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Modal logic is a kind of logic used to represent statements about necessity and possibility.It plays a major role in philosophy and related fields as a tool for understanding concepts such as knowledge, obligation, and causation.
modal logic: modal operator for “it is possible that”, (in most modal logics it is defined as “¬ ¬”, “it is not necessarily not”).
Most modal logics commonly used nowadays (in terms of having philosophical motivations), e.g. C. I. Lewis's S4 and S5, are normal (and hence are extensions of K). However a number of deontic and epistemic logics, for example, are non-normal, often because they give up the Kripke schema. Every normal modal logic is regular and hence classical.
In logic and philosophy, S5 is one of five systems of modal logic proposed by Clarence Irving Lewis and Cooper Harold Langford in their 1932 book Symbolic Logic. It is a normal modal logic, and one of the oldest systems of modal logic of any kind. It is formed with propositional calculus formulas and tautologies, and inference apparatus with ...
The modal base here is the knowledge of the speaker, the modal force is necessity. By contrast, (5) could be paraphrased as 'Given his abilities, the strength of his teeth, etc., it is possible for John to open a beer bottle with his teeth'. Here, the modal base is defined by a subset of John's abilities, the modal force is possibility.
Modal logic is an extension of classical logic. In its original form, sometimes called "alethic modal logic", it introduces two new symbols: expresses that something is possible while expresses that something is necessary. [126]
The formal fallacy or the modal fallacy is a special type of fallacy that occurs in modal logic. It is the fallacy of placing a proposition in the wrong modal scope, [1] most commonly confusing the scope of what is necessarily true. A statement is considered necessarily true if and only if it is impossible for the statement to be untrue and ...
In modal logic, a regular modal logic is a modal logic containing (as axiom or theorem) the duality of the modal operators: