is the set of primitive propositions.
A proposition is a subset of strings of symbols from the alphabet .
The language (or ) is the set of propositions
is the set of propositions of length .
``not '' | ||
``p or q'' | ||
``p and q'' |
A valuation is a function. .
If valuations have for all then .
Given there exists a valuation such that for all .
If , is true in . is a model of .
Draw a truth table, also note that if then and .
If , and for all means then entails or semantically implies ( ). That is, every model of is a model of .
John Fremlin 2010-02-17