PYB204 Perception & Cognition Lecture Notes PDF

PYB204 Perception & Cognition Problem Solving Reasoning Decision Making CRICOS No.00213J In this unit: Psychophysics Sensation Vision Hearing Pattern recognition P...

PYB204 Perception & Cognition Problem Solving Reasoning Decision Making CRICOS No.00213J In this unit: Psychophysics Sensation Vision Hearing Pattern recognition Perception Space and motion perception Mental imagery Attention and performance Memory Cognition Problem solving Reasoning and decision making Language Navigation Problem solving, reasoning, & decision making Problem solving Problem space and search Operator acquisition and selection Problem representation Reasoning and decision making Reasoning about conditionals Reasoning about probabilities Decision making with subjective utility Problem solving Patient PF (Goel & Grafman, 2000) His right anterior prefrontal cortex was damaged due to a stroke Successful architect before the stroke He seemed perfectly normal and intelligent However, he lost his ability in architectural design Köhler’s (1917) studies Anderson (2020) Problem solving, reasoning, & decision making Problem solving Problem space and search Operator acquisition and selection Problem representation Reasoning and decision making Reasoning about conditionals Reasoning about probabilities Decision making with subjective utility Problem space and search 2 8 3 1 2 3 1 6 4 8 4 7 5 7 6 5 Problem space and search Problem space Consists of various states of the problem Problem state A representation of the problem in some degree of solution problem space start state goal state intermediate states Problem space and search Operator An action that will transform the problem state into another problem state operators start state goal state Problem space and search Problem solving = searching a sequence of states in a problem space that goes from the start state to the goal state Two important questions: What determines the operators available to the problem solver? This defines the problem space How does the problem solver select a particular operator? This determines the path the problem solver will take Problem solving, reasoning, & decision making Problem solving Problem space and search Operator acquisition and selection Problem representation Reasoning and decision making Reasoning about conditionals Reasoning about probabilities Decision making with subjective utility Acquisition of operators Three ways to acquire new operators Discovery Direct instruction Analogy/imitation Thorndike’s (1898) puzzle box Operator selection Three criteria for selecting operators: 1. Backup avoidance 2. Difference reduction 3. Means-ends analysis Operator selection Backup avoidance The tendency in problem solving to avoid operators that take one back to a state already visited Difference reduction The tendency in problem solving to select operators that eliminate a difference between the current state and the goal state It is a useful method, but not always optimal It only considers whether the next step is an improvement and not whether the larger plan will work Start Goal 2 1 6 2 1 6 1 2 3 4 8 4 8 8 4 7 5 3 7 5 3 7 6 5 Operator selection Means-ends analysis: creates a new subgoal to enable an operator to apply An operator is not abandoned even if it cannot be applied immediately identifies the biggest difference between the current state and the goal state and try to eliminate it first Tower of Hanoi problem Animation created by André Karwath, licensed under the Creative Commons Attribution-Share Alike 2.5 Generic license. No change is made. Operator selection Difference reduction doesn’t allow you to solve the Tower of Hanoi problem People tend to adopt the difference reduction strategy first and then start using means-ends analysis when they try to solve the Tower of Hanoi problem (Kotovsky et al., 1985) Patients with prefrontal damage often have difficulty in making backward moves in the Tower of Hanoi problem (Goel & Grafman, 1995) They cannot maintain the goal in working memory very well Problem solving, reasoning, & decision making Problem solving Problem space and search Operator acquisition and selection Problem representation Reasoning and decision making Reasoning about conditionals Reasoning about probabilities Decision making with subjective utility Problem representation How states of a problem are represented has significant effects Successful problem solving depends on representing problems in a way appropriate operators can be applied e.g., mutilated-checkerboard problem Cover the 62 remaining squares using 31 dominos. Each domino covers two adjacent squares Or prove logically why such a covering is impossible Anderson (2020) Problem representation Incubation effects The phenomenon that sometimes solutions to a particular problem come easier after a period of time in which one has ignored trying to solve the problem e.g., Silveira’s (1971) cheap-necklace problem You are given chains 1–4 Opening a link: 2¢; closing it: 3¢ Join all chains into a circle at a cost of 15¢ or less Problem representation Three groups of participants (they all worked on the problem for 30 min) Control: continuous 30 min 55% Group 1: interrupted by 30-min of other activities 64% Group 2: interrupted by a 4-hour break 85% Incubation effects occur because people forget inappropriate ways of solving problems Problem solving, reasoning, & decision making Problem solving Problem space and search Operator acquisition and selection Problem representation Reasoning and decision making Reasoning about conditionals Reasoning about probabilities Decision making with subjective utility Reasoning and decision making Faced with logical problems, people often come to conclusions that are judged as incorrect from the perspective of formal logic and mathematics On the other hand, computer systems that are based on formal logic make so many silly mistakes that humans never make Four areas where human irrationality is often found: Reasoning about conditionals Reasoning about quantifiers Reasoning about probabilities Decision making Reasoning and decision making Faced with logical problems, people often come to conclusions that are judged as incorrect from the perspective of formal logic and mathematics On the other hand, computer systems that are based on formal logic make so many silly mistakes that humans never make Four areas where human irrationality is often found: Reasoning about conditionals Reasoning about quantifiers Reasoning about probabilities Decision making Reasoning about conditionals Conditional statement If A, then B An assertion that if an antecedent (A) is true, then a consequent (B) must be true Wason selection task If a card has a vowel on one side, then it has an even number on the other side. E K 4 7 E K 4 7 2 3 90% E K 4 7 A 60% Wason selection task If a card has a vowel on the one side, then it has an even number on the other side. In other words, neither a vowel nor a consonant on the other side of 4 will falsify the rule. E K 4 7 S E K 4 7 25% O T Wason selection task E K 4 7 90% 15% 60% 25% Only 10% of participants made the right combination of choices (i.e., E and 7) Oaksford & Chater (1994) Wason selection task When presented with neutral material, people have particular difficulty in recognising the importance of exploring the negation of the consequent E K 4 7 90% 15% 60% 25% Permission schema Performance on the selection task can be enhanced when the material has meaningful content Griggs and Cox (1982) “If a person is drinking a beer, then the person must be over 19.” 74% of participants selected the logically correct combination What a person is drinking The person’s age beer soda 22 16 Permission schema Griggs and Cox’s task: 74% If a person is drinking a beer, then the person must be over 19. beer soda 22 16 Wason’s task (e.g., Oaksford & Chater, 1994): 10% If a card has a vowel on the one side, then it has an even number on the other side. E K 4 7 Permission schema Permission schema When the conditional statement is interpreted as a rule about what should be the case, performance on the Wason’s selection task tends to be enhanced Probabilistic interpretation Why do we perform so poorly on the Wason selection task? People tend to select cards that will be informative under a probabilistic model, not a strict logical model If A, then B ® B will probably occur when A occurs Probabilistic interpretation Oaksford and Chater (1994) “If a car has a broken headlight, it will have a broken taillight.” Photo by Laitr Keiows, licensed under CC BY 3.0. No change is made. Probabilistic interpretation Which cars in the car park would you check? If a car has a broken headlight, it will have a broken taillight. Four choices: Cars with broken headlights Cars without broken headlights Cars with broken taillights Cars without broken taillights Logically correct choices Probabilistic interpretation Finding cars that have broken headlights would be reasonable There wouldn’t be many of them anyway If you find one, it is necessary to check its taillight However, do you really want to check all cars that have intact taillights? Photo by Laitr Keiows, licensed under CC BY 3.0. No change is made. Probabilistic interpretation Cars with broken headlights/taillights are very rare Thus, if you find a car with a broken taillight, checking it to see whether it also has a broken headlight helps you make reasonable inference It is not logical, but informative choice We tend to interpret conditional statements on the basis of a probabilistic model, not a strict logical model because doing so actually makes sense in many situations in real life This might be one reason why making the correct (=logical) choice in the original Wason’s selection task is so difficult Problem solving, reasoning, & decision making Problem solving Problem space and search Operator acquisition and selection Problem representation Reasoning and decision making Reasoning about conditionals Reasoning about probabilities Decision making with subjective utility Reasoning about probabilities p = 25% Reasoning about probabilities The smiley is always in one of the two yellow boxes p = 50% Reasoning about probabilities The smiley is in one of the two yellow boxes most of the time 25% < p < 50% Reasoning about probabilities The smiley was always in one of the two yellow boxes! p < 50% Reasoning about probabilities Prior probability The probability that a statement is true before consideration of the evidence Posterior probability The probability that the statement is true after consideration of the evidence To calculate the posterior probability, you need to take into account: Prior probability (base rate) Evidence How reliable the evidence is Bayes’s theorem computes the posterior probability Reasoning about probabilities Base-rate neglect People often fail to take base rates into account in making probability judgments Hammerton (1973) Suppose you take a diagnostic test for a rare form of cancer Only 1 in 10,000 people has this cancer This cancer results in a positive test 95% of the time If a person does not have the cancer, the probability of a positive result is 5% If you get a positive result, how do you feel about it? Reasoning about probabilities Many people feel that the positive result means their chance of actually having the cancer is 95% However, the fact that this type of cancer is very rare (0.01%) is not taken into account The actual probability of having this cancer (given the positive result) is only 0.19% Reasoning about probabilities Judgements of probability/frequency We can be biased in our estimates of probabilities when we must rely on factors such as memory and similarity judgements Tversky and Kahneman (1974) Participants estimated the proportion of English words: that begin with k (e.g., kettle) with k in the third position (e.g., make) They estimated that more words begin with k than have k in the third position However, three times as many words have k in the third position as begin with k Problem solving, reasoning, & decision making Problem solving Problem space and search Operator acquisition and selection Problem representation Reasoning and decision making Reasoning about conditionals Reasoning about probabilities Decision making with subjective utility Decision making Which one would you choose? $8 with probability = 1/3 $8 x 1/3 = $2.67 $3 with probability = 5/6 $3 x 5/6 = $2.50 1 million dollars with probability = 1 1 million $ x 1 = 1 million $ 2.5 million dollars with probability = 1/2 2.5 million $ x 1/2 = 1.25 million $ Decision making Subjective utility The subjective value someone places on something It usually forms a non-linear function Which one would you choose? 1 million dollars with probability = 1 Ux1=U 2.5 million dollars with probability = 1/2 1.2U x 1/2 = 0.6U Decision making The subjective value tends to decrease more steeply in negative direction Which one would you choose? No gain/loss with probability = 1 0x1=0 +1 million dollars with probability = 1/2, or −1 million dollars with probability = 1/2 (1 million $ x 1/2) + (−1 million $ x 1/2) = 0 Decision making People make decisions under uncertainty in terms of subjective utilities and subjective probabilities References All references are from the Anderson text. Some images were taken from earlier editions of the book.