure Theory and Order-Sorted Logic. In particular, the relation type hierarchy of the former theory is a subset of the predicate hierarchy of the latter. Most existing ontology formalisms place greater importance on concept types, but this paper focuses more on relation types, which are in essence predicates on concept types. New notions are introduced and new properties identified with the aim of completing missing arguments in relation types. The end result is a new ontology, that we call the closure of the original ontology, on which automated inference could be more easily produced (e.g., a query-answering system for legal knowledge).

Decidable Order-Sorted Logic Programming for Ontologies and Rules with Argument Restructuring

This paper presents a decidable fragment for combining ontologies and rules in order-sorted logic programming. We describe order-sorted logic programming with sort, predicate, and meta-predicate hierarchies for deriving predicate and meta-predicate assertions. Meta-level predicates (predicates of predicates) are useful for representing relationships between predicate formulas, and further, they conceptually yield a hierarchy similar to the hierarchies of sorts and predicates. By extending the order-sorted Horn-clause calculus, we develop a query-answering system that can answer queries such as atoms and meta-atoms generalized by containing predicate variables. We show that the expressive query-answering system computes every generalized query in single exponential time, i.e., the complexity of our query system is equal to that of DATALOG.

A Logical and Ontological Framework for Compositional Concepts of Objects and Properties

In order to formalize complex and compositional concepts, we propose a logical framework based on an upper ontology constructed from the composition of basic concepts such as properties and objects. In particular, ontologically distinct compositions (called ontological compositions) that are not easily defined by using ISA and PART-OF relations are classified into characterizing, temporal, and spatial compositions (e.g., ’red face’ and ’today’). In this paper, we precisely model such ontological compositions by using monadic second-order logic; properties and objects are expressed as predicates, and attributes are expressed as predicates of predicates. The proposed approach provides a novel technique for the classification of attributes as higher-order concepts, and it clarifies illegal compositions of properties and objects and the uniqueness of temporal attributes. Moreover, our composition ontology is described by a set of RDF triples using the metamodeling of concepts in RDF Schema.

An order-sorted query system for sort, predicate, and meta-predicate hierarchies

This paper presents a decidable order-sorted query system for reasoning between ontologies and rules. We describe order-sorted logic programming with sort, predicate, and meta-predicate hierarchies (OSL3h), which derives predicate and meta-predicate assertions. Meta-level predicates (predicates of predicates) are useful for representing relationships between predicate formulas, and further, they conceptually yield a hierarchy similar to the hierarchies of sorts and predicates. By extending the order-sorted Horn-clause calculus, we develop a query-answering system in OSL3h that can answer queries such as atoms and meta-atoms generalized by containing predicate variables. We show that the expressive query-answering system computes every generalized query in single exponential time, that is, the complexity of our query system is equal to that of DATALOG.

Sorted hyper-predicate knowledge bases for ontologies and rules

In the Semantic Web context, the meta-modeling of concepts in ontologies and rules is required for defining the meanings of upper-level data and vocabularies. For this purpose, we propose a decidable fragment of order-sorted logic programming with hyper-predicate hierarchies. In the sorted language, we can employ simple- and hyper-predicates to express the concepts of sorts, predicates, and meta-predicates by unifying and enhancing them in a hyper-predicate hierarchy. The sorted Horn-clause calculus is extended to develop a query-answering system that can answer queries such as atoms and hyper-atoms generalized to contain predicate variables. We show that each query is computable in NEXPTIME if knowledge bases are function-free and safe. Furthermore, the computation can be reduced to EXPTIME if additional arguments in super-predicates and multiple predicate declarations are restricted.

Representing Event Assertions in an Upper Event Ontology

This paper presents an upper event ontology under Conceptual Structure Theory with an emphasis on formalizing the event relation type hierarchy of the ontology to enable representation and classification of event assertions. The proposed ontology essentially consists of an event type hierarchy created from basic event assertions, an event relation type hierarchy built from predicates on event types and other formal relationships between these structures. Representation of event assertions enables inference on events, which can be used in the Semantic Web for automated inference and query answering.

EVENT INFERENCE WITH RELATION AND META-RELATION TYPE HIERARCHIES IN CONCEPTUAL STRUCTURE THEORY

□ This article proposes a method to perform automated inference from event assertions through the use of an ontology formalized under Conceptual Structure Theory. An upper event ontology is first presented as an example of how the ontology is built and how real-life event assertions and their relations are modeled into its hierarchies of type. Three different types are distinguished: an event type as a basic classification of events of similar nature, an event relation type as a predicate on event types, and an event meta-relation type as a “predicate of predicates” on event types, with formal relationships between them and their properties elicited. The proposed formalization could be leveraged by search engines on the Semantic Web and query-answering systems in specific domains of discourse.