Global Journal of Science Frontier Research, F: Mathematics and Decision Science, Volume 22 Issue 4

Boosting Human Insight by Cooperative AI: Foundations of Shannon-Neumann Logic (section 3.3-3.4) which tracks the human player H ’s current understanding of the conceptual framework. It follows H ’s evolving understanding of the challenge, helping the SN-logic suggest the insightful questions, within each context C . The IQ-game doesn’t define a problem from the start, but instead, let’s H describe the Standard Logic Programming (predicate logic) is very effective when making strict deductions, but it cannot cope with the cooperative 2-person IQ-game. The purpose of SN-Logic is to provide an inference engine with the following requirements: it has to be ... • precise (ambiguity-free) semantics axioms • consistent (contradiction-free) framework within which, all SN-inferences can be made (normal-form inferencing) • transparent (natural language, no hidden layers) • explainable (no unjustifiable moves) • human-aligned (no conflicts of with human cognitive intentions) • non-brittle able to cope with fundamental concepts related to human-insight: causality (causes of insight), time-dependence (evolving understanding), in- formation, probability, uncertainty (Shannon), utility (von Neumann), and insight (paper I). Brittleness is a common cause of AI failures. To satisfy these requirements, we need a consistent set of SN-Logic definitions, axioms and rules, to which we now turn. To reason using a predicate logic (such as SN-Logic), the variables x need spaces X , to scope the quantification : ∀ x ∈ X , ∃ x ∈ X . SN-Logic’s concepts are partitioned in six compact concept spaces, over which we can perform inferences (see appendices A-F): Five vector spaces { T, S D , S C , S G , S S } , are used to describe the human player H ’s changing cognitive mindset C ( t ) , during the IQ-game. The AI agent, A SN , needs to know C ( t ) , because the insightfulness of a question, depends on H ’s in- creasing understanding of the challenge and its possible solutions, as insight is accumulated. The (tensor product) space S A , of possible conceptual actions (operation x ob- ject) provide the raw material to build conceptual solutions. © 2022 Global Journals 1 Year 2022 4 Global Journal of Science Frontier Research Volume XXII Issue ersion I V IV ( F ) III. P redicate SN-L ogic a) SN-Logic requirements b) SN-Logic Spaces N otes