David W. Etherington

Formalizing nonmonotonic reasoning systems

Abstract In recent years, there has been considerable interest in nonmonotonic reasoning systems. Unfortunately, formal rigor has not always kept pace with the enthusiastic propagation of new systems. The argument has long been made that, because of the general intractability of formal systems, it is unreasonable to consider them for practical applications. This is taken as support for the use of systems such as semantic networks which, although not completely understood, can compute quickly. We suggest that this argument is not entirely convincing, and that formalizing such systems may yield dividends in terms of both clarity and correctness. We argue that formal systems, such as Reiters default logic, provide useful tools for the specification and description of nonmonotonic systems. We present new results which enhance this usefulness. To illustrate the benefits of this approach, a theory of inheritance networks is developed. This yields a notion of correct inference, and sufficient conditions for the coherence of network inference representations.

A hierarchy of tractable satisfiability problems

Abstract Propositional satisfiability (SAT) is a well-known NP-complete problem. We define a hierarchy Ω 0 , Ω 1 ,… of classes of formulae such that for any class Ω k , SAT is solvable in O ( n k + 1 ) time. The basic class Ω 0 contains all formulae in conjunctive normal form (CNF) where each conjunct is a Horn clause, and allformulae in CNF where each conjunct is a binary clause. This hierarchy improves upon the hierarchy defined by Gallo and Scutella. We also present a sound and complete algorithm for solving SAT that takes time O ( n k + 1 ) for any formula in the class Ω k .

Nonmonotonicity and the scope of reasoning

Abstract Circumscription, default logic, and autoepistemic logic capture aspects of the nonmonotonicity of human commonsense reasoning. However, Perlis has shown that circumscription suffers from certain counterintuitive limitations, concerning exceptions or “counterexamples” to defaults. We observe that the unfortunate limitations of circumscription are even broader than Perlis originally pointed out. Moreover, these limitations are not peculiar to circumscription; they appear to be endemic in nonmonotonic reasoning formalisms. We develop a general solution, involving restricting the scope of nonmonotonic reasoning, and show that it remedies these problems in a variety of formalisms. Our solution has a number of attractive aspects in addition to its generality. Most importantly, no modification of the underlying formalisms is required, and the result is semantically compatible with existing approaches. Furthermore, the necessary machinery is intuitively plausible and, arguably, useful for other purposes. Finally, the solution is robust: it is relatively tolerant of imprecise determinations of scope.

Domain circumscription: a reevaluation

Some time ago, McCarthy developed the domain circumscription formalism for closed‐world reasoning. Recently, attention has been directed towards other circumscriptive formalisms. The best known of these, predicate and formula circumscription, cannot be used to produce domain‐closure axioms; nor does it appear likely that the other forms can. Since these axioms are important in deductive database theory (and elsewhere), and since domain circumscription often can conjecture these axioms, there is reason to resurrect domain circumscription.

The Fourth International Workshop on Nonmonotonic Reasoning

The Fourth International Workshop on Nonmonotonic Reasoning brought together active researchers in nonmonotonic reasoning to discuss current research, results, and problems of both theoretical and practical natures. There was lively discussion on a number of issues, including future research directions for the field.