Suppose I reasoned thus: The killer is either in the attic or the basement. 4. To do this, the proof has to be set up in a certain way. Hi y’all! C _________________, #4 In this case, our left disjunct in premise 1 is itself a negation, while premise 2 is simply a negation of that left disjunct. For example, consider the following argument: 1. C _________________ Conjunction has the following form: What this rule says, in words, is that if you have asserted two different propositions, then you are entitled to assert the conjunction of those two propositions. A _________________ What might not be as obvious is the form that this argument has. That is, line 1 is a conjunction (since the dot is the main operator of the sentence) and line 2 is inferring one of the conjuncts of that conjunction in line 1. Start studying Logic - 8 Rules of Inference. Thus, the obvious inferences ultimately justify the non-obvious inference being made in the argument. That is a disjunctive syllogism. Change ), You are commenting using your Twitter account. Today, we’re gonna look at the 8 basic rules and then we’ll look at the replacement rules and more. 5. H _________________ Can you fill in the blanks with the phrases that would make this argument valid? Although you cannot construct a proof to show that an argument is invalid, you can construct proofs to show that an argument is valid. K _________________ As before, the conclusion we are trying to derive is denoted by the “therefore” sign, “∴”.) Once you think about it, this inference should be pretty obvious. It derives a conclusion from a given fact or premise. 2. A proof is a series of statements, starting with the premises and ending with the conclusion, where each additional statement after the premises is derived from some previous line(s) of the proof using one of the valid forms of inference. 8-26-2018 Rules of Inference and Logic Proofs A proof is an argument from hypotheses (assumptions) to a conclusion.Each step of the argument follows the laws of logic. I love this stuff because it’s very procedural and the proofs they give for you to solve are like puzzles and puzzles are super fun. ~D _________________ Have questions or comments? Notice that the last line of the proof is the conclusion that we are supposed to derive and that each statement that I have derived (i.e., lines 4 and 5) has a rule to the right. 3. We can use modus tollens to complete the proof we started above: 1. The first premise asserts a statement (which in this case is complex—a disjunction) and the conclusion is a disjunction of that statement and some other statement. 3. This is the rule that I introduced in the first section of this chapter. A _________________ 6. Simplification is a prime example of one of the more obvious rules. Note: the conclusion is written to the right of the last premise, following the “/∴“ symbols. The first premise is a disjunction. However, every form of inference that we will introduce in this section should be obvious—that is the point of calling them basic forms of inference. ~R _______________ Rule of Inference. On to the next page! A v B 3. We will start with the rule called “simplification,” which has the following form: What this rule says, in words, is that if we have asserted a conjunction then we are entitled to infer either one of the conjuncts. However, once you understand the conditions under which a disjunction is true, then it should be obvious why this form of inference is valid. ( Log Out /  3. Here’s the simple justification of the rule. 4. ~B _________________ is a valid inference because it has the same form as disjunctive syllogism. ~D ⋅ ~B In the next section I will walk you through some basic proofs that utilize these 8 rules.