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2003?5?????101????

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�1. ??????

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�3. ??????????

�4. ???????

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�1. ???????Symbolic Logic?

Definition 1.1?Pierce?

????????????????????????????????

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Definition 1.2?Longman???

Symbol=a sign, shape, or object which represents a person, idea, value, etc.

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Definition 1.3?Hjelmslev?

??=???expression?????meaning?

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??=??????

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??????????????????�???????????

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????

�Aristotle?384�322 B.C.????� ??????

�F. Bacon?1561�1626?????

�R. Descartes?1596-1650???????????????????

�Leibniz?1646�1716?Leibniz????????????????????????

�G. Boole?1815�1864????????????????Boolean algebra?

�G. Frege?1848�1925?1879??Begriffsschrift???????????????????????PK?

�G. Peano?1858�1932??????????PA?Peano�s Arithmatic??

�G. Cantor?1845�1918???Set Theory????????????

�B. Russell?1872�1970?????Whitehead??Principia Mathematica?3????????????

�D. Hilbert?1862�1943??????????????????????????

�A. Turing?1913�1954???Turing�s Machine???????????Computation?????

�K. G�del?1906-1978?PK?????? PA???????

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???2000?????TIMES???????20???????the greatest mind?Turing?G�del???????????????

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�2. The 1^st order predicate calculus

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??????

?1?????

?1.1??????individual variables?

?1.1.1?v???

?1.1.2??x????????

?1.1.3????????

?i.e., In BNF?V=v|V??

?1.2??????individual constants?

?1.2.1?c???;

?1.2.2??d????????

?1.2.3???????.

?2?????functions?

?2.1?????f₀?f₁?f₂?�

?2.2?????g₀?g₁?g₂?�

????f???arity?>0?

?3?????predicates?

?3.1?????p₀?p₁?�

?3.2?????q₀?q₁?� ??????????

????p???arity?>0?

?4????propositions?

?4.1?????P₀?P₁?�

?4.2?????T?F

?5?????Connectives???????.

?6????quantifiers?� ?

?7?????????� ?[ ?]?{?}

???????????????????syntax?

??2.1??,term?

?1?????;

?2??f?n????t₁?�?t_n????f?t₁,�,t_n????

?3??????

??2.2?????,atomic formula?

?1?????????

?2??p?n????t₁?�?t_n????p?t₁,�,t_n?????

?3?????????.

??2.3???,formula?

?1?????????

?2??????????;

?3???????????????;

?4??????x???????????;

?5???????

???????????????????sentence??

Frege??????????PK?

PK??????axiom??????rule???????PK?????

???|�????|�???????????????????

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???MP??|�(??????),

PK?????consistent?????complete??

??????????(syntax)??????????semantics??

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�3. ??????????interpretation?

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?1????????????,?????1??, ??

?2??????????????mapping????+ .

?3?????????????????????�=�???�??�.

?4????????????, ??�????�.

?5????T?F?????. PK?2-valued logic?2?????

?6???????it is not the case that??????and????????or?;

????imply??????equivalent?

?7????for all?????for some?

???greaterthan?x,y??,??greaterthan?x,y????x??y???????????x??y?x??y?

??is true or �is not true?.

????????(powerful)???????????expressive power?????B.Russell????????????? ???????????????????????????????????????????????????????????????????????????????????????.?????????1980s???????????? Prolog??????

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�4. ????????Understanding of natural languages in ?

???????????????????????????????????????????????????????limitation??

?1?�� ????????????

?2?�� To be or not to be?????�x?????�???????????????????�????�??????

????????????tense logic???????

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?3????????????????????????

?3.1???p?q???q?p?????????????????????????

?3.2?????????????????????,

�????????�??p???� q????,????p?q????p?q??

?3.3???????????�?�?�???????�?�?�???????????????????????

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?4?????????arity

?????????????�?�?�?3????

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?5???????????????????????????????????Russell???????????????????descriptor ???x.(x)=??????(x)??x.

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?6???????????, ???????????????.

????????????????.� 1960s????Fuzzy Logic?????.

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?7????????????????????????????????????

?7.1????????????,????????.

?7.2????????????????

?7.3?All that glitters is not gold.

?glitter?x?gold?x??

?7.4?????? ?????????,????�?�???????

?7.5??????????????�?�???

?7.6????????????????????????????

�?�?�?�?�?�???

?7.7????????

?7.8????????????

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?8??????????????????????????????

????????A man, a plan, a canal: Panama

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?1??????????2???????3??????4??????????

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