********************** * INFERENCE RULES * ********************** : is therefore; 'v' is OR; ~ is NOT; ^ is AND; -> is implication ------------------------------------------------------------------------ CONJUNCTION p ABSORPTION p -> q q --------------- -- : p -> (p ^ q) : p^q -------------------------------------------------------------------------- MODUS p -> q MODUS p -> q PONENS p TOLLENS ~q ------ ------- : q : ~p -------------------------------------------------------------------------- HYPOTHETICAL p->q DISJUNCTIVE p v q SYLLOGISM q->r SYLLOGISM ~ p ---- ------ : p->r : q -------------------------------------------------------------------------- SIMPLIFICATION p ADDITION p q --- ------- : p : p v q -------------------------------------------------------------------------- CONSTRUCTIVE (p->q) ^ (r->s) RESOLUTION p v q DILEMMA p v r ~p v r -------------- ------- : q v s : q v r -------------------------------------------------------------------------- FALLACY OF p->q FALLACY OF p->q AFFIRMING THE q DENYING THE ~p CONSEQUENCE ----- ANTECEDENT ------ : p : ~q -------------------------------------------------------------------------- RULES FOR QUANTIFIED STATEMENTS, for Universe U and c and x in U Universal Instantiation Ax P(x) ------- : P(c) for an arbitrary c -------------------------------------------------------------------------- Universal Generalization P(c) for an arbitrary c --------- : Ax P(x) -------------------------------------------------------------------------- Existential Instantiation Ex P(x) ------- : P(c) for a particular c -------------------------------------------------------------------------- Existential Generalization P(c) for a particular c --------- : Ex P(x)