A few more useful 8-valued logics for reasoning with tetralattice \(EIGHT_{4}\)
This paper provides a generalization of the initial values of Belnap's \(4\)-valued logic [see \textit{N. D. Belnap}, ``A useful four-valued logic'', in: J. M. Dunn et al. (eds.), Modern uses of multiple-valued logic. Fifth international symposium, Bloomington, 1975, 5--37 (1977; Zbl 0424.03012); ``How a computer should think'', in: G. Ryle (ed.), Contemporary aspects of philosophy. Oriel Press. 30--55 (1977)], based on the idea of Kleene's concept of `logic of uncertainty'. The author arrived at the set of eight generalized truth values which may be regarded even more natural as far as the intuitive perspective is concerned. In order to clarify this generalization, a new algebraic structure, the tetralattice \(EIGHT_4\), is introduced, which combines four different ordering relations defined independently: information ordering, truth ordering, falsity ordering and uncertainty ordering. An adequate axiomatization for this logic is proposed as well.
scientific article; zbMATH DE number 5633563