# 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<T>, dropEnrichments: boolean) -> poset<T>
format enum:
- mcdp, latex
### Voting
voter:
- poset: poset
- next_antichain(voted_antichain: voted_antichain<T>) -> Either<antichain<T>, poset>
antichain<T: posetspace>:
- id: uuid
- element: element<T>
- comparisons: set of elements<T>
voted_antichain<T: posetspace>:
- id: uuid
- antichain: antichain<T>
- new_less: set of elements<T>
- new_greater: set of elements<T>
### Enricher
enricher:
- poset: poset
- enrichment: posetspace
- enrich(relations: set<(relation<poset>, element<enrichment>)>) -> poset
## Details
We will use the [posets](https://pypi.org/project/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](https://networkx.org) for the complex poset operations involved in consensus and voting.
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"description": "# Coposet\n\nCoposet is a tool for manipulating posets and allowing them to be and exporting them to various formats.\n\n## Posets (Partially Ordered Sets)\n\nA poset is a set with a partial order relation (\u2264) that is:\n- **Reflexive**: a \u2264 a\n- **Antisymmetric**: if a \u2264 b and b \u2264 a, then a = b\n- **Transitive**: if a \u2264 b and b \u2264 c, then a \u2264 c\n\nThe product of two posets P and Q creates a new poset P \u00d7 Q where:\n - Elements: All pairs (p, q) where p \u2208 P and q \u2208 Q\n - Ordering: (p1, q1) \u2264 (p2, q2) if and only if p1 \u2264 p2 in P AND q1 \u2264 q2 in Q\n\n## Schema\n\n### Core\n\nposetspace:\n- id: uuid\n- name: string\n- description: string\n- posets: list of posets\n- default_poset: poset\n- elements: list of elements\n- projections?: list of posetspaces\n- injections?: list of posetspaces\n- consensus(consensus_type) -> poset\n\nposet:\n- id: uuid\n- name: string\n- description: string\n- posetspace: posetspace\n- relations: list of relations\n- enrichment?: posetspace\n- product(poset, poset) -> (poset, posetspace)\n- coproduct(poset, poset) -> (poset, posetspace)\n- export(format: format) -> string\n\nelement:\n- id: uuid\n- name: string\n- description: string\n- posetspace: posetspace\n\nrelation<T: posetspace, E: posetspace>:\n- id: uuid\n- less: element<where less.posetspace == T>\n- greater: element<where greater.posetspace == T>\n- enrichment?: element<where enrichment.posetspace == E>\n\n### Helpers\n\nconsensus_type:\n- derive<T: posetspace>(array of posets<T>, dropEnrichments: boolean) -> poset<T>\n\nformat enum:\n- mcdp, latex\n\n### Voting\nvoter:\n- poset: poset\n- next_antichain(voted_antichain: voted_antichain<T>) -> Either<antichain<T>, poset>\n\nantichain<T: posetspace>:\n- id: uuid\n- element: element<T>\n- comparisons: set of elements<T>\n\nvoted_antichain<T: posetspace>:\n- id: uuid\n- antichain: antichain<T>\n- new_less: set of elements<T>\n- new_greater: set of elements<T>\n\n### Enricher\n\nenricher:\n- poset: poset\n- enrichment: posetspace\n- enrich(relations: set<(relation<poset>, element<enrichment>)>) -> poset\n\n\n## Details\n\nWe will use the [posets](https://pypi.org/project/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.\n\nWe should look into using [networkx](https://networkx.org) for the complex poset operations involved in consensus and voting.\n",
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