What is modal logic?
In the most common interpretation of modal logic, one considers “logically possible worlds”. If a statement is true in all possible worlds, then it is a necessary truth. If a statement happens to be true in our world, but is not true in all possible worlds, then it is a contingent truth.
What is modal logic with example?
Even in modal logic, one may wish to restrict the range of possible worlds which are relevant in determining whether ◻A is true at a given world. For example, I might say that it is necessary for me to pay my bills, even though I know full well that there is a possible world where I fail to pay them.
What is modal logic in AI?
Modal logic began as the study of different sorts of modalities, or modes of truth: alethic (“necessarily”), epistemic (“it is known that”), deontic (“it ought to be the case that”), temporal (“it has been the case that”), among others.
Is modal logic classical logic?
Every regular modal logic is classical, and every normal modal logic is regular and hence classical.
Is modal a logic math?
Publisher Summary. Formal modal logic is mostly mathematical in its methods, regardless of area of application. This chapter presents a wide variety of mathematical techniques developed over decades of studying the intricate details of modal logic.
What is S4 modal logic?
The epistemic logics S4 and S4(m) Then the interpretation of □ is that “If p is necessarily true then it is necessarily necessarily true.” S4 modal logic appears in many temporal logics.
Who invented modal logic?
C. I. Lewis
5. Conditional and Relevance Logics. The founder of modal logic, C. I. Lewis, defined a series of modal logics which did not have \(\Box\) as a primitive symbol.
Why is modal logic important?
The reason we want to utilize modal logic is to precisify ordinary language. Ordinary language is notoriously ambiguous and the analysis of ordinary language modal operators is fraught with difficulty. By regimenting our discourse into formal (quantified) modal logic we can eliminate some of these ambiguities.
Is modal logic true?
A modal is an expression (like ‘necessarily’ or ‘possibly’) that is used to qualify the truth of a judgement. Modal logic is, strictly speaking, the study of the deductive behavior of the expressions ‘it is necessary that’ and ‘it is possible that’.
What is a Kripke frame?
A Kripke frame or modal frame is a pair. , where W is a (possibly empty) set, and R is a binary relation on W. Elements of W are called nodes or worlds, and R is known as the accessibility relation.