lect21 - INTRO LOGIC DAY 21 1 UNIT 4 Derivations in...

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1 1 INTRO LOGIC DAY 21 2 UNIT 4 Derivations in Predicate Logic
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2 3 Overview Exam 1: Sentential Logic Translations (+) Exam 2: Sentential Logic Derivations Exam 3: Predicate Logic Translations Exam 4: Predicate Logic Derivations Exam 5: (finals week) very similar to Exam 3 Exam 6: (finals week) very similar to Exam 4 9 9 9 + + + Exams 5 and 6 are scheduled for Thursday Dec 15 8:00 a.m. Mahar Auditorium 4 Predicate Logic Subsumes Sentential Logic Every rule of Sentential Logic is also a rule of Predicate Logic. ± CD ± ± D ± ± O ± ± O ± etc. Every strategy of Sentential Logic is also a strategy of Predicate Logic. ± ² : G ± I ± ² : ±G ± ² : G ± H ± ² : G & H ± etc.
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3 5 (7) (6) (5) (4) (3) (2) (1) SL-Example 1 if everyone is un-H, then no one is H 4, ??? 2, ??? DD ± : È As ± xHx ± D ± : ± ± xHx As ² x ± Hx CD ± : ² x ± Hx ² ± ± xHx (8) Æ ??, Æ I ² O ± O 6 (4) (3) (2) (1) SL-Example 2 if not everyone is H, then someone is not H ??? ? ± D? ± : ± x ± Hx As ± ² xHx CD ± : ± ² xHx ² ± x ± Hx 2, ± ² O
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4 7 (7) (6) (5) (4) (3) (2) (1) SL-Example 3 if no one is H , then k is not H ??? } : È Hk } : ± Hk ± ± xHx } : ± ± xHx ± ± Hk Æ 2, DD As ± D As CD ??, Æ I ± ± O 8 (10) (9) (8) (7) (6) (5) (4) (3) (2) (1) SL-Example 4 if someone is F or H, then someone is F or someone is H 7, ???
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lect21 - INTRO LOGIC DAY 21 1 UNIT 4 Derivations in...

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