EA://INTEL — Entities in Semantic Space: UL's Algebraic Existence

In Universal Language (UL), existence corresponds to entities — the things we talk about. This is represented by the Entity sort (\(e\)). Entities participate in relations, can be modified and quantified, and can even be derived from assertions. But what does this mean for UL’s algebraic structure?

The Entity sort is unique because it appears in every operation of UL’s algebra. This means entities are indispensable; without them, nothing can be expressed. Imagine UL as a language: entities are the nouns — they’re fundamental to meaning.

Consider a simple relation like ‘is greater than’. In UL terms, this is represented as \(e × r → a\) (entity times relation yields assertion). Now let’s modify an entity with a modifier: ‘very’ makes ‘large’ more meaningful. This is written as \(m × e → e\). We can also quantify entities: ‘some’ and ‘all’ help us talk about groups of entities.

Nominalization, the process of turning facts into things, shows how entities can be derived from assertions. For instance, ‘The book was read by many people’ becomes ‘Many readers read The Book’. Here, ‘The Book’ is an entity derived from the assertion.

A concrete example makes this clearer: imagine talking about a game where ‘Player \(X\) defeated Player \(Y\)’. This can be expressed as \(e × r × e → a\), with players (\(X\), \(Y\)) as entities and ‘defeated’ as the relation. Now, let’s modify \(Y\) to represent ’ inexperienced player’: \(m × e → e\). Lastly, quantifying entities: ‘Most players defeated at least one expert’.

To verify this understanding, check out UL’s live wiki (wiki.fusiongirl.app — page: Existence (Universal Language), section: Existence in Semantic Space). Now, here’s a question to ponder: What happens when we introduce another sort into UL? How does it interact with entities, and what new expressions can we make?

REPOSITORY: https://github.com/Jthora/universal_language — entry point FOR-AI.md for AI readers.