Communication
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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. [1]

## Accessibility relation

In modal logic, an accessibility relation R is a binary relation such that R \subseteq W \times W where W is a set of possible worlds.

## Alvin Plantinga

Alvin Carl Plantinga (born November 15, 1932) is a prominent American analytic philosopher who works primarily in the fields of logic, justification, philosophy of religion, and epistemology.

## 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.

## Cooper Harold Langford

Cooper Harold Langford (25 August 1895, Dublin, Logan County, Arkansas – 28 August 1964) was an analytic philosopher and mathematical logician who co-authored the book Symbolic Logic (1932) with C. I. Lewis.

## Equivalence relation

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

## Kripke semantics

Kripke semantics (also known as relational semantics or frame semantics, and often confused with possible world semantics) is a formal semantics for non-classical logic systems created in the late 1950s and early 1960s by Saul Kripke and André Joyal.

## 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.

## Normal modal logic

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

## NP-completeness

In computational complexity theory, an NP-complete decision problem is one belonging to both the NP and the NP-hard complexity classes.

## Ontological argument

An ontological argument is a philosophical argument for the existence of God that uses ontology.

## Philosophy

Philosophy (from Greek φιλοσοφία, philosophia, literally "love of wisdom") is the study of general and fundamental problems concerning matters such as existence, knowledge, values, reason, mind, and language.

## Possible world

In philosophy and logic, the concept of a possible world is used to express modal claims.

## Propositional calculus

Propositional calculus is a branch of logic.

## Reflexive relation

In mathematics, a binary relation R over a set X is reflexive if every element of X is related to itself.

## Substitution (logic)

Substitution is a fundamental concept in logic.

## Symmetric relation

In mathematics and other areas, a binary relation R over a set X is symmetric if it holds for all a and b in X that a is related to b if and only if b is related to a. In mathematical notation, this is: Symmetry, along with reflexivity and transitivity, are the three defining properties of an equivalence relation.

## Tautology (logic)

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

## Transitive relation

In mathematics, a binary relation over a set is transitive if whenever an element is related to an element and is related to an element then is also related to.

## References

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