In mathematical logic, an ω-consistent (or omega-consistent, also called numerically segregative1) theory is a theory (collection of sentences) that is not only (syntactically) consistent (that is, does not prove a contradiction), but also avoids proving certain infinite combinations of sentences that are intuitively contradictory. The name is due to Kurt Gödel, who introduced the concept in the course of proving the incompleteness theorem.
Now in Jain dialectic we have the following statements:
These seven propositions also known as saptabhangi are:
syād-asti: "in some ways it is" syād-nāsti: "in some ways it is not" syād-asti-nāsti: "in some ways it is and it is not" syād-asti-avaktavyaḥ: "in some ways it is and it is indescribable" syād-nāsti-avaktavyaḥ: "in some ways it is not and it is indescribable" syād-asti-nāsti-avaktavyaḥ: "in some ways it is, it is not and it is indescribable" syād-avaktavyaḥ: "in some ways it is indescribable"
I just need a hint to convert the latter sentences to logical form.