Tree Tutorial 6: Functional Terms and First Order Theories
6/5/12
Tutorial:
The word 'terms' in logic means 'names' and thus far we have met two kinds of terms: constants (or proper names), and variables.
The word 'terms' in logic means 'names' and thus far we have met two kinds of terms: constants (or proper names), and variables.
To become familiar with the new rules for predicate logic trees with identity.
It is possible to use trees with formulas containing identity. Really there are two different ways to implement it: either there are two new rules, or there is one new rule and a new way of closing a branch from a single formula. Both will be described.
To become familiar with the new rules for predicate logic trees.
There are further rules for predicate logic trees (which we will come to shortly).
You can try material of your own below.
Here are a few hints
To become familiar with the notions of closed and complete trees. To be able to use trees to test for satisfiability and invalidity.
In Tutorial 1, we met the notions of closed and open branches (a closed branch was one containing a formula and also the negation of that formula, an open branch was a branch that was not closed).
[This is a Video, click the Play button to view it..]
To become familiar with the rules for propositional truth trees.
Trees are going to be used to 'picture' the truth conditions or requirements for a formula (then, as the technique is developed, for several formulas at once).
Any easy way to remember the rules is to regard them as having been built from the truth tables.
The truth table for 'and' is
Conjunction
'Trees' are a type of structure within the mathematical theory of graphs.
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