Terminology

Arguments (Lập luận)

• A sequence of propositions

Premises (Tiền đề)

• All propositions but the final one

Conclusion (Kết luận)

• Final proposition

Valid Arguments

• if the truth of premises imply that the conclusion is true

Argument form

• is a sequence of compound propositions involving propositional variables.
• An argument form is valid if no matter which particular propositions are substituted for the propositional variables in its premises, the conclusion is true if the premises are all true.

Rules of Inference for Propositional Logic

Fallacies

• These fallacies resemble rules of inference, but are based on contingencies rather than tautologies
• Fallacy of denying the hypothesis

$$((p\to q)\wedge \neg p)\to \neg q$$

• Fallacy of affirming the conclusion

$$((p\to q)\wedge q)\to p$$

Rules of Inference for Quantified Statements

Combining Rules of Inference for Propositions and Quantified Statements

• Universal modus ponens

• Universal modus tollens