Information and evidence in logic systems

A logic system S describing a world W contains certain semantic information about W. We define the quantity of this information, and the information value of a formula F relative to S. A close relationship is revealed between the information of S and the cardinality of the set of its models. Then the evidence of a formula F given by S is introduced providing basis for reasoning by evidence as a way of non-monotonic reasoning. The latter is presented in the form of plausible world assumption, PWA possessing certain advantages over the known approaches to non-monotonic reasoning: PWA computes a plausible model for any first-order logic system, and provides a high degree of relative monotonicity to its beliefs. The most important feature of PWA is its semantic plausibility demonstrated by a number of examples.