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In statistics, the mode is the value that appears most often in a set of data values. [1] If X is a discrete random variable, the mode is the value x at which the probability mass function takes its maximum value (i.e., x=argmax x i P(X = x i)). In other words, it is the value that is most likely to be sampled.
Modal logics include additional modal operators, such as an operator which states that a particular formula is not only true, but necessarily true. Although modal logic is not often used to axiomatize mathematics, it has been used to study the properties of first-order provability [ 39 ] and set-theoretic forcing.
modal logic modal operator for “it is possible that”, (in most modal logics it is defined as “¬ ¬”, “it is not necessarily not”). ∃ x P ( x ) {\displaystyle \Diamond \exists xP(x)} says “it is possible that something has property P {\displaystyle P} ”
The term "mode" in this context refers to any peak of the distribution, not just to the strict definition of mode which is usual in statistics. If there is a single mode, the distribution function is called "unimodal". If it has more modes it is "bimodal" (2), "trimodal" (3), etc., or in general, "multimodal". [2]
A modal connective (or modal operator) is a logical connective for modal logic.It is an operator which forms propositions from propositions. In general, a modal operator has the "formal" property of being non-truth-functional in the following sense: The truth-value of composite formulae sometimes depend on factors other than the actual truth-value of their components.
Modal algebras provide models of propositional modal logics in the same way as Boolean algebras are models of classical logic. In particular, the variety of all modal algebras is the equivalent algebraic semantics of the modal logic K in the sense of abstract algebraic logic , and the lattice of its subvarieties is dually isomorphic to the ...
In modal logic, a classical modal logic L is any modal logic containing (as axiom or theorem) the duality of the modal operators A ↔ ¬ ¬ A {\displaystyle \Diamond A\leftrightarrow \lnot \Box \lnot A}
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.