Variable precision logic

摘要

Variable precision logic is concerned with problems of reasoning with incomplete information and resource constraints. It offers mechanisms for handling trade-offs between the precision of inferences and the computational efficiency of deriving them. Two aspects of precision are the specificity of conclusions and the certainty of belief in them; we address primarily certainty and employ censored production rules as an underlying representational and computational mechanism. These censored production rules are created by augmenting ordinary production rules with an exception condition and are written in the form “if A then B unless C”, where C is the exception condition.From a control viewpoint, censored production rules are intended for situations in which the implication A ⇒ B holds frequently and the assertion C holds rarely. Systems using censored production rules are free to ignore the exception conditions when resources are tight. Given more time, the exception conditions are examined, lending credibility to high-speed answers or changing them. Such logical systems, therefore, exhibit variable certainty of conclusions, reflecting variable investment 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 censored production rule expresses important information (e.g., a causal relationship), while the “unless C” part acts only as a switch that changes the polarity of B to ¬B when 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 δ is the certainty when the truth value of C is unknown, and γ is the certainty when C is known to be false.