Augmented Knowledge Base (AKB) and Augmented Reasoning (AR)*

Augmented Knowledge Base (AKB) and Augmented Reasoning (AR) were recently introduced by Eugene Santos, Jr., Eunice E. Santos, Eugene S. Santos and Evelyn W. Santos to supplement Bayesian Knowledge Base (BKB), and expand the applicability of BKBs.

AKB is a new computational model for knowledge bases involving uncertainties and/or incompleteness. It encompasses most of the well-known formalisms of knowledge bases together with their associated reasoning schemes, including probabilistic logic, Dempster-Schaefer theory, Bayesian network, Bayesian knowledge base, fuzzy logic, numerical ATMS, incidence calculus, etc.

AR is a new computational scheme that works with most knowledge bases. It is particularly suited for AKBs.

Knowledge-based systems involving uncertainties have been studied widely. Various approaches have been introduced to model such knowledge bases. The basic building blocks of these knowledge bases are knowledge, which are usually represented as rules, propositions, or other equivalent means. Each object in the knowledge base is associated with or mapped to a number, variably referred to as belief, certainty factor, likelihood, weight, etc

In contrast, an augmented knowledge base consists of ordered pairs of the form (E, A), where A is a proposition or rule in the traditional sense, and E is a set corresponding to the body of evidence that supports A. Moreover, each given body of evidence (not each rule) is mapped to or associated with a value.

Since bodies of evidence are sets, one could consider the relations among the bodies of evidence. The ability of AKBs to deal with relationships among the bodies of evidence, or its capability to take into account constraints imposed on the bodies of evidence, is a unique feature of AKB, which can lead to more powerful, robust, accurate and/or refined characterizations of the knowledge base.

Inference or reasoning in an AKB is done in two separate phases: Form the body of evidence that supports the desired rule, and then determine the value associated with the resulting body of evidence. The second phase can be done in many different ways, including the reasoning scheme AR based on the recently introduced constraint stochastic independence method. AR provides a clear probabilistic semantics, resulting in the elimination of virtually all known anomalies associated with existing formalisms of uncertain reasoning and knowledge bases.

In addition to deductive reasoning, AKBs can also serve as a computational framework for inductive inference. Augmented inductive inference, among other things, can be used to extract meaningful new knowledge from AKBs provided certain consistency conditions are met. The required consistency can be guaranteed via higher order AKBs.

Furthermore, relational database can be formulated using Free-Form Database (FFDB), which is a special form of AKB. This allows relational databases to be used and examined with a new perspective and a new set of tools. Moreover, FFDB can also be used to formulate augmented deductive database, as well as, augmented inductive database. The latter can serve as formal model for extracting new information from relational databases, e.g., data mining

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*patent pending