This document is in the process of being written, so expect missing and incomplete parts.

Ligature's Data Model

Below is a pseudocode representation of Ligature's data model.

LanguageTag(string)
TypeTag(string)
Individual(string)
Role(string)
ConceptName(string)

Filler =
    | Individual of Individual
    | String of String
    | LangString of String, LanguageTag
    | TypedString of String, TypeTag
    | Float of f64
    | Integer of bigint

Assertion = 
    | Triple(Individual, Role, Filler) 
    | Instance(Individual, ConceptName)

ConceptExpression = 
    | ConceptName of ConceptName
    | Top 
    | Bottom 
    | And(List<ConceptExpression>)
    | Exists(Role, Option<ConceptExpression>)

Definition = 
    | Implies(ConceptExpression, ConceptExpression)
    | Equivalent(ConceptExpression, ConceptExpression)

PatternPart =
    | TriplePattern of Individual | Slot, Role | Slot, Filler | Slot
    | InstancePattern of Individual | Slot, ConceptName

Pattern = Set<PatternPart>

Rule = Pattern, Pattern

KnowledgeBase(Set<Definition>, Set<Rule>, Set<Assertion>)

Individual

An individual element of a domain that is being described. You can describe an element by making assertions involving the element. Below each type of assertion is explained.

Instance

Individuals can belong to sets known as concepts. We'll explain concepts further below. Below we are stating that a potato is a Vegetable.

instance(potato Vegetable)

Triple

Triples use a role to connect two elements. Triples are directed from one element to another.

For example we can use the knows role to connect alice and betty.

alice knows betty

or expressed in our pseudocode above

Triple(Individual("alice") Role("knows") Individual("betty"))

in Wander

triple(^alice ^knows ^betty)

Concepts

Concepts are sets of Individuals. Examples could be the species of an animal or a tag used in a blog. As shown above you can say that Individuals are instances of concepts.

Concept Expressions

Ligature allows you to represent complex concepts with concept expresssions. Below I will explain each type of concept expression and how they can be combined.

Top and Bottom Concepts

There are two concepts built into Ligature, the top and bottom concepts. The top concept represents all elements in a system and the bottom concept is empty.

Conjunction

Using logical operators you can define complex concepts like this.

In slightly more formal notation

CarnivorousPlant ≡ Carnivore ⊓ Plant
betty : CarnivorousPlant

translated into pseudo-code

Equivalent(
    AtomicConcept("CarnivorousPlant"), 
    AndConcept([
        AtomicConcept("Carnivore"), 
        AtomicConcept("Plant")]))
Element(
    Element("betty", None, None),
    AtomicConcept("CarnivorousPlant"))

in Wander

equivalent(CarnivorousPlant and(Carnivore Plant))

Here we are saying the concept CarnivorousPlant is equivalent to the combination of being a Carnivore and being a Plant. We then say that betty is a CarnivorousPlant.

Existential

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