Open problem: Are operators in Homotopy Level Two Computing isomorphic to deterministic operators?

[bvssvni]

In the paper Homotopy Level Two Computing, a NAND-2 gate and "qubit" (~) was defined such that ~~a == a.

The problem is that ~ is non-deterministic, due to use of rbit (a synchronizing bit), so determining the complexity of this logic is non-trivial.

If Homotopy Level Two Computing is isomorphic to deterministic opereators, then the paper Complexity of Path Semantics uses correct assumptions. However, if this does not hold, then the complexity of Path Semantics might be even higher.

The problem is whether the logic is isomorphic to a deterministic 4-value logic (or possibly some higher N-value logic), or not.

Implications for Seshatism vs Platonism

One of most important language biases in Path Semantics is Seshatism vs Platonism

• Seshatism: !~a
• Platonism: ~a

Proofs in brute force theorem proving evaluates all possible bit-patterns, so it is not possible to interpret truth tables directly in a sense that some proposition a has a concrete encoding. Instead, language bias arises from which theorems can be proved in the overall mathematical language.

1. If there exists an isomorphism, then perhaps one can translate encoding of propositions into other forms
2. If 2) then perhaps one can translate into a form easier to interpret in relation to Seshatism vs Platonism