Syntactic Considerations

  • Kenneth A. Bowen
Part of the Synthese Library book series (SYLI, volume 127)


We will adopt a good deal (but not all) of the notations and conventions of Shoenfield (1967) used for classical predicate logic. In particular, some of our metavariables are as follows: u, v, … for expressions, A, B, C, … for formulas, a, b, c, … for terms, and x, y, z, … for variables. We will use (1.1)
$${A_{{x_1}}} \ldots {x_n}\left[ {{a_1}, \ldots {a_n}} \right]$$
to indicate the result of simultaneously substituting the terms a 1,…, a n for the variables x 1,…, x n , respectively, where for i = 1, …, n, a i is free for x i. If the free variables of A are x 1,…, x n in alphabetic order (as given below), then A[a 1,…, a n ] is an abbreviation of (1.1).


Modal Logic Predicate Symbol Modus Ponens Modal Language Rule Schema 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer Science+Business Media Dordrecht 1979

Authors and Affiliations

  • Kenneth A. Bowen
    • 1
  1. 1.Syracuse UniversityUSA

Personalised recommendations