Abstract

The development of the method of logical matrices at the turn of 19th Century made it possible to define the concept of many-valued logic. Since the first construction of the system of three-valued logic by ukasiewicz in 1918 several matrix based logics have been proposed, cf. [8]. The aim of the present paper is to touch upon some problems related to the topic, which would permit one to get a viewpoint upon the nature of many-valuedness. First, we show that the multiplication of logical values is not a sufficient condition to obtain a non-two-valued logic. Second, we discuss an ingenious solution by R. Suszko [11] explaining through the sentential identity an ontological nature of non-classical logical values. Next, we present a kind of metalogical relation of inference, so-called q-consequence, being three-valued in its spirit. The last chapter will bring a concise description of two ukasiewicz “manyvalued” systems of modalities and an application of the paradigm of q-consequence to these systems