1. Data and Knowledge Representation Lecture 1 Qing Zeng, Ph.D.

2. Introduction Instructor, Harvard Medical School Instructor, Harvard Medical School Research Associate, Brigham and Women’s Hospital Research Associate, Brigham and Women’s Hospital

3. My Research Semantic Knowledge-based System Semantic Knowledge-based System Information retrieval Information retrieval Information integration/presentation Information integration/presentation Consumer Information Retrieval Consumer Information Retrieval Flow Cytometry-based Proteomics Flow Cytometry-based Proteomics Share Pathology Information Network Share Pathology Information Network

4. Main Textbook Knowledge Representation: Logical, Philosophical, and Computational Foundations by John F. Sowa Knowledge Representation: Logical, Philosophical, and Computational Foundations by John F. Sowa $74 from Amazon.com $74 from Amazon.com

5. Motivation Representing data and knowledge for computing Representing data and knowledge for computing Develop Develop Maintain Maintain Share Share

6. Medical Data and Knowledge Large variety of data and knowledge Large variety of data and knowledge Many possible representations Many possible representations Implication of representation on computing Implication of representation on computing

7. Example of Medical Data This is a 51-year-old female admitted through the emergency room with syncopal episode with chest pain and also noted to have epigastric discomfort. The patient was admitted and started on Lovenox and nitroglycerin paste. The patient had serial cardiac enzymes and ruled out for myocardial infarction. The patient underwent a dual isotope stress test. There was no evidence of reversible ischemia on the Cardiolite scan. The patient has been ambulated. The patient had a Holter monitor placed but the report is not available at this time. The patient has remained hemodynamically stable. Will discharge.

8. Examples of Medical Knowledge Nitrates are a safe and effective treatment that can be used in patients with angina and left ventricular systolic dysfunction. Nitrates are a safe and effective treatment that can be used in patients with angina and left ventricular systolic dysfunction. On the basis of currently published evidence, amlodipine is the calcium channel antagonist that it is safest to use in patients with heart failure and left ventricular systolic dysfunction. On the basis of currently published evidence, amlodipine is the calcium channel antagonist that it is safest to use in patients with heart failure and left ventricular systolic dysfunction. Coronary artery bypass grafting may be indicated, in some, for relief of angina Coronary artery bypass grafting may be indicated, in some, for relief of angina All patients with heart failure and angina should be referred for specialist assessment. All patients with heart failure and angina should be referred for specialist assessment. Patients with angina and mild to moderately symptomatically severe heart failure that is well controlled, and who have no other contraindications to major surgery, should be considered for coronary artery bypass grafting on prognostic (as well as symptomatic) grounds. Patients with angina and mild to moderately symptomatically severe heart failure that is well controlled, and who have no other contraindications to major surgery, should be considered for coronary artery bypass grafting on prognostic (as well as symptomatic) grounds.

9. Challenge Philosophical difference Philosophical difference Domain difference Domain difference Application difference Application difference Developer difference Developer difference Liability Liability Cost Cost

10. Formalism and Conceptualization Natural Language is the most expressive form of formalism and conceptualization Natural Language is the most expressive form of formalism and conceptualization Conceptualization is an abstract and simplified view of the world Conceptualization is an abstract and simplified view of the world Such simplification allow computer and human alike to communicate in an unambiguous fashion (e.g. “and” vs. “&”) Such simplification allow computer and human alike to communicate in an unambiguous fashion (e.g. “and” vs. “&”)

11. Logic A tool for reasoning A tool for reasoning Provide basic concepts used in many computer science fields (AI, IR, DB, etc..) Provide basic concepts used in many computer science fields (AI, IR, DB, etc..) Used in many medical applications Used in many medical applications

12. Propositional Logic Proposition Proposition Basic operators Basic operators Language Language Truth table Truth table Boolean Algebra Boolean Algebra

13. Proposition A proposition is a symbolic variable whose value must be either True or False, and which stands for a natural language statement which could be either true or false A proposition is a symbolic variable whose value must be either True or False, and which stands for a natural language statement which could be either true or false Examples: Examples: A = Smith has chest pain A = Smith has chest pain B = Smith is depressed B = Smith is depressed C = It is raining C = It is raining

14. Operators Logic And Logic And Inclusive Or Inclusive Or Exclusive Or Exclusive Or Logic Not Logic Not Logical Implication Logical Implication Logical Equivalence Logical Equivalence

15. Logical And Λ AB A Λ B FalseFalseFalse FalseTrueFalse TrueFalseFalse TrueTrueTrue

16. Inclusive Logical Or (V) AB A V B FalseFalseFalse FalseTrueTrue TrueFalseTrue TrueTrueTrue

17. Exclusive Logical Or ( ) AB A B FalseFalseFalse FalseTrueTrue TrueFalseTrue TrueTrueFalse

18. Inclusive vs. Exclusive Natural language “Or” can mean either Natural language “Or” can mean either Either discharge the patient, or admit him Either discharge the patient, or admit him I will to take the medication, or the fever will be worse I will to take the medication, or the fever will be worse Take 2 or 3 pills per day Take 2 or 3 pills per day Exclusive not often used (except in circuit design) Exclusive not often used (except in circuit design)

19. Medical Example “Heart AND Lung disease”: does patients have to have both? Or either? “Heart AND Lung disease”: does patients have to have both? Or either? “ Foot AND mouth disease ” : what does “ AND ” mean in this case? “ Foot AND mouth disease ” : what does “ AND ” mean in this case? Further reading: Mendonca EA, Cimino JJ, Campbell KE, Spackman KA. Evaluation of a proposed method for representing drug terminology. Proc AMIA Symp. 1999;:47-51. Further reading: Mendonca EA, Cimino JJ, Campbell KE, Spackman KA. Evaluation of a proposed method for representing drug terminology. Proc AMIA Symp. 1999;:47-51.

20. Logical Not ( ¬ ) A ¬A¬A¬A¬A FalseTrue TrueFalse

21. Logical Implication ( → ) AB A → B FalseFalseTrue FalseTrueTrue TrueFalseFalse TrueTrueTrue

22. Understanding “→” This is an operator. Although we call it “imply” or “implication”, do not try to understand its semantic from the name. We could have called it “I” and still define its semantic the same way. This is an operator. Although we call it “imply” or “implication”, do not try to understand its semantic from the name. We could have called it “I” and still define its semantic the same way. A →B “means” A is sufficient, but not necessary to make B true. A →B “means” A is sufficient, but not necessary to make B true. E.g. Let A be “having cold” and B be “drink water”, A → B can be interpreted as “should drink water” when “having cold”. However, you can drink water even when you don’t have cold. Thus A → B still is true when A is not true. E.g. Let A be “having cold” and B be “drink water”, A → B can be interpreted as “should drink water” when “having cold”. However, you can drink water even when you don’t have cold. Thus A → B still is true when A is not true.

23. Logical Equivalence ( ↔ ) AB A ↔ B FalseFalseTrue FalseTrueFalse TrueFalseFalse TrueTrueTrue

24. Understanding “→” A →B is different from A=B A →B is different from A=B A: a person is pregnant. B: a person is woman. A: a person is pregnant. B: a person is woman. In this case, A →B is true, A=B is not. In this case, A →B is true, A=B is not. Use formal logic to represent knowledge of the real world, not the other way around. Use formal logic to represent knowledge of the real world, not the other way around.

25. Well-Formed Formulas Formula Formula A term (string) in prepositional logic A term (string) in prepositional logic Well-formed formula (WFF) Well-formed formula (WFF) A term that is constructed correctly according to propositional logic syntax rules A term that is constructed correctly according to propositional logic syntax rules

26. WFF Constants: False, True Constants: False, True Variables: P, Q, R Variables: P, Q, R If a is WFF, ¬ a is WFF If a is WFF, ¬ a is WFF If a and b are WFF, aΛb are WFF If a and b are WFF, aΛb are WFF If a and b are WFF, aνb are WFF If a and b are WFF, aνb are WFF If a and b are WFF, a → b are WFF If a and b are WFF, a → b are WFF If a and b are WFF, a ↔ b are WFF If a and b are WFF, a ↔ b are WFF Any formula that cannot be constructed using these rules are not WFF Any formula that cannot be constructed using these rules are not WFF

27. Precedence of Logical Operators ¬ Λ V → ↔

28. Let Try An Example Order Test A for all male over 70, smokers with family history of cancer, and women with chronic cough and family history of cancer. Otherwise, do not order it. Order Test A for all male over 70, smokers with family history of cancer, and women with chronic cough and family history of cancer. Otherwise, do not order it. Male: a person being male Male: a person being male Old: a person being over 70 Old: a person being over 70 Smoker: a person being a smoker Smoker: a person being a smoker Cough: a person having chronic cough Cough: a person having chronic cough FHC: a person having family history of cancer FHC: a person having family history of cancer OrderA: Order Test A OrderA: Order Test A (Male ۸ Old) V (Smoker ۸ FHC) V (¬Male ۸ Cough ۸ FHC) ↔ OrderA

29. Examples Smokers are those who are currently smoking or had quit smoking for less than 6 months Smokers are those who are currently smoking or had quit smoking for less than 6 months A document is completed only after signed by both the chief resident and the attending physician. A document is completed only after signed by both the chief resident and the attending physician. Smith is depressed whenever it rains Smith is depressed whenever it rains

30. A Few Comments Use parentheses if precedence not clear Use parentheses if precedence not clear Very similar to programming language operators’ precedence Very similar to programming language operators’ precedence Precedence in natural language depend more on context Precedence in natural language depend more on context E.g. “no heart and lung disease” E.g. “no heart and lung disease” E.g. “no family history and healthy life style”. E.g. “no family history and healthy life style”.

31. Truth Table An easy way to evaluate propositions An easy way to evaluate propositions AB A ν B ¬B¬B¬B¬B (A ν B) Λ ¬ B 00010 01100 10111 11100

32. Let Try An Example Order Test A for all male over 70, smokers with family history of cancer, and women with chronic cough and family history of cancer. Other wise, do not order it. Order Test A for all male over 70, smokers with family history of cancer, and women with chronic cough and family history of cancer. Other wise, do not order it. (Male ۸¬Young) V (Smoker ۸ FHC) V (¬Male ۸ Cough ۸ FHC) ↔ OrderA MaleYoung(<=70)SmokerFHCCough Order Test A TTT TTT TTTTFT TTTFTF TTTFFF TTFTTF ……

33. Tautology and Contradiction Male V ¬ Male Male V ¬ Male Tautology: proposition that is always true Tautology: proposition that is always true Healthy Λ ¬ Healthy Healthy Λ ¬ Healthy Contradiction: proposition that is always false Contradiction: proposition that is always false

34. Extra Reading Aho’s book chapter 12 Aho’s book chapter 12 Sowa’s book p1-39 Sowa’s book p1-39

35. Homework