The paper discusses a mathematical nature of signs and symbols, and relates it to information processing and understanding, structure of the mind and brain, learning, and pattern recognition. I discuss past limitations of algorithms and neural networks, combina-torial complexity, the roles of concepts and emotions in mind’s mechanisms, and various types of logic underlying mathematical techniqu...

air conditioning is widely applied for the improvement of standard of living in human life. this present investigation focused on the prediction of indoor air quality characteristics of air conditioned car using fuzzy logic algorithm. the conditioned space was selected and the experiments were planned as per design of experiments to study the effect of human load, fresh air supply and air veloc...

The hot controversy about the role of logic in AI has been repeated so far and probably will continue on as usual. An important fact is that the “logic” as the center of the controversy is classical mathematical logic and/or its various extensions, though there are some “more logical” logic systems. Until recently, what is debated by the researchers working on the fundamentals of AI is, among o...

From the viewpoint of logic, we have qualitatively shown that classical mathematical logic, its various classical conservative extensions, and traditional relevant logics are not suitable to underlying forward reasoning and/or deduction for discovery because their logical theorems include a lot of paradoxes of conditional, and shown that strong relevant logics are more hopeful candidates for th...

Classical logic is usually interpreted as the logic of propositions. But from Boole’s original development up to modern categorical logic, there has always been the alternative interpretation of classical logic as the logic of subsets of any given (non-empty) universe set. Partitions on a universe set are dual to subsets of a universe set in the sense of the reverse-the-arrows category-theoreti...

Doubt could be expressed that a special section on late 19th century mathematics, or, more specifically, on Victorian mathematics, was an appropriate place for a lecture on 19th century logic. Most 19th century scholars would have been of the opinion that philosophers are responsible for research on logic. On the other hand, the history of late 19th century logic indicates clearly a very dynami...

This paper concerns the reception of the new logic and logicism of Frege and Russell among the German Neo-Kantian philosophers of the Marburg school. Paul Natorp and Ernst Cassirer both object to Frege’s and Russell’s conception of the ground, nature, and demarcation of logic. This objection depends on the distinctive Marburg school philosophy of logic, arst articulated by Hermann Cohen: that “...

We present an introduction to geometric logic and the mathematical structures associated with it, such as categorical logic and toposes. We also describe some of its applications in computer science including its potential as a logic for spec-iication languages.