# What are the practical applications of formal logic, outside of math and computer programming?

I am studying a bit of this and so far it seems that, apart from math and computer science, the discipline of Logic is very inward-facing...with logicians proving things for other logicians. This may just be a feature of the materials I am learning from, but it leaves me wondering about interdiscipliary work being done. Specifically, can classical (propositional and first order predicate) and/or non-classical (i.e., fuzzy, intuitionist, relevant etc) logics provide unique insights or analysis in the following domains:

1. History
2. Law
3. Psychology
4. Engineering

I know this is a bit broad, just looking for smattering of concrete examples indexed to these domains.

Thanks

• Are you interested only in logic or also in other math branches, say, probability or statistics?
– DBK
Nov 24, 2013 at 7:50
• Just logic..probability and statistics is essential to my job, which intersects with economics, law, and policy. Plenty of examples there. Just wanted to know what formal logic can bring to the table in the above areas.
– user4634
Nov 24, 2013 at 20:13
• Thanks all for the comments. It seems that insofar as formal logic is concerned, its usefulness is for other fields that are highly symbolic. I have since come across the field of "informal logic" and find that its approach hews much closer to what lawyers, scientists, and humanities professionals use. I think this stems from the fact that for most arguments, its not the STRUCTURAL validity that is in question, but the SEMANTIC validity within a valid logical structure. E.g., If A then B is structurally valid, but "If its raining then the ground is dry" is semantically invalid.
– user4634
Nov 26, 2013 at 14:30
• @Eupraxis1981, I think this is a good insight. The key to connecting it to formal logical tools is to look at what semantic assumptions formal logicians are making (e.g. in the set theoretic models they appeal to) and to try to look at where the modelling assumptions hold, and how changes to what we assume change what inference rules hold as a matter of generality. Apr 10, 2014 at 7:18

It's used in two fields that I can speak of:

1. Electronics: We use boolean logic at the level of predicates. I've not come across propositional logic here. Some of the advances in the field are from finding optimal circuits for complex tasks.
2. Linguistics: A few different kinds of logic are at the heart of many grammar formalisms such as CCG and Logical Grammar

The structures of formal logic are widely applicable even in situations that don't have the same rigor. To use one of your examples, imagine you were a lawyer, asked to disprove a statement in court. If you had studied formal logic, you would know one of the best ways to establish something cannot be true is to assume it is true and then produce a contradiction. You could follow that same general strategy, even if you weren't exactly following all formal logical rules.

You mentioned programming --as a professional programmer, I find having studied logic useful not just at the level of using logical operators such as "AND", "OR" or "NOT" in programming statements, but also in terms of the overall structure of programs.

I'm not an engineer, but I imagine you can use a lot of the same kind of structural skills in producing a workable physical structure, even if electronic engineering isn't your area.

It is also being used in Artificial Intelligence (AI). There are many branches in AI that use mathematical logic. For instance situation calculus is a formalism for modelling actions (for example a robot doing some tasks). It is also used in planning, business process modelling, ... .

Temporal logics are being used for modelling systems that flow of time is important.

Epistemic logic is used in economics (bounded rationality, game theory, ...).

Temporal logics are being used in computer engineering, in software verification.

Actually almost in every kind of modelling, mathematical logic have something to say and can be used.

Formal testing and specifications of signal systems (railways) and many other applications. se Prover. This company was founded by a logician and uses advanced logical algoritms. They have a patent on modus ponens... or so the joke goes.

Law.

Mathematics is not the only example of deductive logic, though it is the most important. Another example is law. I do not mean legislation, where the question is what law ought to be. I mean the business of the law-courts, which is concerned with what the law is. The laws, as enacted, lay down general principles, and the courts have to apply them to particular circumstances. Sometimes the logic is simple: murderers are to suffer the death penalty, this man is a murderer, therefore this man is to suffer the death penalty. But in more complicated cases, such as elaborate financial fraud, it may be very difficult to draw the necessary deductive inferences from the existing laws; if the swindler is sufficiently ingenious, there may be no laws applicable to his case.

Russell, Bertrand. The Art of Philosophizing. New York: Philosophical Library, 1968. 40. Print.

Modern lawyers are probably the closest things to renaissance men, in the sense that there are increasing demands for them to quickly pick up any subject, be it environmental, financial, industrial or commercial. Law is no longer as boring as it used to be. A middle-aged engineer who is losing out in office politics and is stuck in a dead-end job is a perfect fit for a high-end lawyer. Not only that his past experiences are extremely useful, but also that his primitive desires for knowledge will be abundantly satisfied.