When search techniques are used to solve a practical problem, the solution produced is often brittle in the sense that small execution difficulties can have an arbitrarily large effect on the viability of the solution. The AI community has responded to this difficulty by investigating the development of "robust problem solvers" that are intended to be proof against this difficulty. We argue that robustness is best cast not as a property of the problem solver, but as a property of the solution. We introduce a new class of models for a logical theory, called supermodels, that captures this idea. Supermodels guarantee that the model in question is robust, and allow us to quantify the degree to which it is so. We investigate the theoretical properties of supermodels, showing that finding supermodels is typically of the same theoretical complexity as finding models. We provide a general way to modify a logical theory so that a model of the modified theory is a supermodel of the original. Ex...

Unit resolution is arguably the most useful known algorithm for tractable reasoning in propositional logic. Intuitively, if one knows a, b, and a b oe c, then c should be an obvious implication. However, devising a tractable semantics that allows unit resolution has proven to be an elusive goal. We propose a 3-valued semantics for a tractable fragment of propositional logic that is inherently non-deterministic: the denotation of a formula is not uniquely determined by the denotation of the variables it contains. We show that this semantics yields a tractable, sound and complete, decision procedure. We generalize this semantics to a family of semantics, tied to Dalal's notion of intricacy, of increasing deductive power and computational complexity. Introduction Despite the recent advances in propositional reasoning power [Selman, Kautz, & Cohen 1993; Crawford & Auton 1996; Bayardo & Miranker 1996; Bayardo & Schrag 1997], knowledge-bases of the size required for common-sense reasoni...