Alfred Tarski was the first mathematician to give a formal definition of what it means for a formula to be “true” in a structure. To do this, we need to provide a meaning to terms, and truth-values to the formulas. In doing this, free variables cause a problem : what value are they going to have ? One possible answer is to supply temporary values for the free variables, and define our notions in terms of these temporary values.
Now we are set to define satisfaction. Again we have to take care of free variables by assigning temporary values to them via a function . We define the relation by induction on the construction of formulas :
In case for some of , we have , we say that models, or is a model of, or satisfies . If has the free variables , and , we also write or instead of . In case is a sentence (formula with no free variables), we write .
|Date of creation||2013-03-22 12:43:56|
|Last modified on||2013-03-22 12:43:56|
|Last modified by||CWoo (3771)|