Variable Precision Logic

Unknown author (1985-08-01)

Variable precision logic is concerned with problems of reasoning with incomplete information and under time constraints. It offers mechanisms for handling trade-offs between the precision of inferences and the computational efficiency of deriving them. Of the two aspects of precision, the specificity of conclusions and the certainty of belief in them, we address here primarily the latter, and employ censored production rules as an underlying representational and computational mechanism. Such rules are created by augmenting ordinary production rules with an exception condition and are written in the form if A then D unless C, where C is the exception condition. From a control viewpoint, censored production rules are intended for situations in which the implication A {arrow} B holds frequently and the assertion C holds rarely. Systems using censored production rules are free to ignore the exception conditions, when time is a premium. Given more time, the exception conditions are examined, lending credibility to initial, high-speed answers, or changing them. Such logical systems therefore exhibit variable certainty of conclusions, reflecting variable investments of computational resources in conducting reasoning. From a logical viewpoint, the unless operator between B and C acts as the exclusive-or operator. From an expository viewpoint, the if A then B part of the censored production rule expresses an important information (e.g., a causal relationship), while the unless C part acts only as a switch that changes the polarity of B to ??hen C holds. Expositive properties are captured quantitatively by augmenting censored rules with two parameters that indicate the certainty of the implication if A then B. Parameter 6 is the certainty when the truth value C is unknown, and 7 is the certainty when C is known to be false.