Quasi-matrix logic as a paraconsistent logic for dubitable information
Yu V. Ivlev · Logic and Logical Philosophy · 2004
We distinguish three types of statements -indubitably true statements (the value "n"), indubitably false statements (the value "i") and statements of dubitable information (the value "c").A set (Q, G, gf 1 , . . ., gf s ) is a quasi-matrix.Q and G are non-empty sets.G ⊂ Q. gf 1 , . . ., gf s are quasi-functions.If a function is a correspondence in virtue of which an object from some (function) domain is related with a certain object (from the range of the function) then the quasi-function is a correspondence in virtue of which an object from some domain is related with some object from a certain subset of some set (from the range of the quasi-function).Examples.Function: {(a, d), (b, k), (c, k)}.Quasi-functions:and ⊻ 4 are two and four-places strong disjunction (in metalanguage) respectively.We can say: a quasi-function is a set of sets of functions.The language has the symbols T , K, ¬, ∧, ∨, ⊃ that are defined through the following tables: