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Normal modal logic

Index Normal modal logic

In logic, a normal modal logic is a set L of modal formulas such that L contains. [1]

15 relations: Clarence Irving Lewis, Deontic logic, Directed set, Epistemic modal logic, Equivalence relation, Logic, Modal logic, Modus ponens, Partially ordered set, Preorder, Provability logic, S5 (modal logic), Saul Kripke, Tautology (logic), Weak ordering.

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.

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Deontic logic

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

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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.

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Epistemic modal logic

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

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Equivalence relation

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

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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.

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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.

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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.

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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.

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Preorder

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

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Provability logic

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

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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.

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Saul Kripke

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

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Tautology (logic)

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

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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.

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K (logic), S4 (logic), S4 (modal logic), S4 (normal modal logic).

References

[1] https://en.wikipedia.org/wiki/Normal_modal_logic

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