Lp, a logic for representing and reasoning with statistical knowledge
Fahiem Bacchus · Computational Intelligence · 1990
This paper presents a logical formalism for representing and reasoning with statistical knowledge. One of the key features of the formalism is its ability to deal with qualitative statistical information. It is argued that statistical knowledge, especially that of a qualitative nature, is an important component of our world knowledge and that such knowledge is used in many different reasoning tasks. The work is further motivated by the observation that previous formalisms for representing probabilistic information are inadequate for representing statistical knowledge. The representation mechanism takes the form of a logic that is capable of representing a wide variety of statistical knowledge, and that possesses an intuitive formal semantics based on the simple notions of sets of objects and probabilities defined over those sets. Furthermore, a proof theory is developed and is shown to be sound and complete. The formalism offers a perspicuous and powerful representational tool for statistical knowledge, and a proof theory which provides a formal specification for a wide class of deductive inferences. The specification provided by the proof theory subsumes most probabilistic inference procedures previously developed in AI. The formalism also subsumes ordinary first‐order logic, offering a smooth integration of logical and statistical knowledge.