Intelligence research direction
Computable abstraction
Two research lines on computable abstraction, natural intelligence and computational complexity.
Central hypothesis
Natural intelligence may depend on a computable process that constructs and recursively reuses context-sensitive abstractions.
Rather than treating every detail and possibility independently, an intelligent system can preserve what matters for a task, collapse irrelevant distinctions and create new operational primitives for further reasoning.
Two principal research lines
General theory
Computable abstraction as a mechanism of natural intelligence
Can abstraction be characterised as an effectively computable operation that changes an agent's representational system, creates new reusable primitives and reorganises future reasoning around them?
An abstraction operator that maps a current representation and its context to a revised representation whose new abstractions can be used in later rounds of reasoning.
Define abstraction
Establish a representation-independent criterion that distinguishes genuine abstraction from compression, memorisation or a feature that is merely decodable.
Explain construction
Determine what drives the formation of one abstraction rather than another, including relevance, prediction, action, invariance, reuse and computational cost.
Formalise context
Explain how goals and context determine which distinctions must be preserved, which can be collapsed and when finer distinctions must be recovered.
Model recursive reuse
Characterise how new abstractions become operational primitives and then participate in the construction of higher-order abstractions.
Test across domains
Look for the same construction principle in concept learning, perception, language, mathematical invention and structured problem solving.
Establish evidence
Measure causal use, transfer, compositionality, construction cost, revision and failure, while testing whether the theory reduces to an existing formalism.
Specific complexity programme
Can abstraction overcome computational complexity?
This line asks when recursively constructed, exact abstractions can replace exponentially many raw computational states with a tractable hierarchy of context-dependent states.
3-SAT and related constraint problems, where a variable's Boolean value is separated from its contextual role in the remaining formula.
From state space to abstraction hierarchy
Define exact decision-sufficient abstractions, quotient raw states by their relevant consequences and allow higher-order abstractions to summarise interactions among lower-level structures.
Existence, recognition and construction
Separate whether a compact abstraction exists from whether it can be recognised and constructed efficiently. Measure hierarchy cost, construction time, inference work and the number of distinct abstract states.
Known structure and hard instances
Compare the mechanism with treewidth, backdoors, knowledge compilation, decision diagrams, modern SAT solving and proof complexity. Use adversarial formula families to expose unavoidable blow-ups.
Staged research programme
Define exact contextual states and compare them with established local reasoning methods.
Allow the system to create new abstract objects with explicit interfaces and verifiable semantics.
Permit abstractions to become primitives for recursively higher-order abstraction.
Compare against SAT solving, decision diagrams, structural methods and knowledge compilation.
Test adversarial families and establish where compact abstractions cannot be constructed efficiently.
Status of the strongest conjecture
A universal polynomial abstraction constructor for 3-SAT would imply P equals NP.
The research does not claim that such a constructor has been found or that the conjecture is established. This implication defines the burden of proof. Even if the universal conjecture fails, exact or approximate results for important structured families could still produce useful algorithms and a theory of abstraction-mediated complexity reduction.
How the lines fit together
Develop the general mechanical theory: what abstraction is, how context guides it and how representations are extended recursively.
Subject that mechanism to a precise mathematical stress test: can it expose and construct structure that changes the effective cost of reasoning?
The second line is therefore not a minor application of the first. It is a distinct, focused programme that tests one of computable abstraction’s most consequential possibilities under the standards of complexity theory.