In everyday life, there can be evidence to support both a proposition and the negation of it.
I guess paraconsistent logic is an appropriate way to model this.
Is there any research in that direction?
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Yes, there is research in the field of paraconsistent logic, which is a type of logic that allows for the coexistence of contradictory statements. In everyday life, it is often the case that there is evidence to support both a proposition and its negation, and paraconsistent logic provides a way to model and reason about such situations.
In paraconsistent logic, contradictory statements are not automatically assumed to be false, as they are in classical logic. Instead, they are treated as separate and independent propositions, and rules are developed for dealing with them in a consistent and coherent manner.
There are many different approaches to paraconsistent logic, and researchers have proposed various systems and methods for dealing with contradictory statements. Some of these approaches are based on the idea of "dialetheism," which is the view that some statements can be both true and false at the same time. Other approaches focus on developing non-classical logical operators and truth values that allow for the representation of contradictory statements.
Overall, there is a significant amount of research in the field of paraconsistent logic, and many philosophers and logicians have studied and contributed to the development of this area of logic.