The Semantic Tangle

By Jessica Lake

I have been thinking about semantic knowledge.

Habitually.

Note I use “knowledge” rather than “memory.” It is in observance of the popular ideal of sweet memory. The provenance of episodic memory.

There are no memories here. This is the Land of Knowledge.

After months of musing, my conception of what’s up with knowledge is beginning to mature.

So, I would like to share it with you.

What immediately follows is a list of basics, each building on the former. This will give you the footing.

* Knowledge applies a lossy compression to heterogeneous episodes. It rolls them up into statistical regularities. Life without the living.

* These regularities are persisted and organized within semantic knowledge for flexible associative access.

It seems clear that the content of knowledge varies in regular structures.

* Constraints—a declaration of a prohibited feature. Some expressed in words, others in abstraction.

* Lexicon—this is the treasure trove of spoken language. A searchable catalogue of spoken words and usage.

* Syntax template—syntax suggests itself as a series of templates expectant of completion by thought. Think MadLib.

* Facts—brief texts of something of merit. It could be heard once or many times.

* Regularity—a compression of a routine experience. Such as childhood summers, school time, or your mother.

* Rule—a payload fired by a pattern trigger. Behavior that responds to current circumstance.

* Model—the representation of statistical regularity expressed as a transform for prediction.

Semantic Representation

Some things are hidden from me within knowledge. Others are obvious. I can see words and meanings. But abstractions elude me.

My vision of semantic knowledge does not express itself as a classical DAG network or a hyperdimensional space. My nature is to prune relentlessly.

Imagine knowledge as a diffuse tangle of millions of colored strings in a void. Each string a unique constraint. You search for objects by what they are not.

You’re trying to find a word. No, that’s not right. That’s too rigid. No. Something softer. But not too soft.

Constraint search is natural.

Do not sweat the void. It is amorphous and sufficient to hold the tangle. It permits imagination.

Axiom: Any known can be isolated at the intersection of its constraints.

The constraint intersection is persisted with a tag embossed with a word or phrase. A tag gives the known an identity so it may be referenced. The constraints involved form a constraint-set.

DAG: Who doesn’t love a directed acyclic graph? You traverse its directed edges, passing through nodes. The pathway is a sequence of decisions very much like Candy Land.

NODE: A node is a place of rest. It may afford properties. Its address is imperatively derived. Alter the dependent network and you’ve altered the address. Adding or removing a node requires thought of dependencies.

What happens to successive nodes?

The Tangle: has no such state and no sequences. Its identity is declarative—you light the constraint-set up. You apply the elements in any order, or all at once. There is no traversal. There are no dependencies.

All that distinguishes one tag from another is the particular set of constraints that intersects there.

DEFINITION: The Tangle is a means of isolating a tag. It does not rely on coordinates, tuples, or traversal. It relies on a {C}. As a set is inherently unordered, so too is the tag it defines.

{C} Constraint-Set

The collection of constraints defining a tag is called its {C}.

A {C} can therefore stand alone as a specification of a tag. It says what the tag is entirely in terms of the constraints that define it.

A tag has no semantic identity independent of its {C}. It does, however, have an identity for reference.

This reverses the usual intuition of a semantic network. In a network, an identifiable node exists and relationships connect that node to other nodes.

Here there are no semantic nodes.

Identity arises from the cumulative constraints used to isolate a tag.

Constraint Convergence

A single constraint may apply to many tags.

Applying that constraint therefore isolates a population of tags sharing the same prohibition.

A second constraint reduces that population to those tags sharing both prohibitions.

Additional constraints progressively reduce the surviving population.

Constraint Convergence can therefore terminate at different levels of specificity.

If the applied constraints are sufficient to distinguish a single tag, the convergence identifies that tag.

If they are insufficient to distinguish a single tag, the result is a group of tags sharing the applied prohibitions.

Thus, the same mechanism can identify either an individual regularity or a group of related regularities.

Conceptually:

one constraint → large population

additional constraints → progressively smaller population

sufficient constraints

→ tag

The identity of the result is determined not by arriving at a node but by the cumulative {C} that isolates it.

Learning

The architecture is inherently extensible.

Observations may reveal regularities that cannot be adequately distinguished using the constraints already present in semantic knowledge.

When this occurs, a new constraint can be created.

That constraint is simply added to the existing model and applies wherever the newly discovered prohibition is relevant.

Its addition creates new combinations of constraints and therefore permits distinctions that could not previously be made.

Existing semantic knowledge does not necessarily have to be reconstructed.

Instead, learning can progressively increase the discriminatory resolution of the existing representation by adding constraints.

New experience can therefore produce:

new constraints →

new intersections →

finer discrimination

This permits semantic knowledge to become increasingly differentiated as experience accumulates.

Realms

For tractability, the complete semantic representation can be partitioned into realms.

A realm corresponds to a particular aspect of reality.

The purpose of realms is expediency rather than semantic. Partitioning reduces collisions between unrelated operations and permits asynchronous reads and writes to different portions of semantic knowledge.

Realms should therefore not be confused with semantic categories.

Categories emerge from shared constraints.

Realms partition the machinery that stores and processes those constraints.

In Closing

The model can be reduced to several propositions:

* Cognition extracts statistical regularities from reality.

* Semantic knowledge persists those regularities.

* A regularity may grant or deny attributes.

* Prohibitions are represented as constraints. Constraint Convergence operates on those constraints.

* Semantic knowledge contains no semantic nodes and is not represented as a DAG or high-dimensional space.

* Constraints may intersect as required to isolate a tag, without imposed order or structure.

* An intersection of constraints is represented by a tag.

* A tag has no independent semantic content. It is defined entirely by its {C} and serves as an identity for reference.

* The constraints defining a tag constitute its {C}.

* Applying constraints progressively isolates tags sharing those prohibitions.

* A partial {C} may identify a group of tags; a sufficiently discriminating {C} isolates a single tag.

* New knowledge can introduce new constraints, increasing semantic resolution without requiring wholesale reconstruction of existing knowledge.

* Realms partition semantic knowledge for concurrency and collision reduction but do not themselves define semantic categories.

The central architectural claim is therefore:

Semantic identity is not stored in nodes. It emerges from the cumulative intersection of constraints.