Abstract
D. G. Schwartz introduced the formal system Σ of subjective epistemic reasoning in which belief was measured along a series of linguistic degrees, e.g. unequivocally believes, strongly believes, fairly confidently believes, somewhat believes, neither believes nor disbelieves, somewhat disbelieves, fairly confidently disbelieves, strongly disbelieves, unequivocally disbelieves. The purpose of this paper is to present two axiomatizations for D.G. Schwartz's system, by using the matrix of many-valued logic. Then we prove the completeness theorem as well as the soundness theorem.
