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# Normal modal logic

In logic, a normal modal logic is a set L of modal formulas such that L contains. 

## Clarence Irving Lewis

Clarence Irving Lewis (April 12, 1883 – February 3, 1964), usually cited as C. I. Lewis, was an American academic philosopher and the founder of conceptual pragmatism.

## Deontic logic

Deontic logic is the field of philosophical logic that is concerned with obligation, permission, and related concepts.

## Directed set

In mathematics, a directed set (or a directed preorder or a filtered set) is a nonempty set A together with a reflexive and transitive binary relation ≤ (that is, a preorder), with the additional property that every pair of elements has an upper bound.

## Epistemic modal logic

Epistemic modal logic is a subfield of modal logic that is concerned with reasoning about knowledge.

## Equivalence relation

In mathematics, an equivalence relation is a binary relation that is reflexive, symmetric and transitive.

## Logic

Logic (from the logikḗ), originally meaning "the word" or "what is spoken", but coming to mean "thought" or "reason", is a subject concerned with the most general laws of truth, and is now generally held to consist of the systematic study of the form of valid inference.

## Modal logic

Modal logic is a type of formal logic primarily developed in the 1960s that extends classical propositional and predicate logic to include operators expressing modality.

## Modus ponens

In propositional logic, modus ponens (MP; also modus ponendo ponens (Latin for "mode that affirms by affirming") or implication elimination) is a rule of inference.

## Partially ordered set

In mathematics, especially order theory, a partially ordered set (also poset) formalizes and generalizes the intuitive concept of an ordering, sequencing, or arrangement of the elements of a set.

## Preorder

In mathematics, especially in order theory, a preorder or quasiorder is a binary relation that is reflexive and transitive.

## Provability logic

Provability logic is a modal logic, in which the box (or "necessity") operator is interpreted as 'it is provable that'.

## S5 (modal logic)

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.

## Saul Kripke

Saul Aaron Kripke (born November 13, 1940) is an American philosopher and logician.

## Tautology (logic)

In logic, a tautology (from the Greek word ταυτολογία) is a formula or assertion that is true in every possible interpretation.

## Weak ordering

In mathematics, especially order theory, a weak ordering is a mathematical formalization of the intuitive notion of a ranking of a set, some of whose members may be tied with each other.

## References

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