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 The AI’s capacity to generate SN-insightful I + questions, from a vast possibil- ity of insightless I 0 ones (with actions ∈ S A ), resides in the structure a high- dimensional insight-gain tensor µ ( when, where, what, which ) ≡ µ ( p, action ) , for each challenge class and reasoning frame . So the full rank-7 tensor is actually µ ( class, frame, topic, p 1 , p 2 , p 3 , action ) . This function outputs the value g of in- sight gain associated to exploring a question which ≡ q ( p, action ) ∈ Q , where p ∈ P encodes H ’s targeted insight gains. To be useful, the tensor µ is required to satisfy the following properties: • µ : Cl × F r × P × S A → [0 , 1] , where Cl = set of challenge classes, F r = set of reasoning frameworks (frame+topic), P = T × S 1 × S 2 , S A = O p × O b , S 1 = S D or S G , and S 2 = S C or S Q • it is a measure of insight gain µ ( class, frame, topic, p, action ) = g ∈ [0 , 1] (normalized) • probability of all possible actions with a mindset p , must sum to one (unitarity) • µ crit ∈ ]0 , 1[ (minimum critical insight-gain value µ > µ crit ) • g = 0 when q ( p, action ) is SN-insightless I 0 , given the mindset p • g = 1 when q ( p, action ) is maximally SN-insightful I + , given the mindset p • µ is initialized by satisfying heuristics from causality, information, logic, planning, problem solving and utility. These constraints pro- vide the initial (challenge class-independent) approximation for µ • µ gets optimized (fine-tuned) for specific classes of challenges, by cooperative learning , using the IQ-game’s session episodes © 2022 Global Journals 1 Year 2022 10 Global Journal of Science Frontier Research Volume XXII Issue ersion I V IV ( F ) b) Constraints on Insight-Gain Tensors μ N otes We can now illustrate how SN-Logic is used, on a real challenge. In the IQ-game, both players (human: H , A SN ) agree to use simple cooperative strategies , given H ’s current mindset C : (1) A SN suggests its guess at a most insightful question ( q ∈ Q ∗ ( C ) ) (2) H reports questions q she actually finds insightful The game’s Q&A session, cycles over each obstacle, encountered within a chal- lenge. Hundreds of such sub-problems may be encountered, to solve a challenge. Usually, the number and nature of these obstacles is unknown ahead of time, in real-world challenges. For clarity, we use a single, static, not so complex, yet most difficult challenge. The scenario is: a young post-doctoral researcher, H , is trying to find a good quan- tum field topic, to spend her next ten years on. The first few moves (Q&As) of the two-person IQ-game, could proceed as follows: Q from A SN : ’Greetings! What class of challenge are we exploring today (sam- ple which depends on what SN-Logic is being used for): V. V alidation T est : P ost -D oc R esearcher’s D ilemma