Coposet

Coposet is a tool for manipulating posets and allowing them to be and exporting them to various formats.

Posets (Partially Ordered Sets)

A poset is a set with a partial order relation (≤) that is:

• Reflexive: a ≤ a
• Antisymmetric: if a ≤ b and b ≤ a, then a = b
• Transitive: if a ≤ b and b ≤ c, then a ≤ c

The product of two posets P and Q creates a new poset P × Q where:

• Elements: All pairs (p, q) where p ∈ P and q ∈ Q
• Ordering: (p1, q1) ≤ (p2, q2) if and only if p1 ≤ p2 in P AND q1 ≤ q2 in Q

Schema

Core

posetspace:

• id: uuid
• name: string
• description: string
• posets: list of posets
• default_poset: poset
• elements: list of elements
• projections?: list of posetspaces
• injections?: list of posetspaces
• consensus(consensus_type) -> poset

poset:

• id: uuid
• name: string
• description: string
• posetspace: posetspace
• relations: list of relations
• enrichment?: posetspace
• product(poset, poset) -> (poset, posetspace)
• coproduct(poset, poset) -> (poset, posetspace)
• export(format: format) -> string

element:

• id: uuid
• name: string
• description: string
• posetspace: posetspace

relation<T: posetspace, E: posetspace>:

• id: uuid
• less: element<where less.posetspace == T>
• greater: element<where greater.posetspace == T>
• enrichment?: element<where enrichment.posetspace == E>

Helpers

consensus_type:

• derive<T: posetspace>(array of posets, dropEnrichments: boolean) -> poset

format enum:

• mcdp, latex

Voting

voter:

• poset: poset
• next_antichain(voted_antichain: voted_antichain) -> Either<antichain, poset>

antichain<T: posetspace>:

• id: uuid
• element: element
• comparisons: set of elements

voted_antichain<T: posetspace>:

• id: uuid
• antichain: antichain
• new_less: set of elements
• new_greater: set of elements

Enricher

enricher:

• poset: poset
• enrichment: posetspace
• enrich(relations: set<(relation, element)>) -> poset

Details

We will use the posets library for the basic poset operations under the hood. This will be connected by a thin interface that converts the posets from the posets library to the coposet types we need to add on our layer of voting and consensus.

We should look into using networkx for the complex poset operations involved in consensus and voting.