任何一本談謂詞邏輯的書均有量詞轉(zhuǎn)化法則!
(1)(∃x)(P(x)∧(∀y)(R(x,y)→L(x,y)))P(P規(guī)則)
(2) P(a)∧(∀y)(R(a,y)→L(a,y)) T(T規(guī)則) (1)ES(存在指定規(guī)則)
(3)P(a)T(2)
(4) (∀y)(R(a,y)→L(a,y)) T(2)
(5) (∀x)(P(x)→(∀y)(Q(y)→┐L(x,y)))P
(6) (P(a)→(∀y)(Q(y)→┐L(a,y)))T(5) US(全稱指定規(guī)則)
(7) (∀y)(Q(y)→┐L(a,y)))T(3)(6)
(8) (R(a,b)→L(a,b)) T(4) US
(9) (Q(b)→┐L(a,b))) T(7) US
(10)L(a,b)→┐Q(b) T(9)
(11)R(a,b)→┐Q(b)T(8) (10)
(12)┐R(a,b)∨┐Q(b) T(11)
(13) (∃y)┐(R(y,b)∧Q(b))T(12) EG(存在推廣規(guī)則)
(14) (∀x)(∃y) ( ┐(R(y,x)∧Q(x)))T(13) UG(全稱推廣規(guī)則)
(15) ┐(∃x)(∀y)(R(y,x)∧Q(x)) T(14)