Transreal Logical Space of All Propositions
Transreal numbers provide a total semantics containing classical truth values, dialetheaic, fuzzy and gap values. A paraconsistent Sheffer Stroke generalises all classical logics to a paraconsistent form. We introduce logical spaces of all possible worlds and all propositions. We operate on a proposition, in all possible worlds, at the same time. We define logical transformations, possibility and necessity relations, in proposition space, and give a criterion to determine whether a proposition is classical. We show that proofs, based on the conditional, infer gaps only from gaps and that negative and positive infinity operate as bottom and top values.
Haeng Kon Kim; Mayhar A. Amouzegar; Sio-Iong Ao. Transactions on Engineering Technologies, World Congress on Engineering and Computer Science. London: Springer, pp. 227-242, 2015.