一阶逻辑-量词的位置

时间:2018-11-26 09:30:29

标签: logic logical-operators predicate first-order-logic

当用→表示时,是否在含义之前或之后使用量词?

例如语句“每个人都爱国王”(两种不同的语义解释)

  1. 每个人都爱一个国王,这些国王可能彼此不同。 2018-11-26T15:14:32.438+0600 E STORAGE [initandlisten] WiredTiger error (13) [1543223672:438144][32673:0x7fee423e3a40], wiredtiger_open: __posix_open_file, 715: /var/lib/mongodb/WiredTiger.turtle: handle-open: open: Permission denied Raw: [1543223672:438144][32673:0x7fee423e3a40], wiredtiger_open: __posix_open_file, 715: /var/lib/mongodb/WiredTiger.turtle: handle-open: open: Permission denied 2018-11-26T15:14:32.438+0600 E STORAGE [initandlisten] WiredTiger error (13) [1543223672:438429][32673:0x7fee423e3a40], wiredtiger_open: __posix_open_file, 715: /var/lib/mongodb/WiredTiger.turtle: handle-open: open: Permission denied Raw: [1543223672:438429][32673:0x7fee423e3a40], wiredtiger_open: __posix_open_file, 715: /var/lib/mongodb/WiredTiger.turtle: handle-open: open: Permission denied 2018-11-26T15:14:32.438+0600 E STORAGE [initandlisten] WiredTiger error (13) [1543223672:438594][32673:0x7fee423e3a40], wiredtiger_open: __posix_open_file, 715: /var/lib/mongodb/WiredTiger.turtle: handle-open: open: Permission denied Raw: [1543223672:438594][32673:0x7fee423e3a40], wiredtiger_open: __posix_open_file, 715: /var/lib/mongodb/WiredTiger.turtle: handle-open: open: Permission denied 2018-11-26T15:14:32.438+0600 W STORAGE [initandlisten] Failed to start up WiredTiger under any compatibility version. 2018-11-26T15:14:32.438+0600 F STORAGE [initandlisten] Reason: 13: Permission denied 2018-11-26T15:14:32.438+0600 F - [initandlisten] Fatal Assertion 28595 at src/mongo/db/storage/wiredtiger/wiredtiger_kv_engine.cpp 646 2018-11-26T15:14:32.438+0600 F - [initandlisten] ***aborting after fassert() failure
  2. 每个人都爱一个国王。 ∀x IsMan(x) → ∃y (IsKing(y) ∧ Loves(x,y))

对于#1,将其写为∃y, ∀x (IsKing(y) ∧ IsMan(x)) → Loves(x,y)是否正确?

对于#2,∀x, ∃y, (IsMan(x) ∧ IsKing(y)) → Loves(x,y)呢?

1 个答案:

答案 0 :(得分:0)

是的,量词的顺序决定着公式的可满足性/有效性。

一种确定的方法是知道(A → B)(not A or B)是相同的,并且(not (∀x x))(∃x (not x))是相同的。

因此,当您拥有(∃x, ∀y x → y)时,它与(∀x ∃y ((not x) or y))相同。

(∃x, x → ∀y y)不同的地方是((∀x (not x) or (∀y y))