A new algebraic model for implementing expert systems represented under the `concept-attribute-value' paradigm (Q417951)

The paper introduces a new knowledge representation paradigm based on computing Gröbner bases. It takes an existing knowledge base in a ``concept-attribute-value'' format and converts it into an algebraic model which represents knowledge by means of polynomials. It is advocated that this transformation results in more straightforward, intuitive, and efficient way for knowledge processing.NEWLINENEWLINE Section 2 presents an overview of the ``concept-attribute-value'' representation, and Section 3 defines the algebraic model for it. It is shown how, by using this model, the following two problems can be tackled in algebraic terms: (1) determine whether a formula is derivable from a knowledge base, and (2) determine whether there is no possible state in a given knowledge base. The proofs are given in Section 6. An extended example in Section 4 illustrates the proposed algebraic paradigm. The example compares the implementation of an abstract expert system according to the algebraic model based on propositional logic and the algebraic model presented in the paper. Both implementations use the algebraic software CoCoA.NEWLINENEWLINE In Section 5, the author advocates the advantages of the proposed model for computing a polynomial-based knowledge representation over the one based on propositional logic, namely: (i) more natural way to represent knowledge, (ii) a simpler way to generate algebraic models, and (iii) a faster performance.