An embedding of N. A. Vasil'ev's imaginary logic into quantified three-valued logic (Q2751839)

One of the predecessors of paraconsistent logic, N. A. Vasil'ev, offered a syllogistic type system which contained not only affirmative and negative statements, but also contradictory (``indifferent'') statements with the copula ``is and is not simultaneously''. Vasil'ev named this system ``imaginary non-Aristotelian logic''.NEWLINENEWLINENEWLINEThe author of the paper under review gives a formalization of this system. He presents a formal calculus \textbf{IL} and an adequate semantics for Vasil'ev's logic which is based on the idea to associate with each general term a number of different extensional characteristics -- its domain, anti-domain and contradictory domain. Model structures of this semantics are also useful for quantified three-valued logic. The author offers a natural translation of the imaginary logic statements into the language of quantified three-valued logic and proves that \textbf{IL} is embedded into the quantified three-valued Łukasiewicz logic.NEWLINENEWLINEFor the entire collection see [Zbl 0960.00036].