Notice the following similarity between the vector space dual and negation in propositional logic:
$$ V^* \equiv V \rightarrow F $$ $$ P^c \equiv P \rightarrow \bot $$
Is there some general notion of duality behind this?
Also, a tensor is known to be of type $V \times \cdots \times V \times V^* \times \cdots \times V^* \rightarrow F$ or perhaps more suggestively $V \rightarrow \cdots \rightarrow V \rightarrow V^* \rightarrow \cdots \rightarrow V^* \rightarrow F$.
Does this give an equivalent notion of a "tensor" in propositional logic? Perhaps through Curry-Howard?