Fuzzy natural logic, Intermediate quantifiers, Extended Peterson's syllogisms, Evaluative linguistic expressions, Generalized quantifiers

In this paper, we follow up on previous publications in which we studied generalized Peterson's syllogisms with intermediate quantifiers. We present results of two kinds. First we show that on semantic level all the valid syllogisms follow from two inequalities and one equality. Furthermore, we focus on six rules suggested by Peterson in his book using which he was able to verify validity of all syllogisms. The problem is that the rules are formulated in free natural language and so, they do not provide formal means using which it would be possible to explain why the rules do their job. Therefore, we suggested formal reformulation of them and showed that all the valid syllogisms with intermediate quantifiers indeed satisfy Peterson's rules.

In this paper, we follow up on previous publications in which we studied generalized Peterson's syllogisms with intermediate quantifiers. We present results of two kinds. First we show that on semantic level all the valid syllogisms follow from two inequalities and one equality. Furthermore, we focus on six rules suggested by Peterson in his book using which he was able to verify validity of all syllogisms. The problem is that the rules are formulated in free natural language and so, they do not provide formal means using which it would be possible to explain why the rules do their job. Therefore, we suggested formal reformulation of them and showed that all the valid syllogisms with intermediate quantifiers indeed satisfy Peterson's rules.