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 SN normal-form for minimizing inferences Given a minimizing mindset C min ( frame, topic, p ) , where p ∈ P = { when, where, what } : if ∃ action ∈ S A , such that µ min ( frame, topic, p, action ) > µ crit , then q ( p, action ) ∈ Q ∗ min ( C min ) ⊂ Q min , and q ( p, action ) is SN-insightful , within C min SN normal-form for maximizing inferences Given a maximizing mindset C max ( frame, topic, p ) , where p ∈ P = { when, where, what } : if ∃ action ∈ S A , such that µ max ( frame, topic, p, action ) > µ crit , then q ( p, action ) ∈ Q ∗ max ( C max ) ⊂ Q max , and q ( p, action ) is SN-insightful , within C max The sets Q ∗ ( C ) , are maximum-insight subsets of Q min or Q max , and µ ( frame, topic, p, action ) is an insight-gain tensor (discussed shortly) whose insight gains are above a minimum critical cutoff µ crit . The purpose of an insight-gain cutoff scale is intuitive, but its mathematical justification is outside the scope of this paper, which focuses only on logical validity , and ignores scientific soundness . The cutoff is related to a scale-invariance due to a conformal symmetry, under the renormalization of probabilities (unitarity). Scale-separation is used in quantum field theories [13], but justified by the conformal symmetry [14] of a renormalization group [15]. To perform successful inferences autonomously, the AI agent needs to possess the means of deciding whether a predicate variable action ∈ S A , leads to insight gains above a minimum lower bound (that is, action ∈ S ∗ A ( C ) ⊂ S A ). The insight- gain tensor provides the SN-agent, the ability to select sound inferences, from a vast number of merely, valid ones (that is, of SN normal-form). The AI performs SN normal-form inferences, to suggest insightful questions to ex- plore, given human-targeted insight gains C ( p ) . These ’most insightful’ questions, lie in a restricted subspace Q ∗ ( C ) = { Q ∗ min ( C min ) , Q ∗ max ( C max ) } , within a large space Q , of possible questions ( Card ( Q ) = 10 7 ). Given a current mindset C ( p ) , A SN must find a subspace of questions Q ∗ ( C ) . This is where an insight-gain mea- sure µ ( p, action ) (convolution tensors and their kernels, used to restrict searches to optimal sub-spaces) are essential, to make sound inferences (real-world accurate), rather than merely valid ones (SN normal-form inferences). This will be presented elsewhere. For now, we simply discuss general constraints imposed by SN-Logic, on the tensor elements. 1 Year 2022 9 © 2022 Global Journals Global Journal of Science Frontier Research Volume XXII Issue ersion I V IV ( F ) IV. I nsight G ain T ensors μ a) Need for Insight-Gain Tensors 13. Dyson F., (1949) The radiation theories of Tomonaga, Schwinger and Feynman, Phys. Rev. 75, 486. R ef