Fuzzy Logic is extended toward dynamic adaptation of the degree of fuzziness. The motivation is to explain the process of learning as joint model improvement and fuzziness reduction. A learning system with fuzzy models is introduced. Initially, the system is in a highly fuzzy state of uncertain knowledge, and it dynamically evolves into a low-fuzzy state of certain knowledge. We present an imag...

Kant discovered a philosophical problem with mathematical proof. Despite being a priori, its methodology involves more than analytic truth. But what else is involved? This problem is widely taken to have been solved by Frege’s extension of logic beyond its restricted (and largely Aristotelian) form. Nevertheless, a successor problem remains: both traditional and contemporary (classical) mathema...

We present a conceptual analysis of the notions of actual physical property and potential physical property as used by theoretical physicists/mathematicians working in the domain of operational quantum logic. We investigate how these notions are being used today and what role they play in the specified field of research. In order to do so, we will give a brief introduction to this area of resea...

The fate of logical ideas is whimsical. Very often time only gives us the opportunity to appraise the strength of forecasting of the scholar, the scale of his ideas, their orientation to the future, and the role and place of the scholar in the intellectual history of mankind. ''Time has a difficult delivery, but never a miscarriage''-as one aphorism put it. Today, the significance of the logica...

This paper translates Aristotle’s syllogistic logic of the Analytica priora into the sphere of computational-combinatorical research methods. The task is accomplished by formalising Aristotle’s logical system in terms of rule-based reduction relations on a suitable basic set, which allow us to apply standard concepts of the theory of such structures (Newman lemma) to the ancient logical system....