Break of Logic Symmetry by Self-conflicting Agents: Descriptive vs. Prescriptive Rules

Classical axiomatic uncertainty theories (probability theory and others) model reasoning of rational agents. These theories are prescriptive, i.e., prescribe how a rational agent should reason about uncertainties. In particular, it is prescribed that (1) uncertainty P of any sentencep is evaluated by a single scalar P(p) value, (2) the truth-value of any tautology (por-p) is true, and (3) the truth-value of any contradiction (pnland-p) is false for every proposition p. However, real agents can be quite irrational in many aspects and do not follow rational prescriptions. In this paper, we build a logic of irrational and conflicting agents called I-agent logic of uncertainty (IALU) as a vector logic of evaluations of sentences. This logic does not prescribe rules on how an agent should reason rationally, but describe rules on how agents reason irrationally. This is a descriptive not prescriptive theory in contrast with the classical logic and the probability theories. This provides a new possibility to better understand and model uncertainties associated with social conflict phenomena. We show that the fuzzy logic has a potential to become a scalar version of a descriptive logic of irrational agents because it satisfies several necessary conditions of IALU