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 • Vector space T of exploration stages : vector variable [ when ∈ T ] describe the current stage when of the exploration cycle. The vector [ when ] rotates in T over time (appendix A). • Vector space S D of mental obstacles : vector variable [ where ∈ S D ] describes where the human player’s H difficulties reside. The vector [ where ] rotates in S D over time while exploring the challenge (appendix B). • Vector space S C of difficulty causes : vector variable [ what ∈ S C ] de- scribes what in the reasoning’s framework, is causing H difficulty. The vector [ what ] rotates in S C over time while exploring the challenge (ap- pendix C). • Vector space S G of mental goals : vector variable [ where ∈ S G ] describes the solution quality, H intends to improve. The vector [ where ] rotates in S G over time while exploring the challenge (appendix D) • Vector space S S of solution elements : vector variable [ what ∈ S S ] de- scribe what aspect of the solution, H intends to improve. The vector [ what ] rotates in S S over time while exploring the challenge (appendix E) • Tensor space of conceptual actions S A = O p × O b : action variable [ which ≡ action ∈ S A ] is composed of a mental operation (verb ∈ O p ) at- tached to a target object (noun ∈ O b ) ). Space S A provides the building- blocks of conceptual solutions. (appendix F). SN-Logic’s role, is to provide guidance for insight-building via a Q&A process: suggesting when/where to pose which questions about what topic. To be used in inferences, the meanings of the parts of speech (variables { when, where, what, which } ), and the sentence structure (questions which ≡ q ∈ Q ), have to be both consistent and precise . A SN needs a basic grammar (syntax, semantics, vocabulary) to communicate effectively with the human player H , in a consistent and precise manner. SN- Logic is based on four consistent (contradiction-free) axioms, to define its semantics precisely (ambiguity-free). Let the human-player H ’s cognitive mindset C ( framework, p ) be defined by the current reasoning framework (next section), and three (intention) parameters: p = { when = p 1 , where = p 2 , what = p 3 } , then: (Sem 1) Shannon-informative questions: a question (which) q ( p, action ) , that reduces uncertainty (Shannon entropy) for H , who’s mindset is C ( framework, p ) (Sem 2) Neumann-useful questions: a question (which) q ( p, action ) , that has a human-aligned (via the 2-person IQ-game) utility , within a mindset C ( framework, p ) . It helps H make progress towards a solution. (Sem 3) SN-insightful questions: question (which) q ( p, action ) satisfying (Sem 1, Sem 2) is SN-insightful , within a mindset C ( framework, p ) , otherwise it is SN-insightless . (Sem 4) SN-Valid inferences: an inference is SN-valid, if and only if it has the SN normal form (section 3.6) 1 Year 2022 5 © 2022 Global Journals Global Journal of Science Frontier Research Volume XXII Issue ersion I V IV ( F ) c) SN-Grammar: Axioms of Semantics N otes