A Concise Introduction to Mathematical Logic pp 1-40

Part of the Universitext book series (UTX)

Propositional Logic



Propositional logic, by which we here mean two-valued propositional logic, arises from analyzing connections of given sentences A, B, such as
$$\mathit{A\ and\ B,\quad A\ or\ B,\quad not\ A,\quad if \ A\ then\ B}.$$
These connection operations can be approximately described by two-valued logic. There are other connections that have temporal or local features, for instance, first A then B or here A there B, as well as unary modal operators like it is necessarily true that, whose analysis goes beyond the scope of two-valued logic. These operators are the subject of temporal, modal, or other subdisciplines of many-valued or nonclassical logic. Furthermore, the connections that we began with may have a meaning in other versions of logic that two-valued logic only incompletely captures. This pertains in particular to their meaning in natural or everyday language, where meaning may strongly depend on context.


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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Fachbereich Mathematik und InformatikBerlinGermany

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