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 These SN axioms of semantics, allow the AI to cope with core concepts of causality (causes of insight), dynamics (changing reasoning frames) information, probability, uncertainty [6], utility [7] and insight (paper I). These are necessary components of an insight-boosting AI. The axioms Sem1, Sem2 restrict the form of allowed questions. This constraint is used by a Q-generator of questions q ∈ Q , to which we now turn. The cooperative IQ-game is driven by dual-objectives : to minimize the problem’s causes of difficulty , and to maximize the solution’s quality . The optimization must continuously adapt to H ’s understanding of the challenge, over an IQ-game session). The SN-grammar has a simple syntax, specified for each question class Q . All questions q ∈ Q will fall into two classes Q = { Q min , Q max } , from two comple- mentary (dual) perspectives: (a) causes of cognitive difficulty (to minimize ), (b) qualities of solution (to maximize ). Each question class generates many of specific questions, aimed at making insight-gains. The purpose of SN-Logic is to incrementally boost our insight about solutions, by suggesting when/where to pose which types of questions about what topic, while adapting to a moving target: our current understanding the obstacles in a challenge The question generator, or Q-gen , of difficulty-minimizing questions, uses a spe- cific syntax for an evolving cognitive mindset C min ( frame, topic, p 1 , p 2 , p 3 ) . There is a lot of freedom in which questions to pose, even at a specific place and time, within a well-defined framework. We select a set of six commonly useful problem- solving questions, to illustrate the procedure. Q-Gen Syntax: difficulty-minimizing questions q ( p, action ) ∈ Q min q min 1 : at what exploration stage are we in now? (specifies when = p 1 ∈ T ) q min 2 : what reasoning frame are we operating in, now? (specifies [frame]) q min 3 : what topic in [frame] are we focusing on, now? (specifies [topic]) q min 4 : where does the main difficulty reside? (specifies where = p 2 ∈ S D ) q min 5 : what, more specifically, causes this difficulty? (specifies what = p 3 ∈ S C ) q min 6 : can you reduce the difficulty ( where ) and avoid its causes ( what ), by using these actions? (specifies action ∈ S A and which = q min 6 ∈ Q min ) The variable [ action ] ( ∈ S A ≡ O P × O b ), is a product [ verb operation ] ( ∈ O p ) x [ noun object ] ( ∈ O b ) (appendices and section 5). The [frame] variable, labels the reasoning framework currently being used (e.g. a discipline, a subject, a specialty, a model, a system, a theory, a technology etc.). This framework can change from one exploration stage to the next. It is a moving target, which mirrors our current understanding of a complex challenge. The [topic] variable, labels a set of items we’re focusing on, within [frame] (e.g. agents, assumptions, bounds, properties, qualities, relations, statements, strategies, tactics, techniques etc.). Typically, [topic] is a tool we use within [frame], to make progress. For a concrete example, see section 5. Questions q ∈ Q min are SN-insightful , only if they are SN-informative (axiom Sem 1): they attempt to reduce a maximum possible amount of uncertainty (alter- natives, ignorance, options, possibilities), within the context C min . The generator of quality-maximizing questions, uses a specific syntax for an evolving cognitive mindset C max ( frame, topic, p 1 , p 2 , p 3 ) : © 2022 Global Journals 1 Year 2022 6 Global Journal of Science Frontier Research Volume XXII Issue ersion I V IV ( F ) d) SN-Grammar: Syntax for Dual-Optimization 6. Shannon C. and Weaver W. (1949) The mathematical theory of communications , Univ. Illinois Press. R ef