The notions of meta-ontology enhance the ability to process knowledge in information systems; in particular, ontological property classification deals with the kinds of properties in taxonomic knowledge based on a philosophical analysis. The goal of this paper is to devise a reasoning mechanism to check the ontological and logical consistency of knowledge bases, which is important for reasoning services on taxonomic knowledge. We first consider an ontological property classification that is extended to capture individual existence and time and situation dependencies. To incorporate

Integrating ontologies and rules on the Semantic Web enables software agents to interoperate between them; however, this leads to two problems. First, reasoning services in SWRL (a combination of OWL and RuleML) are not decidable. Second, no studies have focused on distributed reasoning services for integrating ontologies and rules in multiple knowledge bases. In order to address these problems, we consider distributed reasoning services for ontologies and rules with decidable and effective computation. In this paper, we describe multiple order-sorted logic programming that transfers rigid properties from knowledge bases. Our order-sorted logic contains types (rigid sorts), non-rigid sorts, and unary predicates that distinctly express essential sorts, non-essential sorts, and non-sortal properties. We formalize the order-sorted Horn-clause calculus for such expressions in a single knowledge base. This calculus is extended by embedding rigid-property derivation for multiple knowledge bases, each of which can transfer rigidproperty information from other knowledge bases. In order to enable the reasoning to be effective and decidable, we design a query-answering system that combines order-sorted linear resolution and rigid-property resolution as top-down algorithms.

Abstract. For knowledge representation and reasoning, there is a need to consider the nature of events because event data describe various features and behaviors of the occurrences of actions and changes in the real world. In this paper, we propose to establish an upper event-ontology in order-sorted logic as an infrastructure for event knowledge bases. Our event ontology contains a classification of event entities (e.g., natural events and artificial events) and event relationships (e.g., causal relations and next-event relations). These ontological characterizations are needed for a theoretical basis of applications such as implementation of event databases, detection of event relationships, and annotation of event data. 1

An event, as opposed to an atemporal property, has its own time and location and occurs once. Although the notion of events has been found in researches on ontology, logic, linguistics, artificial intelligence and deductive databases, the different approaches to this notion do not seem to capture the various logical aspects of events. This paper proposes an event logic with expressions such as quantification over events, event sort-hierarchy, and composition and disjointness of events. In the logic, events are regarded as constants, sorts, predicates and variables in an order-sorted second-order language, which provides knowledge representation and reasoning for event assertions. In order to implement a query answering system, we present a sorted tableau calculus for the refutation of event formulas in logic.

The notions of meta-ontology enhance the ability to process knowledge in information systems; in particular, ontological property classification deals with the kinds of properties in taxonomic knowledge based on a philosophical analysis. The goal of this paper is to devise a reasoning mechanism to check the ontological and logical consistency of knowledge bases, which is important for reasoning services on taxonomic knowledge. We first

In the field of ontology, several property classifications have been defined as metaontologies wherein the properties of individuals are rigorously classified as sortal/nonsortal, rigid/anti-rigid/non-rigid, etc. through philosophical analysis. The notions of such meta-ontologies enable the processing of properties that allow us to reason about taxonomic knowledge in information systems. The goal of our research is to devise a reasoning mechanism that verifies the ontological consistency of knowledge bases in addition to their logical consistency. We first propose an ontological property classification based on individual existence and temporal and situational aspects of properties that establishes an infrastructure for knowledge bases. Second, by combining order-sorted logic and quantified modal logic, we develop an order-sorted modal logic in order to incorporate meta-ontologies into logical reasoning systems that involve rigidity, sortality, and three types of modal operators (temporal/situational/any-world). In the extended logic, sorted expressions and modalities suitably represent the ontological axioms of properties, which are interpreted in different types of possible worlds and in varying domains in Kripke semantics. As a reasoning system of the logic, we present a prefixed tableau calculus to test the satisfiability of sorted modal formulas including the ontological property classification. 1

Order-sorted logic is a useful tool for knowledge representation and reasoning because it enables representation of sorted terms and formulas along with partially ordered sorts (called sort-hierarchy). However, this logic cannot represent more complex sorted expressions when they are true in any possible world (as rigid) or some possible worlds (as modality) such as time, space, belief, or situation. In this study, we extend order-sorted logic by introducing existential rigidity and many modalities. In the extended logic, sorted modal formulas are interpreted over the Cartesian product of sets of possible worlds. We present a new labeled tableau calculus to check the (un)satisfiability and validity of sorted modal formulas. 1

This paper proposes a new semantics that characterizes the time and/or situation dependencies of properties, together with the ontological notion of existential rigidity. For this purpose, we present order-sorted tempo-situational logic (OSTSL) with rigid/anti-rigid sorts and an existential predicate. In this logic, rigid/anti-rigid sorted terms enable the expressions for sortal properties, and temporal and situational operators suitably represent the ontological axioms of existential rigidity and time and/or situation dependencies. A specific semantics of OSTSL adheres to the temporal and situational behaviors of properties based on existential rigidity. As a result, the semantics guarantees that the ontological axioms of properties expressed by sorted tempo-situational formulas are logically valid. key words: formal ontology, semantic web, order-sorted logic 1.