Research map
What can a system distinguish, and how do those distinctions change?
This is the organising question behind B-Theory. The path below links existing mathematical work to proposed research directions. These stages show a conceptual progression, not a claim that one paper proves the next.
Represent
Represent a state
A system needs a formal way to describe possible states and operations on them.
Correspondence Matrices
How can logical operations be represented and combined without losing their meaning across symbolic and numeric forms?
Related manuscript: Correspondence and Logical Matrices: A Typed Boolean Operator CalculusRead this project Research frameworkAlgebraic Logic
Which algebraic structures let us describe logical states and operations consistently?
Read this projectObserve
Observe and distinguish
Available tests determine which states remain indistinguishable and what changes when observations improve.
ProLT Observation Topologies
Which logical states can a chosen family of observations distinguish?
Related manuscript: Observation Topologies for Finite Propositional Semantics: Distinguishability, Distance, and InferenceRead this project Research manuscriptBinary Order Thinning
When does a new Boolean distinction preserve the topology of an ordered state space?
Related manuscript: Binary Order Thinning of Finite Posets: Homology, Collapses, and Sharp LimitsRead this project Research draftObservation Refinement
What structural changes occur when a system learns to make a distinction it could not make before?
Related manuscript: Successive Concept Differentiation as Observation RefinementRead this project Research noteHierarchical Concepts
How does limited observation turn a fine-grained hierarchy into coarser, usable concepts?
Related manuscript: Hierarchical Concepts Under Finite Resolution: Observation Quotients and Adaptive SymmetryRead this project Research branchMeasurement and RF-IDENT
Can an observer identify every state using only the tests it has, while keeping each step admissible?
Read this projectOrganize
Organize relationships
Structure can be studied through hierarchy, topology, homology, composition, and factorization.
Logical Homology
Which structural features of a logical space persist when its relationships change?
Read this project Research noteStructured Boolean Factorization
When can a complex Boolean structure be decomposed into independent parts?
Related manuscript: Vtree Alignment and Higher-Order Four-Corner Defects in Exact Boolean FactorizationRead this projectBecome
Model change and reflection
A finite technical report connects permitted sensing to prediction under known actions. Continuous change and self-modeling remain proposed directions.
Acquirable Predictive Models
Can a system obtain the distinctions it needs to predict future outputs, using only the tests it is allowed to perform?
Related manuscript: From Observable States to Acquirable Predictive ModelsRead this project Proposed directionEvolutionary Logic
When does a continuously changing system acquire a different observable logical state?
Read this project Proposed directionInformation and Boundaries
Which observations across a boundary help a system maintain and revise an internal model?
Read this project Proposed directionReflective Self-Models
What would make a model genuinely about the system that maintains it?
Read this projectThe idea in miniature
Change the available observations
In this simple example, a new test splits a group of states that previously looked the same.
Four cards. Two possible tests.
You can see all four cards below. The observer can only read the properties you enable.
Each card is written AB: A is colour (0 = teal, 1 = gold); B is shape (0 = circle, 1 = square). So 01 is a teal square.
Before you change a test: predict which cards will still look the same to the observer.
From four cards to questions about a system’s own observations and limits.
Watch larger, with chapters and transcript2 observable groups. The observer knows the colour, but cannot tell a circle from a square.
Teal (A = 0)
00Teal circle01Teal square
Gold (A = 1)
10Gold circle11Gold square
What changed? The cards stay fixed; what changes is which cards the observer can distinguish. Adding a test can split a group. It cannot merge groups the observer could already tell apart.
The mathematics behind the example
1 bit of uncertainty remains about the full state: one more yes/no answer identifies the card.
This toy model treats all four cards as equally likely. The uncertainty is Shannon conditional entropy about the full state given the selected observations. It is not a measure of consciousness.
The groups here use complete yes/no records. The ProLT explanation also studies a different construction, where only positive answers count as observations.
Research status
Results, tools, and open questions
A manuscript establishes only its stated mathematical results. The proposed links to cognition and self-awareness remain questions for further modeling and empirical work.
Read the paper guide