Expressiveness and tractability in knowledge representation and reasoning1

Abstract

A fundamental computational limit on automated reasoning and its effect on knowledge representation is examined. Basically, the problem is that it can be more difficult to reason correctly with one representational language than with another and, moreover, that this difficulty increases dramatically as the expressive power of the language increases. This leads to a tradeoff between the expressiveness of a representational language and its computational tractability. Here we show that this tradeoff can be seen to underlie the differences among a number of existing represcntational formalisms. in addition to motivating many of the current research issues in knowledge representation.Cet article 6tudie une limitation computationnclle fondamentale du raisonnement automatique et examine ses effets sur la repdsentation de connaissances. A la base le probkme tient en ce qu'il peut Etre plus difficile de raisonner avec un langage de repdsentation qu'avec un autre et que cette difficult6 augmente consid6rablement i! mesure que croft le pouvoir expressif du langage. Ccci donne lieu un compromis entre le pouvoir expressif d'un langage de repdsentation et sa tractibilitt computationnelle. Nous montrons que ce compromis peut ttre vu comme I'une des causes fondamentales de la diffkrence qui existe entre nombre de formalismes dc repdsentation existants et peut motiver plusieurs recherches courantes en repdsentation de connaissances.Mots clis : repdsentation de connaissances. complexit6 du raisonnement. logique du premier ordre. schtmas, r5seaux strnantiques, bases de donntes. Comput. Intell. 3, 78-93 (1987)

An Approach to Temporal-Aware Procurement of Web Services

“…As a matter of fact, in logics there exist a tradeoff between expressiveness and the computability of reasoning procedures [12], so the more expressive temporal DL languages are known to be undecidable, that is to say, there is no algorithm for computing the satisfiability of a DL specification. Most of temporal DL reasoners overcome this problem by making the language less expressive, or treating the time as a concrete domain in order to use hibrid reasoners so that temporal specifications are processed by external solvers, such as the CSP solvers.…”

Web-centred end-user component modelling

“…Additionally, it indicates the computational complexity associated with the two fundamental operations targeted by the mathematical reasoning: subsumption (|= C c D) and instance checking (|= C(i)). Table 1 shows that, according to the naming scheme defined by Baader et al [52], we use ALCsNOQ^ description logic [54,55]. The naming scheme consists of assigning a letter or symbol to each expressive extensión of elementary attributive language (AL) logic.…”

Fuzzy Cognitive Map and Bayesian Belief Network for Causal Knowledge Engineering: A Comparative Study

“…The expressiveness of knowledge representation framework is a measure of what can be specified by an expert, and more importantly, what can be left unspecified, when the framework is used [6]. In BBN, domain experts are allowed to assign different prior probabilities to different states of a variable.…”

“…To be more focused, we confine our scope of study to the comparison from the perspective of knowledge engineering. We consider the following set of criteria: usability in causal modeling [4,5], expressiveness in causal representation [6,7,8,9], adequacy and efficiency in causal reasoning [7,9], formality in semantics, and soundness in inference [7,9,10,11]. These are commonly used criteria in knowledge engineering for the evaluation of traditional knowledge representation frameworks.…”