How true it is = who says it's true
In this chiefly expository paper the author presents the idea of taking the truth value of a formula to be the set of agents who accept the formula as true. This leads to a truth value space as an arbitrary (finite) Boolean algebra. This is formalized and a complete tableau system provided for a modal logic with propositional constants. This way of looking at things has utility especially for knowledge representation for multiple agents. This is illustrated through discussion of the `muddy children problem'. Nevertheless, as the case study shows, open problems remain regarding the proper formalization of various natural language statements, such as express negative knowledge and common knowledge. The ideas presented here are developed more fully and technically in other works by the author, and others; cf. e.g. [\textit{M. Fitting}, Ann. Soc. Math. Pol., Ser. IV, Fundam. Inf. 15, No.~3--4, 235--254 (1991; Zbl 0745.03018)], [\textit{M. Fitting}, Ann. Soc. Math. Pol., Ser. IV, Fundam. Inf. 17, No.~1--2, 55--73 (1992; Zbl 0772.03006)], [\textit{M. Fitting}, Stud. Log. 55, No.~1, 63--87 (1995; Zbl 0837.03017)].
scientific article; zbMATH DE number 5552255
scientific article