Propositional Calculus I: The Formal Language, Rules of Inference (initial), Application to Some Motivating Problems

Transcription

1 Propositional Calculus I: The Formal Language, Rules of Inference (initial), Application to Some Motivating Problems Selmer Bringsjord Rensselaer AI & Reasoning (RAIR) Lab Department of Cognitive Science Department of Computer Science Lally School of Management & Technology Rensselaer Polytechnic Institute (RPI) Troy, New York USA Intro to Logic 2/1/2018

2 Logistics

3 Logistics

4 Logistics Note: Should now have laptop with you and ready to go with Slate installed but if not, then certainly on Monday Feb 5!

5 Logistics Note: Should now have laptop with you and ready to go with Slate installed but if not, then certainly on Monday Feb 5!

6 Logistics Note: Should now have laptop with you and ready to go with Slate installed but if not, then certainly on Monday Feb 5! And HyperGrader will debut in class on Feb 12, led by Rini.

7 Logistics Note: Should now have laptop with you and ready to go with Slate installed but if not, then certainly on Monday Feb 5! And HyperGrader will debut in class on Feb 12, led by Rini.

8 Logistics Note: Should now have laptop with you and ready to go with Slate installed but if not, then certainly on Monday Feb 5! And HyperGrader will debut in class on Feb 12, led by Rini. Cannot use without valid, registered code!

9 Re the CD

10 Re the CD

11 Re the CD

12 Re the CD Once seal broken, no return. Remember from first class, can opt for Stanford paradigm, with its software instead of LAMA paradigm!

13 Your code for Slate & HyperGrader for the semester:

14 Your code for Slate & HyperGrader for the semester:

15 Save sleeve & CD, snapshot sleeve & archive!!

16 Save sleeve & CD, snapshot sleeve & archive!!

17 What s on the CD?

18 What s on the CD?

19 What s on the CD? Mac OS

20 What s on the CD? Windows Mac OS

21 What s on the CD? textbook Windows Mac OS

22 What s on the CD? textbook Windows Mac OS

23 What s on the CD? textbook Windows Mac OS Complete, sign, pdf to Selmer.Bringsjord@gmail.com

24 Initial Steps

25 Initial Steps Snapshot sleeve with code, and archive.

26 Initial Steps Snapshot sleeve with code, and archive. Copy the folder from CD to your laptop.

27 Initial Steps Snapshot sleeve with code, and archive. Copy the folder from CD to your laptop. Eject CD and bank-vault -save both!

28 Initial Steps Snapshot sleeve with code, and archive. Copy the folder from CD to your laptop. Eject CD and bank-vault -save both! Depending upon whether you re Windows or MacOS, expand the relevant zipped file to obtain Slate.

29 Initial Steps Snapshot sleeve with code, and archive. Copy the folder from CD to your laptop. Eject CD and bank-vault -save both! Depending upon whether you re Windows or MacOS, expand the relevant zipped file to obtain Slate. Open Slate

30 Initial Steps Snapshot sleeve with code, and archive. Copy the folder from CD to your laptop. Eject CD and bank-vault -save both! Depending upon whether you re Windows or MacOS, expand the relevant zipped file to obtain Slate. Open Slate & today I ll explain and show some simple moves in Slate (though of course I ve already shown some moves in class).

31 Propositional Calculus I: The Formal Language, Rules of Inference (initial), Application to Some Motivating Problems Selmer Bringsjord Rensselaer AI & Reasoning (RAIR) Lab Department of Cognitive Science Department of Computer Science Lally School of Management & Technology Rensselaer Polytechnic Institute (RPI) Troy, New York USA Intro to Logic 2/1/2018

32 Note:

33 Note: skipping to ~ p. 34!

34 Note: skipping to ~ p. 34!

35 Note: skipping to ~ p. 34! M. Chi: Self-testers end up being self-made.

36 Note: skipping to ~ p. 34! M. Chi: Self-testers end up being self-made.

37 Note: skipping to ~ p. 34! M. Chi: Self-testers end up being self-made. What category of English sentences does logic focus on?

38 The Formal Language

39 The Formal Language Exercise: Is this language Roger-decidable? Prove it!

40 NYS 1 Revisited Given the statements a b b c a which one of the following statements must also be true? c b c h a none of the above

41 NYS 1 Revisited Given the statements a b b c a which one of the following statements must also be true? c b c h a none of the above

42 Our First Rule of Inference: PC (Entailment) Oracle

43 Our First Rule of Inference: PC (Entailment) Oracle

44 Our First Rule of Inference: PC (Entailment) Oracle

45 The Rules of Inference: PC (Consequence) Oracle

46 The Rules of Inference: PC (Consequence) Oracle

47 The Problem in Slate 14

48 The Problem in Slate 14

49 Given the statements c c a a b b d (d e) NYS 3 Revisited which one of the following statements must also be true? c e h a all of the above

50 Given the statements c c a a b b d (d e) NYS 3 Revisited which one of the following statements must also be true? c e h a all of the above

51 NYS 3 Revisited Given the statements c c a a b Exercise: Show in Slate that each of b d the first four options can be proved (d e) using the PC entailment oracle. which one of the following statements must also be true? c e h a all of the above