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Ontological Domains, Semantic Sorts and Systematic Ambiguity
 International Journal of HumanComputer Studies
, 1995
"... This paper is concerned with some aspects of the relationship between ontologica! knowledge and natural language understanding. More specifically, I will consider how knowledge of ontological domains and knowledge of lexical meaning work together in the interpretation of linguistic expressions. An e ..."
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Cited by 26 (1 self)
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This paper is concerned with some aspects of the relationship between ontologica! knowledge and natural language understanding. More specifically, I will consider how knowledge of ontological domains and knowledge of lexical meaning work together in the interpretation of linguistic expressions. An essential assumption is that in accordance with ontological distinctions there are various semantic sorts which linguistic expressions can be divided. The specific purpose of the paper is to explore how under these conditions the intricate problem of systematic ambiguity can be dealt with. Here the term "systematic ambiguity " stands for the phenomenon that a word or a phrase has several possible meanings which systematically related to one another and from which a suitable meaning can be selected dependently on the linguistic and nonlinguistic context of use. Taking into consideration that many predicative expressions impose on their arguments certain sortal selection restrictions. I will deal with the phenomenon that a word or a phrase being systematically ambiguous in some cases adapt itself to the semantic format of the expression it is combined with. Such an adaptation eliminating one or more possible meaning of the word or phrase is in fact a coercion of its semantic sort. I will argue for an approach which takes into account a set of semantic coercion operations to meet sortal constraints. Moreover, I will show how such sort coercions performed in language understanding are sanctioned by world knowledge. © 1995 Academic Press Limited 1.
ONIONS: An Ontological Methodology for Taxonomic Knowledge Integration
 ECAI96 Workshop on Ontological Engineering
, 1996
"... We describe ONIONS, a methodology for integrating ontologicallyheterogeneous taxonomic knowledge and its current application to medical domain. Some clarification is given of our intended meaning of ontology and related notions, then main problems of ontology design are addressed, with a short comp ..."
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Cited by 17 (1 self)
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We describe ONIONS, a methodology for integrating ontologicallyheterogeneous taxonomic knowledge and its current application to medical domain. Some clarification is given of our intended meaning of ontology and related notions, then main problems of ontology design are addressed, with a short comparison with alternative approaches. The methodology is described as a sequence of phases. The toplevel of the current integrated ontology of heterogeneous medical taxonomies is presented in an ordersorted logic. ONIONS includes no claim of global objectivity (it performs an integration of explicit or explicited ontologies of given taxonomic sources), but provides a feasible solution to the problems of modelling stopover and cognitive basicality. ONIONS has been defined in order to be applied to sources within the same domain, nevertheless it has been applied to a very wide and inherently heterogeneous domain like medicine, so complex that it can be considered in itself an integration of subdomains. 1.
Ontological Knowledge Base Reasoning with SortHierarchy and Rigidity
 In Proceedings of Knowledge Representation (KR2004
, 2004
"... Although sorts and unary predicates are semantically identical in ordersorted logic, they are classified as different kinds of properties in formal ontology (e.g. sortal and nonsortal). This ontological analysis is an essential notion to deal with properties (or sorts) of objects in knowledge re ..."
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Although sorts and unary predicates are semantically identical in ordersorted logic, they are classified as different kinds of properties in formal ontology (e.g. sortal and nonsortal). This ontological analysis is an essential notion to deal with properties (or sorts) of objects in knowledge representation and reasoning. In this paper, we propose an extension of an ordersorted logic with the ontological property classification. This logic contains types (rigid sorts), nonrigid sorts and unary predicates to distinguishably express the properties: substantial sorts, nonsubstantial sorts and nonsortal properties. We define a sorted Hornclause calculus for such property expressions in a knowledge base. Based on the calculus, we develop a reasoning algorithm for many separated knowledge bases where each knowledge base can extract rigid property information from other knowledge bases (called rigid property derivation).
Distributed reasoning with ontologies and rules in ordersorted logic programming
 Journal of Web Semantics
"... 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 ..."
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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 ordersorted logic programming that transfers rigid properties from knowledge bases. Our ordersorted logic contains types (rigid sorts), nonrigid sorts, and unary predicates that distinctly express essential sorts, nonessential sorts, and nonsortal properties. We formalize the ordersorted Hornclause calculus for such expressions in a single knowledge base. This calculus is extended by embedding rigidproperty 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 queryanswering system that combines ordersorted linear resolution and rigidproperty resolution as topdown algorithms.
Combining ObjectOriented and Logic Paradigms: A Modal Logic Programming Approach
 European Conference on ObjectOriented Programming (ECOOP'92
, 1992
"... . In this paper, a number of existing solutions and suggestions towards combining the objectoriented (OO) and logic programming paradigms have been briefly studied and categorized, and a sketch of a new solution has been proposed which tries to capture the essence of OO in terms of modal logic, and ..."
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. In this paper, a number of existing solutions and suggestions towards combining the objectoriented (OO) and logic programming paradigms have been briefly studied and categorized, and a sketch of a new solution has been proposed which tries to capture the essence of OO in terms of modal logic, and which could be implemented as a modal logic programming system. The proposal is based on the belief that two orthogonal dimensions  object hierarchy and time  are involved in OO that in many respects are similar. For the onedimensional (static) case, three logics  MU, MU, and MU²  have been designed, each allowing a different variety of inheritance modes. The twodimensional (dynamic) case has been treated in a logic 2MU and its corresponding variants. Under certain OOmotivated definitions of Horn clause, the resolution calculi of these logics turn out to be complete. 1 Introduction Since 19834 [ST83, Zan84], more than 20 mergers of the OO and logic paradigms (see Section 2) have be...
Existential Rigidity and Many Modalities in OrderSorted Logic
"... Ordersorted 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 sorthierarchy). However, this logic cannot represent more complex sorted expressions when they are true in any pos ..."
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Ordersorted 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 sorthierarchy). 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 ordersorted 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
A Logic of Actions Revisited
"... We propose a theory for reasoning about actions based on ordersorted predicate logic where one can consider an elaborate taxonomy of objects. We are interested in the projection problem: whether a statement is true after executing a sequence of actions. To solve it we design a regression operator ..."
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We propose a theory for reasoning about actions based on ordersorted predicate logic where one can consider an elaborate taxonomy of objects. We are interested in the projection problem: whether a statement is true after executing a sequence of actions. To solve it we design a regression operator that takes advantage of wellsorted unification between terms. We show that answering projection queries in our logical theories is sound and complete with respect to that of in Reiter’s basic action theories. Moreover, we demonstrate that our regression operator based on ordersorted logic can provide significant computational advantages in comparison to Reiter’s regression operator. 1
Abstract OrderSorted Logic Programming with Predicate Hierarchy
"... Ordersorted logic has been formalized as firstorder logic with sorted terms where sorts are ordered to build a hierarchy (called a sorthierarchy). These sorted logics lead to useful expressions and inference methods for structural knowledge that ordinary firstorder logic lacks. Nitta et al. poin ..."
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Ordersorted logic has been formalized as firstorder logic with sorted terms where sorts are ordered to build a hierarchy (called a sorthierarchy). These sorted logics lead to useful expressions and inference methods for structural knowledge that ordinary firstorder logic lacks. Nitta et al. pointed out that for legal reasoning a sorthierarchy (or a sorted term) is not sufficient to describe structural knowledge for event assertions, which express facts caused at some particular time and place. The event assertions are represented by predicates with n arguments (i.e. nary predicates), and then a particular kind of hierarchy (called a predicate hierarchy) is built by a relationship among the predicates. To deal with such a predicate hierarchy, which is more intricate than a sorthierarchy, Nitta et al. implemented a typed (sorted) logic programming language extended to include a hierarchy of verbal concepts (corresponding to predicates). However, the inference system lacks a theoretical foundation because its hierarchical expressions exceed the formalization of ordersorted logic. In this paper, we formalize a logic programming language with not only a sorthierarchy but also a predicate hierarchy. This language can derive general and concrete expressions in the two kinds of hierarchies. For the hierarchical reasoning of predicates, we propose a manipulation of arguments in which surplus and missing arguments in derived predicates are eliminated and supplemented. As discussed by Allen, McDermott and Shoham in research on temporal logic and as applied by Nitta et al. to legal reasoning, if each predicate is interpreted as an event or action (not as a static property), then missing arguments should be supplemented by existential terms in the argument manipulation. Based on this, we develop a Horn clause resolution system extended to add inference rules of predicate hierarchies. With a semantic model restricted by interpreting a predicate hierarchy, the soundness and completeness of the Hornclause resolution is proven.
1 The Typed Situation Calculus
"... ABSTRACT. We propose a theory for reasoning about actions based on ordersorted predicate logic where one can consider an elaborate taxonomy of objects. We are interested in the projection problem: whether a statement is true after executing a sequence of actions. To solve it we design a regression ..."
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ABSTRACT. We propose a theory for reasoning about actions based on ordersorted predicate logic where one can consider an elaborate taxonomy of objects. We are interested in the projection problem: whether a statement is true after executing a sequence of actions. To solve it we design a regression operator takes advantage of wellsorted unification between terms. We show that answering projection queries in our logical theories is sound and complete wrt answering similar queries in Reiter’s basic action theories. This proves correctness of our approach. Moreover, we demonstrate that our regression operator based on ordersorted logic can provide significant computational advantages in comparison to Reiter’s regression operator. 1