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Modal poker on tv logic, or intensional logic is the branch of logic that deals with sentences that are qualified by modalities such as can, could, might, may, must, possibly, and necessarily, and others. Any logical system making use of modal operators, such as possibly, or necessarily is thus also called a modal logic. Modal logics are characterized poker on tv by semantic intensionality: non-modal logics all have the feature that the truth value of a complex sentence is determined by the truth values of its sub-sentences. They are thus extensional. In modal logics, by contrast, this does not hold: both "George W. Bush is President

of the United States" and "2 + 2 4" are true, yet "Necessarily, George W. Bush is President of the United States" is false, while "Necessarily, 2 + 2 4" is true.A formal modal logic represents modalities using modal connective operators. The basic set of modal operators are usually given to be $\backslash Box$ and $\backslash Diamond$. In alethic modal logic the $\backslash Box$ represents necessity and the $\backslash Diamond$ possibility. A sentence is

said to be necessary if it could poker on tv not possibly be false;is $\backslash Box\; p$ is equivalent to $\backslash neg\; \backslash Diamond\; \backslash neg\; p$ Necessitation Rule: If p is a theorem of K, then so is $\backslash Box\; p$. $\backslash Box\; p\; \backslash rightarrow\; p$ K is a weak modal logic, however. In particular, it leaves it open that a proposition be necessary but only contingently necessary. That is, it is not a theorem of K that if $\backslash Box\; p$ is true

then $\backslash Box\; \backslash Box\; p$ is true, i.e., that necessary truths are necessarily necessary. This may not be a great defect for K, since these seem like awfully strange poker on tv questions and any attempt to answer them involves us in confusing issues. In any case, different solutions to questions such as these produce different systems of modal logic.The system most commonly used today is modal logic S5, which robustly answers the questions

by adding axioms which make all modal truths necessary: for example, if its possible that p, then its necessarily possible that p, and if its necessary that p its also necessary that its necessary. This has been thought by many to be justified on the grounds that it is the system which is obtained when we demand that every possible world is possible relative to every other world. Nevertheless, other systems of modal logic

have been formulated, in part, because S5 may not be a good fit for every kind of metaphysical poker on tv modality of interest to us. Development of the field of poker on tv modal logic Although Aristotles logic is almost entirely concerned with the theory of the categorical syllogism, his work also contains some extended arguments on points of modal logic and their connection with potentialities and with time. Following on his works, the Scholastics developed the groundwork for a rigorous theory of modal logic, mostly within the context of commentary

on the logic of statements about essence and accident Among the medieval writers, some of the most important works on modal logic can be found in the works of William of Ockham and John Duns Scotus. The contemporary logical analysis of modality can be traced to C. I. Lewiss "A Survey of Symbolic Logic" , in which he developed the logical systems S1-S5. J. C. C. McKinsey used algebraic methods to prove the decidability of Lewis S2 and S4 in 1941.

Saul Kripke developed the relational semantics for modal logics . Vaughan Pratt introduced poker on tv dynamic logic in 1976. Amir Pnueli proposed the use of temporal logic to formalise the behaviour of continually operating concurrent programs in 1977.Temporal logic is closely related to modal logic, as adding modal operators F and P, meaning, respectively, henceforth and hitherto, leads to a system of temporal logic.Flavours of modal logics include: propositional dynamic logic , propositional linear temporal logic , linear temporal logic , computational tree logic , Hennessy-Milner logic, S1-S5, and

T. References 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, . G.E. Hughes and M.J. poker on tv Cresswell, "An Introduction to Modal Logic", Methuen, 1968. J. Jay Zeeman, 1973. Modal Logic. Clarendon Press .See alsoHybrid logicInterpretability logicKripke semanticsExternal links Bibliography of Non-Standard Logics by Peter Suber Advances in Modal Logic AcknowledgementsThis article contains some material originally from the Free On-line Dictionary of Computing which is used with Wikipedia:Foldoc license under the GFDL.LogicModal logic de:Modallogikfr:Logique modalenl:Modale logicaja:様相論理学