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17
A Feature Logic with Subsorts
 LILOG Report 33, IWBS, IBM Deutschland
, 1992
"... This paper presents a set description logic with subsorts, feature selection (the inverse of unary function application), agreement, intersection, union and complement. We define a model theoretic open world semantics and show that sorted feature structures constitute a canonical model, that is, ..."
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Cited by 72 (4 self)
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This paper presents a set description logic with subsorts, feature selection (the inverse of unary function application), agreement, intersection, union and complement. We define a model theoretic open world semantics and show that sorted feature structures constitute a canonical model, that is, without loss of generality subsumption and consistency of set descriptions can be considered with respect to feature structures only. We show that deciding consistency of set descriptions is an NPcomplete problem. To appear in: J. Wedekind and C. Rohrer (eds.), Unification in Grammar. The MIT Press, 1992 This text is a minor revision of LILOG Report 33, May 1988, IBM Deutschland, IWBS, Postfach 800880, 7000 Stuttgart 80, Germany. The research reported here has been done while the author was with IBM Deutschland. The author's article [23] is a more recent work on feature logics. 1 1 Introduction This paper presents a set description logic that generalizes and integrates formalisms...
Logic Programming over Polymorphically OrderSorted Types
, 1989
"... This thesis presents the foundations for relational logic programming over polymorphically ordersorted data types. This type discipline combines the notion of parametric polymorphism, which has been developed for higherorder functional programming, with the notion of ordersorted typing, which ha ..."
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Cited by 58 (0 self)
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This thesis presents the foundations for relational logic programming over polymorphically ordersorted data types. This type discipline combines the notion of parametric polymorphism, which has been developed for higherorder functional programming, with the notion of ordersorted typing, which has been developed for equational firstorder specification and programming. Polymorphically ordersorted types are obtained as canonical models of a class of specifications in a suitable logic accommodating sort functions. Algorithms for constraint solving, type checking and type inference are given and proven correct.
Specification Matching for Software Reuse: A Foundation
 In Proceedings of the ACM Symposium on Software Reuse
, 1995
"... Using formal specifications to represent software components facilitates the determination of reusability because they more precisely characterize the functionality of the software, and the welldefined syntax makes processing amenable to automation. We present specification matching as a method for ..."
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Cited by 31 (3 self)
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Using formal specifications to represent software components facilitates the determination of reusability because they more precisely characterize the functionality of the software, and the welldefined syntax makes processing amenable to automation. We present specification matching as a method for classification, retrieval, and modification of reusable components. A software component is specified in terms of ordersorted predicate logic. For both components and methods, we consider not only exact match, but also relaxed match and logical match for performing specification matching over a library of reusable software components. 1 Introduction Software reuse has been claimed to be a means for overcoming the software crisis [1, 2]. However, current techniques to represent and manage software component libraries are not sufficient. Information retrieval methods based on analyses of naturallanguage documentation have been proposed [3, 4] for constructing software libraries. Unfortuna...
Ontological knowledge base reasoning with sorthierarchy and rigidity
 In Proceedings of the Ninth International Conference on the Principles of Knowledge Representation and Reasoning (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 repr ..."
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Cited by 13 (10 self)
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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).
A Formal Approach to Reusing More General Components
 In IEEE 9th KnowledgeBased Software Engineering Conference
, 1994
"... Using formal specifications to represent software components facilitates the determination of reusability because they more precisely characterize the functionality of the software, and the welldefined syntax makes processing amenable to automation. This paper presents an approach, based on formal ..."
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Cited by 11 (2 self)
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Using formal specifications to represent software components facilitates the determination of reusability because they more precisely characterize the functionality of the software, and the welldefined syntax makes processing amenable to automation. This paper presents an approach, based on formal methods, to the modification of reusable software components. From a twotiered hierarchy of reusable software components, the existing components that are more general than the query specification are retrieved from the hierarchy. The specification for a more general retrieved component is compared to the query specification to determine what changes need to be applied to the corresponding program component in order to make it satisfy the query specification. This paper also describes an approach for assisting in the modification of more general components and gives an example to demonstrate its use. Keywords: software reuse, formal specifications, program adaptation and modification. 1 I...
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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Cited by 7 (6 self)
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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.
Report of the Logic Programming Language PROTOSL
 Revised version: Working Paper 4, IBM Germany, Scientific Center, Institute for Logics and Linguistics
, 1994
"... : PROTOSL is a language based on logic programming that integrates a variety of concepts for programming large knowledge based systems like a powerful type concept, a module concept, highlevel access to external relational databases, and finite domain constraints. The type concept covers user defi ..."
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Cited by 5 (2 self)
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: PROTOSL is a language based on logic programming that integrates a variety of concepts for programming large knowledge based systems like a powerful type concept, a module concept, highlevel access to external relational databases, and finite domain constraints. The type concept covers user defined sorts, subsort relationships supporting multiple inheritance and parameterized sorts in the form of polymorphism. In addition to relations, also userdefined functions are available. The module concept is similar to that of Modula2 and allows to hide implementation details from the user of a module. Database access and modification is fully embedded in the programming language PROTOSL and can be programmed transparent to the user of a program or a program part. Besides simple links to external relations, nonrecursive as well as recursive function free deduction rules can be defined. PROTOSL also provides an easy way to work with windows via an objectoriented interface to the OSF/Mot...
The completeness of logic programming with sort predicates
 Systems and Computers in Japan 35(1):37–46
, 2004
"... An ordersorted logic can be regarded as a generalized firstorder predicate logic that includes many and ordered sorts (i.e. a sorthierarchy). In the fields of knowledge representation and AI, this logic with sorthierarchy has been used to design a logicbased language appropriate for representin ..."
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Cited by 5 (5 self)
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An ordersorted logic can be regarded as a generalized firstorder predicate logic that includes many and ordered sorts (i.e. a sorthierarchy). In the fields of knowledge representation and AI, this logic with sorthierarchy has been used to design a logicbased language appropriate for representing taxonomic knowledge. By incorporating the sorthierarchy, ordersorted resolution and sorted logic programming have been formalized that provide efficient reasoning mechanisms with structural representation. In this work, Beierle et al. developed an ordersorted logic to couple separated taxonomic knowledge and assertional knowledge. Namely, its language allows us to make use of sorts to denote not only the types of terms but also unary predicates (called sort predicates). In this paper, we propose a sorted logic programming language with sort predicates in order to improve the practicability of the logic proposed by Beierle et al. The linear resolution is obtained by adding inference relative to sort predicates and subsort relations. In the semantics, the terms and formulas that follow the sorted signature extended with sort predicates are interpreted over its corresponding Σ +structures. Finally, we build the Herbrand models of programs containing sort predicates, and thus prove the soundness and completeness of this logic programming. ordersorted logic, sort predicate, logic programming, knowledge base system 1
Unification in an Extensional Lambda Calculus with Ordered Function Sorts and Constant Overloading
, 1994
"... We develop an ordersorted higherorder calculus suitable for automatic theorem proving applications by extending the extensional simply typed lambda calculus with a higherorder ordered sort concept and constant overloading. Huet's wellknown techniques for unifying simply typed lambda terms ar ..."
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Cited by 4 (1 self)
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We develop an ordersorted higherorder calculus suitable for automatic theorem proving applications by extending the extensional simply typed lambda calculus with a higherorder ordered sort concept and constant overloading. Huet's wellknown techniques for unifying simply typed lambda terms are generalized to arrive at a complete transformationbased unification algorithm for this sorted calculus. Consideration of an ordersorted logic with functional base sorts and arbitrary term declarations was originally proposed by the second author in a 1991 paper; we give here a corrected calculus which supports constant rather than arbitrary term declarations, as well as a corrected unification algorithm, and prove in this setting results corresponding to those claimed there.
A Combinatorbased Ordersorted Higherorder Unification Algorithm
, 1993
"... This paper develops a sound and complete transformationbased algorithm for unification in an extensional ordersorted combinatory logic supporting constant overloading and a higherorder sort concept. Appropriate notions of ordersorted weak equality and extensionality  reflecting ordersorted f ..."
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Cited by 1 (0 self)
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This paper develops a sound and complete transformationbased algorithm for unification in an extensional ordersorted combinatory logic supporting constant overloading and a higherorder sort concept. Appropriate notions of ordersorted weak equality and extensionality  reflecting ordersorted fijequality in the corresponding lambda calculus given by Johann and Kohlhase  are defined, and the typed combinatorbased higherorder unification techniques of Dougherty are modified to accommodate unification with respect to the theory they generate. The algorithm presented here can thus be viewed as a combinatory logic counterpart to that of Johann and Kohlhase, as well as a refinement of that of Dougherty, and provides evidence that combinatory logic is wellsuited to serve as a framework for incorporating ordersorted higherorder reasoning into deduction systems aiming to capitalize on both the expressiveness of extensional higherorder logic and the efficiency of ordersorted calc...