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S5 (modal logic)

Index 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]

20 relations: Accessibility relation, Alvin Plantinga, Clarence Irving Lewis, Cooper Harold Langford, Equivalence relation, Kripke semantics, Logic, Modal logic, Modus ponens, Normal modal logic, NP-completeness, Ontological argument, Philosophy, Possible world, Propositional calculus, Reflexive relation, Substitution (logic), Symmetric relation, Tautology (logic), Transitive relation.

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.

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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.

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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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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.

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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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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.

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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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Normal modal logic

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

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

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Ontological argument

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

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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.

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Possible world

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

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Propositional calculus

Propositional calculus is a branch of logic.

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Reflexive relation

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

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Substitution (logic)

Substitution is a fundamental concept in logic.

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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.

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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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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.

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Redirects here:

Axiom S5, Logic S5.


[1] https://en.wikipedia.org/wiki/S5_(modal_logic)

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