Redundancy checking is an important task in the research of knowledge representation and reasoning. In this paper, we consider redundant qualitative constraints. For a set ? of qualitative constraints, we say a constraint ( x R y ) in ? is redundant if it is entailed by the rest of ?. A prime subnetwork of ? is a subset of ? which contains no redundant constraints and has the same solution set as ?. It is natural to ask how to compute such a prime subnetwork, and when it is unique. We show that this problem is in general intractable, but becomes tractable if ? is over a tractable subalgebra S of a qualitative calculus. Furthermore, if S is a subalgebra of the Region Connection Calculus RCC8 in which weak composition distributes over nonempty intersections, then ? has a unique prime subnetwork, which can be obtained in cubic time by removing all redundant constraints simultaneously from ?. As a by-product, we show that any path-consistent network over such a distributive subalgebra is minimal and globally consistent in a qualitative sense. A thorough empirical analysis of the prime subnetwork upon real geographical data sets demonstrates the approach is able to identify significantly more redundant constraints than previously proposed algorithms, especially in constraint networks with larger proportions of partial overlap relations.
This paper presents a new approach, called knowledge-base reduction, to the problem of checking knowledge bases for inconsistency and redundancy. The algorithm presented here makes use of concepts and techniques that have recently been advocated by de Kleer [deKleer, 1986] in conjunction with an assumption-based truth maintenance system. Knowledge-base reduction is more comprehensive than previous approaches to this problem in that it can in principle detect all potential contradictions and redundancies that exist in knowledge bases (having expressive power equivalent to propositional logic). While any approach that makes such a guarantee must be computationally intractable in the worst case, experience with KB-Reducer - a system that implements a specialized version of knowledge-base reduction and is described in this paper - has demonstrated that this technique is feasible and effective for fairly complex "real world" knowledge bases. Although KB-Reducer is currently intended for use by expert system developers, it is also a first step in the direction of providing safe "local end-user modifiability" for distant "sites" in a nationwide network of expert systems. Abstract This paper deals with the problem of removing redundant literals from a given clause. We first consider condensing , a weak type of redundancy elimination. A clause is condensed if it does not subsume any proper subset of itself. It is often useful (and sometimes necessary) to replace a non-condensed clause C by a condensation, i.e., by a condensed subset of C which is subsumed by C . After studying the complexity of an existing clause condensing algorithm, we present a more efficient algorithm and provide arguments for the optimality of the new method. We prove that testing whether a given clause is condensed is co-NP-complete and show that several problems related to clause condensing belong to complexity classes that are, probably, slightly harder than NP. We also consider a stronger version of redundancy elimination: a clause C is strongly condensed iff it does not contain any proper subset C ′ such that C logically implies C ′. We show that the problem of testing whether a clause is strongly condensed is undecidable. Ontologies may contain redundancy in terms of axioms that logically follow from other axioms and that could be removed for the sake of consolidation and conciseness without changing the overall meaning. In this paper, we investigate methods for removing such redundancy from ontologies. We define notions around redundancy and discuss typical cases of redundancy and their relation to ontology engineering and evolution. We provide methods to compute irredundant ontologies both indirectly by calculating justifications, and directly by utilising a hitting set tree algorithm and module extraction techniques for optimization. Moreover, we report on experimental results on removing redundancy from existing ontologies available on the Web. We present a general method for detecting wide classes of redundant production rules (PRs) based on the term rewrite semantics. We present the semantic account, define rule execution over both ground memories and memory schemas, and define redundancy for the PRs. From those definitions, an algorithm is developed that detects wide classes of redundant rules, and which improves upon the previously published methods. A knowledge base is redundant if it contains parts that can be inferred from the rest of it. We study some problems related to the redundancy of a CNF formula. In particular, any CNF formula can be made irredundant by deleting some of its clauses: what results is an irredundant equivalent subset. We study the complexity of problems related to irredundant equivalent subsets: verification, checking existence of an irredundant equivalent subset with a given size, checking necessary and possible presence of clauses in irredundant equivalent subsets, and uniqueness. We also consider the problem of redundancy with different definitions of equivalence.