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

Ligature's Data Model

LanguageTag(string)
Namespace(string)
Individual(string, Optional<Namespace>, Optional<LanguageTag>)
Role(string)

Assertion = 
    | Triple(Individual, Role, Individual) 
    | Instance(Individual, Concept)
    | Same(Individual, Individual)
    | Different(Individual, Individual)

Concept = 
    | AtomicConcept(string)
    | TopConcept 
    | BottomConcept 
    | AndConcept(List<Concept>)
    | OrConcept(List<Concept>)
    | AllConcept(Role, Option<Concept>)
    | ExistsConcept(Role, Option<Concept>)
    | NotConcept(Concept)

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

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

Individual

An individual element being described.

Role

Used to connect two individuals. Roles are directed from one individual to another. We refer to these statements as triples.

Given the triple

alice knows bob

or expressed in our pseudo-code above

Triple(Individual("alice", None, None) Role("knows") Individual("bob", None, None))

alice and bob are indviduals and knows is a role that connects them.

Concepts

Concepts are sets of individuals. Examples could be the species of an animal or a tag used in a blog.

Instance

To say that an individual belongs to a concept we say that the individual is an instance of that concept.

betty is a Cat

or

Instance(Individual("betty", None, None), AtomicConcept("Cat"))

The individual betty belongs to the concept Cat.

Concept Expressions

Ligature allows you to represent complex concepts with concept expresssions. 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")]))
Instance(
    Individual("betty", None, None),
    AtomicConcept("CarnivorousPlant"))

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.

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