Rules of Inference PDF

RULES OF INFERENCE Learning Content Unit 10 (RULES OF INFERENCE An assertion that a given set of proposition P P P., called premises, yields argument or an inference. Such argument can be written as (p, ADA Ap.) 7 thas a consequence) another proposition q, called the conclusion is described as a...

RULES OF INFERENCE Learning Content Unit 10 (RULES OF INFERENCE An assertion that a given set of proposition P P P., called premises, yields argument or an inference. Such argument can be written as (p, ADA Ap.) 7 thas a consequence) another proposition q, called the conclusion is described as an or P Pa Po q Premises Argument or Inference Conclusion The notion of a "logical argument" or "valid argument" is formalized as follows. Definition. An argument (P,A PA... APn) q is said to be valid if q is true whenever all the premises P1, P2, Pn are true. An argument which is not valid is called a fallacy. The following rules of inference can help us to prove the validity of arguments. 1.) Simplification (SP) From a conjunction, we can infer one of the conjuncts. PɅq/p orp Aq/q 2.) Conjunction (CJ) We can infer the conjunction of any given individual statements, for the conjunction of the statements is true. P q/p Aq 3) Addition (AD) To any given statement, we can add any statement whatsoever the disjunction. 41 Absorption (AB) p/pvq A statement may be conjoined to both sides of an implication pq/ (PAT) (QAT) We can also conjoin the antecedent to both sides of the implication. pq/((pp)) (q/p) or pq/p> (p/q) 5.) Disjunctive Syllogism (DS) From a disjunction and a negation of one of its components, we can derive the other component. pvq ~p/q or ~q/p 6.) Modus Ponens (MP) The consequence of a condition can be inferred when conditional statement and its antecedent are asserted. p⇒ q p/q 7) Modus Tollens (MT) We assert the negation of the antecedent if the conditional and the negation of its consequent are given. p⇒q ~q/~p SET THEORY AND LOGIC Unit 10 (RULES OF INFERENCE) Hypothetical Syllogism (HS) From two conditional statements such that the consequent of the first is the antecedent of the second, we infer another conditional whose antecedent is the antecedent of the first and the consequent of the second P⇒q 9) Constructive Dilemma (CD) From a conjunction of two hypothetical statements and a statement that joins the antecedent of the hypothetical, we can infer a disjunction of the consequents. (p = q)^(r =s) pvr/qvs 10) Destructive Dilemma (DD) A disjunction of the negated antecedents may be derived from a conjunction of two hypotheticals and a disjunction of the negation of its consequents. (p⇒ q)^(r=s) ~qV~s/~pV~T