modal logic - définition. Qu'est-ce que modal logic
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Qu'est-ce (qui) est modal logic - définition

FORMAL LOGIC ABLE TO EXPRESS CONCEPTS SUCH AS NECESSITY, POSSIBILITY, PROVABILITY, OBLIGATION, KNOWLEDGE ETC.
Contingent truth; Modal Logic; Metaphysical contingency; Necessary propositions; Impossible propositions; Actual propositions; Semantics of modal logic; Modal logic S5; Necessity (modal logic); Necessity (logic); Necessary (modal logic); Necessary (logic); Intensional logics; Rule of necessitation; Alethic modal logic; Alethic logic; System K; ⟠; Impossible proposition; Metaphysics of modalities; Modalized; Necessary proposition; 4 (axiom); 5 (axiom); History of modal logic; Axioms of modal logic; Semantics for modal logic

modal logic         
<logic> An extension of propositional calculus with operators that express various "modes" of truth. Examples of modes are: necessarily A, possibly A, probably A, it has always been true that A, it is permissible that A, it is believed that A. "It is necessarily true that A" means that things being as they are, A must be true, e.g. "It is necessarily true that x=x" is TRUE while "It is necessarily true that x=y" is FALSE even though "x=y" might be TRUE. Adding modal operators [F] and [P], meaning, respectively, henceforth and hitherto leads to a "temporal logic". Flavours of modal logics include: {Propositional Dynamic Logic} (PDL), Propositional Linear Temporal Logic (PLTL), Linear Temporal Logic (LTL), Computational Tree Logic (CTL), Hennessy-Milner Logic, S1-S5, T. C.I. Lewis, "A Survey of Symbolic Logic", 1918, initiated the modern analysis of modality. He developed the logical systems S1-S5. JCC McKinsey used algebraic methods ({Boolean algebras} with operators) to prove the decidability of Lewis' S2 and S4 in 1941. Saul Kripke developed the {relational semantics} for modal logics (1959, 1963). Vaughan Pratt introduced dynamic logic in 1976. Amir Pnuelli proposed the use of temporal logic to formalise the behaviour of continually operating concurrent programs in 1977. [Robert Goldblatt, "Logics of Time and Computation", CSLI Lecture Notes No. 7, Centre for the Study of Language and Information, Stanford University, Second Edition, 1992, (distributed by University of Chicago Press)]. [Robert Goldblatt, "Mathematics of Modality", CSLI Lecture Notes No. 43, Centre for the Study of Language and Information, Stanford University, 1993, (distributed by University of Chicago Press)]. [G.E. Hughes and M.J. Cresswell, "An Introduction to Modal Logic", Methuen, 1968]. [E.J. Lemmon (with Dana Scott), "An Introduction to Modal Logic", American Philosophical Quarterly Monograpph Series, no. 11 (ed. by Krister Segerberg), Basil Blackwell, Oxford, 1977]. (1995-02-15)
Modal logic         
Modal logic is a collection of formal systems developed to represent statements about necessity and possibility. It plays a major role in philosophy of language, epistemology, metaphysics, and natural language semantics.
Epistemic modal logic         
SUBFIELD OF MODAL LOGIC THAT IS CONCERNED WITH REASONING ABOUT KNOWLEDGE
Distribution axiom; Knowledge generalization rule; Knowledge or truth axiom; Positive introspection axiom; Negative introspection axiom; Epistemic logic; Epistemic Modal Logic
Epistemic modal logic is a subfield of modal logic that is concerned with reasoning about knowledge. While epistemology has a long philosophical tradition dating back to Ancient Greece, epistemic logic is a much more recent development with applications in many fields, including philosophy, theoretical computer science, artificial intelligence, economics and linguistics.

Wikipédia

Modal logic

Modal logic is a collection of formal systems developed to represent statements about necessity and possibility. It plays a major role in philosophy of language, epistemology, metaphysics, and natural language semantics. Modal logics extend other systems by adding unary operators {\displaystyle \Diamond } and {\displaystyle \Box } , representing possibility and necessity respectively. For instance the modal formula P {\displaystyle \Diamond P} can be read as "possibly P {\displaystyle P} " while P {\displaystyle \Box P} can be read as "necessarily P {\displaystyle P} ". Modal logics can be used to represent different phenomena depending on what kind of necessity and possibility is under consideration. When {\displaystyle \Box } is used to represent epistemic necessity, P {\displaystyle \Box P} states that P {\displaystyle P} is epistemically necessary, or in other words that it is known. When {\displaystyle \Box } is used to represent deontic necessity, P {\displaystyle \Box P} states that P {\displaystyle P} is a moral or legal obligation.

In the standard relational semantics for modal logic, formulas are assigned truth values relative to a possible world. A formula's truth value at one possible world can depend on the truth values of other formulas at other accessible possible worlds. In particular, P {\displaystyle \Diamond P} is true at a world if P {\displaystyle P} is true at some accessible possible world, while P {\displaystyle \Box P} is true at a world if P {\displaystyle P} is true at every accessible possible world. A variety of proof systems exist which are sound and complete with respect to the semantics one gets by restricting the accessibility relation. For instance, the deontic modal logic D is sound and complete if one requires the accessibility relation to be serial.

While the intuition behind modal logic dates back to antiquity, the first modal axiomatic systems were developed by C. I. Lewis in 1912. The now-standard relational semantics emerged in the mid twentieth century from work by Arthur Prior, Jaakko Hintikka, and Saul Kripke. Recent developments include alternative topological semantics such as neighborhood semantics as well as applications of the relational semantics beyond its original philosophical motivation. Such applications include game theory, moral and legal theory, web design, multiverse-based set theory, and social epistemology.