lean-catLogic / lean-catLogic/formalization
Develop theory of syntactic posets (Lindenbaum-Tarski algebras)
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Description
Currently, the syntactic poset is just used as a stepping stone to the syntactic category. But of course these structures have a lot of interest on their own. For instance, if the full language + deductive calculus of IPL or CPL is implemented (see #10), then we could formalize the proof that their syntactic posets are Heyting algebras / Boolean algebras, respectively.
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First steps
- Read the whole issue, then the project's contributing guide.
- Comment on the issue to say you are picking it up — it saves two people doing the same work.
- Fork the repository and make your change on a branch.
- Open a pull request that references the issue number.
Research direction
Start by reviewing issue #10, which is identified as the prerequisite for implementing the full language and deductive calculus of IPL or CPL. Determine how the syntactic poset is represented and what is needed to formalize its Heyting-algebra or Boolean-algebra structure; done means the corresponding proof is formalized.
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Assessment
- Domain
- tooling
- Issue type
- Feature
- Difficulty
- 5/5
- Estimated time
- Over a week
- Activity status
- Stale
- Clarity
- Needs clarification
- Newbie friendliness
- 25/100