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 q max 1 : at what exploration stage are we in now? (specifies when = p 1 ∈ T ) q max 2 : what reasoning frame are we operating in, now? (specifies [frame]) q max 3 : what topic in [frame] are we focusing on, now? (specifies [topic]) q max 4 : where do you need a boost (goal)? (specifies where = p 2 ∈ S G ) q max 5 : what solution aspect, do you want to focus on? (specifies what = p 3 ∈ S S ) q max 6 : can you boost your goal ( where ) and the solution’s quality ( what ), by using these actions ? (specifies action ∈ S A and which = q max 6 ∈ Q max ) Questions in Q max are SN-insightful , only if they are SN-informative (axiom Sem 1): they attempt to reduce a maximum amount of uncertainty (alternatives, ignorance, options, possibilities), within the context C max . They are specificity- boosting questions which reduce uncertainty (Shannon entropy) to increase the solution’s quality. The SN concept of insight involves notions in information, logic, probability, uncer- tainty and utility (see paper I). To cope with these, we need a logic with quantifiers for scoping the variables x to specific spaces X . In standard predicate logic, a predicate is a function p of a variable x , which maps a variable x ∈ X , into the predicate’s truth values { T, F } [12]. X → { T, F } and x ∈ X → p ( x ) = T or F In SN-Logic, an SN-predicate is a a function q of a variable x , which maps a variable x ∈ X , into the predicate’s insight values { insightful I + , insightless I 0 } . X → { I + , I 0 } and x ∈ X → q ( x ) = I + or I 0 In SN-Logic we define the two classes (minimizing, maximizing) of predicates q ( x ) , the mindset parameter p ∈ P ≡ { when, where, what } and the predicate variable ’cognitive action ’: • SN-predicate questions q ( p, action ) ∈ Q min , where p ∈ P , action ∈ S A • SN-predicate questions q ( p, action ) ∈ Q max , where p ∈ P , action ∈ S A The parameter p ∈ P is in the space P of cognitive mindsets C min ( framework, p ) : the set of H ’s intentions , during the IQ-game. The AI needs to know this intent, to make useful cooperative suggestions. The mindset parameter p , encodes the type of insight, H wants to boost, at any given time. SN-Logic only requires concept spaces ( { T, S D , S C , S G , S Q , O p , O b } of very small size N = Card ( Space ) ≈ 10 2 (see appendices). • Number of distinct cognitive mindsets : N cogn = O ( Card ( P )) = O ( Card ( T ) × Card ( S D ) × Card ( S C ) = 10 × 10 × 10 = 10 3 • Number of possible conceptual actions : N acts = O ( Card ( S A )) = O ( Card ( O p ) × O ( Card ( O b )) = 10 2 × 10 2 = 10 4 • Number of possible distinct questions : N ques = Card ( Q ) = N cogn × N acts = 10 7 minimizing questions, posed by the Q min -generator (same for maximizing questions). 1 Year 2022 7 © 2022 Global Journals Global Journal of Science Frontier Research Volume XXII Issue ersion I V IV ( F ) Q-Gen Syntax: quality-maximizing questions q ( p, action ) ∈ Q max e) SN-Logic predicates q(x) f) SN-Logic Complexity & Scope 12. Andrews P. B. (2002) An Introduction to Mathematical Logic and Type Theory: To Truth Through Proof, 2nd ed., Berlin: Kluwer Academic Pub. and Springer. R ef