Formal Logic

1. Formal Logic CSC 333

2. How about some examples? • Look at Exercises 1.1.

3. Propositional Logic • A valid argument is composed of hypotheses (given statements) and a conclusion. • Note examples 9 and 10. • If the conclusion inevitably follows from the hypotheses, this form of argument is called modus ponens.

4. Proof Sequence • To prove that a conclusion Q is valid based on a set of hypotheses, we start with the hypotheses, • Then we apply a derivation rule (what’s that?). • A way to “manipulate wffs in a truth-preserving manner” by substituting an equivalency for a hypothesis. • Example: Q v P  P v Q

5. Inference Rules • See Table 1.13 • Note modus ponens. • These rules are almost self-evident. • Try Practice 10, p. 26. A next step, anyone? • Read Example 14 as a good example of derivation rules.

6. Some Heuristics • Trial and error. • Blind alleys happen! • There often is more than one way to arrive at a correct proof sequence • Try to use modus ponens often. • Convert wffs of the form (P ^ Q)’ , (P v Q)’, P v Q to more useful forms (hints, p. 27). • Experience helps!

7. More good stuff . . . • The deduction method • Hypothetical syllogism • Additional rules proved by using rules known to be true. • See Table 1.14.

8. Mentioned last time . . . • Notable terms: • Modus ponens • Modus tollens • Valid argument • Equivalence rules • De Morgan’s laws • Hypothetical syllogism • Quantifiers

9. Quantifier? • For all . . . • There exists . . .