A foundational approach to conjecture and knowledge in knowledge bases
James P. Delgrande · 1985
A foundational investigation of the notion of hypothesis in knowledge representation schemes is presented. The problem has two distinct but related components. The first concerns the ultimately non-deductive problem of forming and maintaining a set of hypotheses, or a theory, based on a stream of ground atomic formulae. The second concerns deductively reasoning with a theory, together with arbitrary known and hypothesised sentences. For the first part, theory formation, a language HL (and from it an algebra and logic) is derived for forming hypotheses framed in set-theoretic terms. Two soundness and completeness results for the logic are presented. The first explicitly links the logic to the algebra; the second treats the logic as a three-valued system. Through the formal systems, the set of potential hypotheses is precisely specified, and a procedure is derived for restoring the consistency of a set of hypotheses after conflicting evidence is encountered. For the second part, reasoning with a theory, an existent first-order language that can represent and reason about what it knows is extended to one that can reason with knowledge and hypothesis. The original proof-theoretic and semantic results for the language are extended appropriately. The relation between these two parts, for introducing and reasoning with hypotheses, is also explored. The theory formation process is considered as a source of hypothetical sentences for the deductive (reasoning) component, and the deductive component is considered as a source of a priori knowledge and hypothesis for the theory formation process.