## Systems Of Reasoning (S1E03) : Semantics, consistency and soundness.

I am going to make this blogpost a bit different. I am going to make it a bit “fun”, and less proof/theorem.

Any propositional variables can be assigned a truth () or falsehood () value through a mapping . Where is a set of all propositional variables. We can show that it’s more general than this, i.e. can be a set that contains all eff

—– HOW?—-

The values can be retrieved through , where we have

- for some propositional variable
- for some wff .
- for some wffs .

**Facts**

- For some wff , we write and say that is a tautology if for any assignment () I make to the internal statements. That is to say that evaluates to true probably because of its structure and not its content.
- If a wff always evaluates to F, then we say is a contradiction.
- implies iff
- is equivalent to iff is a tautology.