Quantifiers, Disjunction, and Truth-Values with Two Numbers

Context: Cognitive studies seem to show that two kinds of tasks are controversial. Both have a quantified premise, a quantified conclusion, and a disjunction in the premise. The difference is that the quantifier (both in the premise and in the conclusion) is existential in one of them, and universal in the other one. In both cases, the conclusion is one of the disjuncts. To infer its disjuncts from a disjunction is not correct in First-Order Predicate Calculus. However, people tend to accept the conclusion when the quantifier is existential and reject it when the quantifier is universal. I try to argue that a non-axiomatic logic with truth-values with two numbers can come to those results too.Methodology: I review the two types of tasks from the resources of that non-axiomatic logic. The main components I consider are the inheritance and instance copulas, and the value of frequency of a statement. The latter value is calculated from all the pieces of evidence the system has and the amount of those pieces supporting the statement.Conclusions: considering components such as those ones, it is possible to check that the non-axiomatic logic can come to the conclusions reported in the literature for the two kinds of tasks analyzed.