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Modal logic is a kind of logic used to represent statements about necessity and possibility. ... For example, in any modal logic based on frame conditions: ...
The smallest logic satisfying the above conditions is called K. 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 ...
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 ...
The result of the evaluation is called the modal force. [2]: 649 For example, the utterance in (4) expresses that, according to what the speaker has observed, it is necessary to conclude that John has a rather high income: (4) John must be earning a lot of money. The modal base here is the knowledge of the speaker, the modal force is necessity.
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 ...
modal logic: modal operator for “it is necessary that” in alethic logic, “it is provable that” in provability logic, “it is obligatory that” in deontic logic, “it is believed that” in doxastic logic.
Epistemic modal logic is a subfield of modal logic that is concerned with reasoning about knowledge.While epistemology has a long philosophical tradition dating back to Ancient Greece, epistemic logic is a much more recent development with applications in many fields, including philosophy, theoretical computer science, artificial intelligence, economics, and linguistics.
In logic, philosophy, and theoretical computer science, dynamic logic is an extension of modal logic capable of encoding properties of computer programs. A simple example of a statement in dynamic logic is