
 Andrews. To Truth through Proof. (Site not responding. Last check: ) 
  Truth table semantics are given (as functions from propositional variables to the set {T,F}), along with the definitions of tautology [=valid in this context], contradiction, and satisfaction. 
  An interpretation is a frame and a function mapping constants of Q0 to the appropriate domains, taking each Q to the appropriate identity relation (as a Curried characteristic function, of course), and taking the description operator to some map from sets of individuals to individuals that takes singletons to their unique element. 
  Representability (of naturals, functions on naturals, and relations on naturals) is defined (as the existence of a closed formula such that Q0inf proves it satisfies the appropriate equations on numerals to represent the function or relation). 
 www.andrew.cmu.edu /user/cebrown/notes/tttp.html (6301 words) 
