On an algebraic system similar to logic using trice (Group, Ring, Language and Related Areas in Computer Science)

Abstract

Our aim is to challenge the principle of bivalence and dualism. In mathematical logic, there is true and false. However, looking at the world in general, it is not always possible to consider absolute true or false. What is believed in one country may not be believed in another, or may have completely opposite values. We want to constitute a means of thinking about this kind of world. Łukasiewicz logic and Kleene logic are many-valued logics, but there are 'true' and 'false' values in them, and they introduce intermediate values orundetermined. This is not what we are aiming for. What we have created does not contain 'false'. We do not believe that there is only one implication. We dare to think of a way to analyze the world that embraces the antinomy. Hence, we assume that what we are aiming for is what we are told we cannot call logic. We do research on special concept 'trice'. It play an important role with regard to this attempt. Therefore, the title is "On an algebraic system similar to logic using trice". We introduce the "stealth absorption law, " an even weaker form of the roundabout absorption law. It's a modest concept that is likely to be overlooked by ordinary logic. However, it can be interpreted as a property that is meant to invalidate the premise.