Consistent Formula

A collection of formulas is consistent if there is a Boolean valuation in which all the formulas are T

To do a consistency check, we can check that:

1. The conjunction of the formulas is satisfiable
2. there is a Boolean valuation that maps each formula in the set to T
3. there is a Boolean valuation that maps the conjunction of the formulas to T
4. the conjunction of the formulas is not a contradiction

We use the Semantic Tableaux usually to prove that a set of formulas is inconsistent.

Proving Consistent/Inconsistent with Semantic Tableaux

• To prove that an argument is inconsistent, just list out the premises and close the branches.

1. premise
2. premise

• To prove that a Valid Argument:

1. premise
2. premise
3. negation of the conclusion