1. NEWELL & SIMON All sciences characterize the essential nature of the systems they study. These characteristics are invariably qualitative in nature, for they set the terms with which more detailed knowledge can be developed… The study of logic and computers has revealed to us that intelligence resides in physical symbol system. This is computer science’s most basic law of qualitative structure. Symbol systems are collections of patterns and processes, the latter being capable of producing, destroying and modifying the former. The most important property of patterns is that they can designate objects, processes or other patterns and that when they designate processes they can be interpreted… A second law of qualitative structure for artificial intelligence is that symbol systems solve problems by generating potential solutions and testing them – that is by searching. Solutions are usually sought by creating symbolic expressions and modifying them sequentially until they satisfy the conditions for a solution. ACM Turing Award Lecture (1976)

2. Physical Symbol System Hypothesis Intelligent activity, in either human or machine, is achieved through the use of: 1. Symbol patterns to represent significant aspects of a problem domain 2.Operations on these patterns to generate potential solutions to problems 3.Search to select a solution from among these possibilities

3. Predicate Calculus Predicate Calculus Symbols: The alphabet that makes up the symbols of the predicate calculus consists of: 1.The set of letter, both upper- and lowercase of the English alphabet 2.The set of digits 0,1,…,9 3.The underscore, _. P: “it rained on Wednesday” P:”weather (wednesday, rain) Variable: X Weather(X, rain)

4. Predicate Calculus Symbols and terms: Predicate calculus symbols include: 1.Truth symbols, true or false 2.Constant symbols are symbol expressions having the first character lowercase 3.Variable symbols are symbol expressions beginning with an uppercase character 4.Function symbols are symbol expressions having the first character lowercase

5. Predicate Calculus Propositional Calculus Symbols: Symbols of: P, Q, R, … Truth symbols: true, false Connectives: ^, , ¬, ,  Propositional Calculus Sentences: Every propositional symbol and truth symbol: true, P, Q, … The negation of a sentence: ¬P, ¬false The conjunction, or and of two sentences: P^ ¬P The disjunction, or or of two sentences: P  ¬P The implication of one sentence for another: P  Q The equivalence of two sentences: P  Q  R

6. Truth Tables Truth table lists all possible truth value assignments to the atomic proposition of an expression and gives the truth value of the expression for each assignment. Truth table enumerates all possible worlds of interpretation. ¬(¬P) = P (P  Q) = (¬P  Q) The contra positive law: (P  Q) = (¬Q  ¬P) De Morgan’s law: ¬(P  Q) = (¬P^¬Q) Commutative law: (P^Q) = (Q^ P) Distributive law: P^(Q  R) = (P^Q)  (P^R) PQP ^Q TTT TFF FTF FFF

7. Examples John loves none but Mary ¬  Y (loves(John, Mary) ^ loves(John,Y) ^(Y  Mary) ¬  Y (loves(John, Y)) ^ (¬ Y=Mary)  Y ¬loves(John,Y)  Y=Mary  Y ¬loves(John,Y)  Y=Mary Everybody loves exactly one person  X  Y loves(X,Y) ^ (  Z loves(X,Z)  Y=Z)  X  Y  (  Z loves(X,Z)  Y=Z) There are at least two (different) X such that A(X)  X  Y (X  Y ^ A(X) ^ A(Y)) There is exactly one X such that A(X)  X A(X) ^ (A(Y)  Y=X)  X  Y (A(Y)  Y=X A(Y)  Y=X ^ Y=X  A(Y)

8. Examples He who is late is to be punished  X isLate(X)  punished(X) Boys who are late are to be punished  Y (isLate(Y) ^ isBoy(Y)  punished(Y) Everyone here is older than everyone there  X,Y (isHere(X) ^ isThere(Y))  olderThan(X,Y)  X isHere(X)  ¬ (  Y isThere(Y) ^ olderThan(Y,X)  Y ¬ isThere(Y)  ¬olderThan(Y,X)  Y isThere(Y)  olderThan(Y,X) Everyone admires himself  X human(X)  admire(X,X) John loves Mary but Mary loves someone else Loves(John,Mary) ^  Y loves(Mary,Y) ^ (Y  John)

9. Examples Example of the use of predicate calculus to describe a simple world. The domain of discourse is a set of family relationships in a biblical genealogy: mother (eve,abel) = Eve is the mother of Abel mother(eve,cain) = … father(adam, abel) = … father(adam,cain) = … In this example we use the predicates mother and father to define a set of parent – child relationships. The implication give general definitions of other relationships  inference rules! parent(X,Y) ^ parent(X,Z)  sibling(Y,Z) Y  Z parent(X,Y)  father(X,Y)  mother(X,Y)

10. Examples If Jones envies Smith or vice versa but they do not envy each other, then Jones envies Smith, if and only if Smith does not envy Jones. 1.((Jones envies Smith)  (Smith envies Jones)) ^ 2.¬ ((Jones envies Smith) ^ (Smith envies Jones))  3.(Jones envies Smith)  4.¬ (Smith envies Jones) (A  B) ^ (¬ (A^B)  (A  ¬ B) (A  B)^(¬(¬(A^B)  (A  ¬ B) TTTFFTTTTTFF TTFTTTFFTTTT FTTTTFFTTFTF FFFFTFFFTFFT

11. A Logic-Based Financial Advisor The function of the advisor is to help a user decide whether to invest in a savings account or the stock market. Some investors may want to to split their money between the two. The investment that will be recommended for individual investors depends on their income and the current amount they have saved according to the following criteria: 1.Individuals with an inadequate savings account should always make increasing the amount saved their first priority, regardless of their income. 2.Individuals with an adequate savings account and an adequate income should consider a riskier but potentially more profitable investment in the stock market. 3.Individuals with a lower income who already have an adequate savings account may want to consider splitting their surplus income between savings and stocks, to increase the cushion in savings while attempting to increase their income through stocks The adequacy of both savings and income is determined by the number of dependents an individual must support. Our rule is to have at least $5000 in the bank for each dependent. An adequate income must be a steady income and supply at least $15000 per year plus an additional $4000 for each dependent.

12. Solution First task: Determine the major features savings_account and income (adequate and inadequate arguments): savings_account(adequate) savings_account(inadequate) income(adequate) income(inadequate) investment (stock, savings and combination arguments) Second task: Determine the rules First rule: (1) savings_account(inadequate)  investment(savings) Second rule: (2) savings_account(adequate) ^ income(adequate)  investment(stocks) Third rule: (3) savings_account(adequate) ^ income(inadequate)  investment(combination)

13. Solution (cont.) To determine the minimum adequate savings the function minsavings is defined: (4)  X amountSaved(X) ^  Y (dependents(Y) ^greater(X,minsavings(Y))  savings_account(adequate) (5)  X amountSaved(X) ^  Y (dependents(Y) ^  greater(X,minsavings(Y))  savings_account(inadequate) Where: minsavings(X) = 5000*X and minincome(X) = 15000 + (4000*X) (6)  X earnings(X,steady) ^  Y (dependents(Y) ^greater(X,minincome(Y))  income(adequate) (7)  X earnings(X,steady) ^  Y (dependents(Y) ^  greater(X,minincome(Y))  income(inadequate) (8)  X earnings(X,unsteady)  income(inadequate) In order to perform a consultation, a description of a particular investor is added to this set of predicate calculus sentences using the predicates amountSaved, earnings and dependents. Thus an individual with 3 dependents, $22000 in savings and a steady income of $25000 would be described by:

14. Solution (cont.) amount_saved(22000) earnings(25000, steady) dependents(3) minsavings(3) = 15000 minincome(3) = 27000 Earnings(25000,steady) ^ dependents(3) ^  greater(25000,minincome(3))  income(inadequate) Amount_saved(22000) ^ dependents(3) ^ greater(22000,minsavings(3))  savings_account(adequate) Savings_account(adequate) ^ income (inadequate)  investment(combination) This is the suggested investment for this individual!