Missing Mathematics§1.6Priority #8

Logic Beyond First-Order

Open

The Gap

No modal, temporal, epistemic, deontic, or counterfactual logic.

Why It Matters

Cannot express: necessity ('must'), possibility ('might'), knowledge ('I know that'), obligation ('you should'), counterfactuals ('if it had rained...').

Resolution

Introduce possible-world enclosures and accessibility relations. Handle necessity, knowledge, obligation within geometric framework.

Impact
high
Tractability
medium
Effort
medium
Category
mathematics

Related Problems

Contribute to This Problem

Interested in working on this research gap? Here's how you can help:

  • Propose a solution — Share your approach in a GitHub discussion or issue
  • Submit a proof sketch — Even partial progress helps advance the field
  • Identify connections — Link this problem to existing mathematical results