 An early example of the former approach was offered in a 1938 paper by the Russian logician D. A. Bochvar (Bochvar 1938 [1981]), where the principle of excluded middle is sacrificed as a consequence of the adoption of what is now known as Kleene’s weak three-valued scheme. An interesting recent attempt based on giving up excluded middle is Field 2004. A rather radical alternative proposal is to embrace a paraconsistent logic and give up the principle of non-contradiction (Priest 1987). A different way of giving up CL is by questioning its structural rules and turn to a substructural logic, as in Mares and Paoli (2014). The problem with all these approaches is whether their underlying logic is strong enough for all the intended applications of property theory, in particular to natural language semantics and the foundations of mathematics.