Order-sorted logic programming with predicate hierarchy
Artificial Intelligence
A hybrid reasoning system for terminologies and first-order clauses in knowledge bases
New Generation Computing
Distributed reasoning with ontologies and rules in order-sorted logic programming
Web Semantics: Science, Services and Agents on the World Wide Web
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All order-sorted logic can be regarded as a generalized first-order predicate logic that includes many and ordered sorts (i.e., a sort-hierarchy). In the fields of knowledge representation and AI, this logic with sort-hierarchy has been used to design a logic-based language appropriate for representing taxonomic knowledge. By incorporating the sort-hierarchy, order-sorted resolution and sorted logic programming have been formalized that provide efficient reasoning mechanisms with structural representation. In this work, Beierle's group developed an order-sorted 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. 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. © 2003 Wiley Periodicals, Inc. Syst Comp Jpn, 35(1): 37–46, 2004; Published online in Wiley InterScience (). DOI 10.1002/scj.10409