What are examples of non classical formal logic being used to solve practical questions?

Question

Algebraic logic is something which exists both in Mathematics and Philosophy. However, I've been feeling discontent with the number of examples presented of using logic to solve work through philosophical problems (eg: of simplfying philosophical statements). Especially that of higher non standard logic (eg: The family of modal logic, temporal logic) etc. Often in books, there is some simple examples in beginning to motivate the basic idea of the non standard logic, but as chapters go on , the connection with reailty is entirely forgotten.

Fuzzy logic in particular, one can find a few examples in eletronics engineering and such (controlling objects such washing machine and so on).

Could some resources/ references be given where this more examples of non standard logic used in real life to solve problems can be foiund?

Answer 1

Many-valued logics are sometimes used in electronic engineering. For example, a control system for a plant might have a sensor attached to an aperture and the logic may need to distinguish three cases, the sensor is reporting that the aperture is open, the sensor is reporting that the aperture is closed, and the sensor is not reporting anything, perhaps because it is broken. Many-valued logics are often described as preserving a designated value, and in such a case the logic would work to preserve the conditions of safe operation.

Many knowledge based systems in artificial intelligence use nonmonotonic logic. If you pick up a standard textbook of knowledge representation, such as Brachman and Levesque's Knowledge Representation and Reasoning, you will find coverage of default logics and autoepistemic logic.

The Bayesian approach to probability in effect treats probability theory as a logic of partial belief. The use of Bayesian techniques to solve problems is very widespread. It is used in everything from weather forecasting, exploration, finance, medicine, environmental prediction, etc. Pretty much anywhere you have to make decisions under uncertainty.

As you mention, fuzzy logic is sometimes used in control systems.

Artificial intelligence systems sometimes use paraconsistent approaches to logic, because they may need to process conflicting information without falling into triviality.

AI systems also sometimes use non-classical approaches to negation, such as 'negation as failure', or they may allow for a strong and weak negation corresponding roughly to: this is definitely false vs. this may be false for all we know.

Linear logic is used in computer science to model functional programming and logic programming, particular with reference to parallel processing. It also has applications in representing the logic of resource-bound interactions.

Modal logic is used within philosophy and linguistics. How practical you consider that to be is a matter of opinion.

Intuitionistic logic is used within contructive mathematics. Some programming languages, such as ML and Haskell are based on intuitionistic logic.

Answer 2

The "Tree" of non-classical logic is quite bushy, and the relationship among the branches is obscure.

The theory and methods of non-classical logic as they have developed do not have the power to handle philosophically interesting problems. Most multi-valued logics lack adequate conditionals and biconditionals, which impedes development of the algebra. Intuitionism and modal logic are generally not truth-functional, which make the decision problem of whether a given formula is or is not a valid theorem non-trivial, and prevent easy use of either the Boolean Algebraic or the truth-table methods of classical logic. Fuzzy logic also does not have robust conditionals.

In about the 1920s, the fields of multi-valued logic, intuitionism, and modal logic were created about the same time, with fuzzy logic and paraconsistent logic coming along later. These fields were deemed inconsistent and irreconcilable and have been pursued separately and independently.

Whether this is really the case, or whether they can be reconciled after all is more of an academic problem than a logical one. There are few people who are sufficiently familiar with the foundational principles of more than one or two of them. Perhaps more importantly, there appears to be little or no professional academic interest in going back to the beginning and trying to reconcile them a century after their origins.

There are probably no easy answers in the literature to finding practical applications for non-classical logic.