There is lot of research in this area, i think of this is an intersection between Computer Science, Philosophy and Law. Its purpose is too formalize contracts and do automatic analysis to prove properties e.g. This tool uses a formal language based on Deontic logic. In particular, today, it is widely used for concurrent (reactive/distributed/parallel) systems.įormal Specification of normative documents Another flavor of modal logic is Deontic Logic, which is concerned with obligation and permission. Later, Amir Pnueli introduced it in Computer Science to describe and reason about discrete dynamical systems. Actually, originated from the work of Artur Prior under the name Tense Logic. Think of □P as 'always' and ◊P as 'eventually'. Temporal Logic in Computer Science Nowadays is common to think of it as some 'flavor' of modal logic. Very general question, maybe i can complement a bit the other answers with some practical use cases that i know: Where A = you will run faster than the speed of light.Īnd this argument is valid within modal logic (well under most modal logics, but that's not really important when learning the basics).įor most extensions to propositional logic, whether it be existence operators, modal operators, identity, etc, they're just to capture translations from english to logic that are not currently captured correctly. The argument in modal logic would look like: So there is something going wrong during the translation from English to logic since that is turning a valid argument into an invalid one. That you will not run faster than the speed of light is guaranteed by the fact that it is impossible for you to do so. But looking at the sentences we clearly can see that the argument is valid. In propositional logic this would be an argument of the form: Therefore, you will not run faster than the speed of light.

Take the argument: It is impossible for you to run faster than the speed of light. I think the simplest explanation is that modal logic allows us to express obviously valid arguments that propositional logic fails to capture. And as the other user said, it deals with semantics.

In this case, it is not necessary that A. If A is to be translated in natural language as “I am here”, the statement “I am here” is apriori true, but we have to know who the speaker is and her location. This does not always mean that it is necessary that A. This is a classic Kripke example: Let’s say that what you mean by “A” is |- A, which means it is always true that A. But if A is true in some worlds, but not all, it is possible that A is true. If A is true in all worlds(actual world, w1, w2, etc.), then it is necessary that A. Usually, when we talk about necessity and possibility in modal logic, we talk about possible worlds (I highly recommend looking into works of Saul Kripke and David Lewis’s counterfactuals): I think the modal logic that you’re referring to is called alethic logic, which deals with necessity and possibility.

It doesn't seem to be oriented towards computation, but it apparently is used for a few things, like model checking and decidability.Īs one of the users said, Modal Logic covers different logics that translate statements that are difficult to translate using the classical logic and yes it falls under the realm of theoretical philosophy and formal semantics and pragmatics. This isn't quite the sort of thing I'm interested in. I specifically picked out temporal logic because it seems like it could have some application. □ and ◊ seem more like arbitrary wrappers that it's desirable to get rid of so that you can actually apply inference rules to the formulas. If I have ∃x A(x), I can say, 'Hey, there's some z such that A(z)'. If I have ◊A, it doesn't give me any information. So far as I'm aware, ◊ doesn't really have a proper inference rule. → is maybe not as useful in some texts as people think, but it's fine. That makes it seem to me like just A means the same thing. In most variations of modal logic, it looks like you can interchange one for the other. Apparently, that's called alethic modal logic, though I didn't know.Ī and □A seem the same.

Ways to use the modal logic playground