A Concise Introduction to Mathematical Logic pp 1-40

Part of the Universitext book series (UTX)

Propositional Logic

Chapter

Abstract

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.

References

  1. KK.
    G. Kreisel, J.-L. Krivine, Elements of Mathematical Logic, North-Holland 1971.Google Scholar
  2. Ra1.
    W. Rautenberg, Klassische und Nichtklassische Aussagenlogik, Vieweg 1979.Google Scholar
  3. Ge.
    G. Gentzen, The Collected Papers of Gerhard Gentzen (editor M. E. Szabo), North-Holland 1969.Google Scholar
  4. RS.
    H. Rasiowa, R. Sikorski, The Mathematics of Metamathematics, Warschau 1963, 3⟨{ rd}⟩ ed. Polish Scientific Publ. 1970.Google Scholar
  5. HeR.
    B. Herrmann, W. Rautenberg, Finite replacement and finite Hilbert-style axiomatizability, Zeitsch. Math. Logik Grundlagen Math. 38 (1982), 327–344.Google Scholar
  6. Kl1.
    S. Kleene, Introduction to Metamathematics, Amsterdam 1952, 2⟨{ nd}⟩ ed. Wolters-Noordhoff 1988.Google Scholar
  7. Ra3.
    _________ , A note on completeness and maximality in propositional logic, Reports on Mathematical Logic 21 (1987), 3–8.Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Fachbereich Mathematik und InformatikBerlinGermany

Personalised recommendations