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Conditional Reasoning

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Everyday situations require us to reason. We receive & seek information ... Every time I eat haddock then I drink gin' No facilitation on Towns & Transport ... – PowerPoint PPT presentation

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Title: Conditional Reasoning


1
Conditional Reasoning
  • Kevin Paterson
  • k.b.paterson_at_derby.ac.uk

2
Topics
  • nature of conditional reasoning
  • inference made with conditionals
  • Wason Selection Task and different effects with
    abstract thematic content
  • different theories that account for performance
    on the selection task

3
Why is reasoning interesting?!
  • Everyday situations require us to reason.
  • We receive seek information that affects
    immediate thoughts, actions, plans, decisions,
    and so on.
  • How this information affects our thinking or
    behaviour depends on nature of the information
    the information we have stored in our memories.
  • Reasoning is means by which we make use of this
    information draw conclusions or inferences from
    it.
  • Rreasoning is fundamental to intelligence.

4
Deductive versus inductive reasoning
  • Can distinguish between two types of reasoning
  • Inductive - conclusions that are probably true
    given the evidence
  • Deductive - conclusions that must be true given
    the evidence

5
Example
  • Simon is the brother of Julie
  • Julie is the mother of Emma
  • Simon is the uncle of Emma
  • Simon is older than Emma

6
Deductive reasoning
  • Three key questions
  • The competence question If people are able to
    reason logically, then what mental events allow
    this to happen?
  • The bias question Why do logical errors occur in
    a systematic and non-random manner, and what do
    these biases tell us about deductive reasoning
    processes?
  • The content question When reasoning is applied
    to real-world situations why does thematic
    content affect reasoning ?

7
  • Propositional reasoning
  • uses connectives not, and, or and if
  • Sentence with if conditional statement
  • Statements using construction
  • if..then.
  • Example
  • If Erica is in Derby, then Kevin is in Edinburgh
  • antecedent consequent
  • According to propositional calculus
  • A proposition can be true or false

8
Truth Tables
  • p q If p then q
  • True True
  • True False False True
  • False False
  • p Erica is in Derby
  • q Kevin is in Edinburgh
  • If p then q
  • If Erica is in Derby, then Kevin is in Edinburgh
  • p implies q, q must occur if p does

9
  • To summarise
  • a conditional statement is true when its
    antecedent and consequent are both true
  • a conditional statement is false when its
    antecedent is true and its consequent is false

10
Inferences in conditionals
  • 2 valid inferences that we can make with
    conditionals
  • Modus Ponens
  • (p) (q)
  • If Erica is in Derby, then Kevin is in Edinburgh
  • Erica is in Derby (p)
  • Therefore Kevin is in Edinburgh (q)
  • If p, then q
  • p,
  • therefore q

11
  • Modus Tollens
  • (p) (q)
  • If Erica is in Derby, then Kevin is in Edinburgh
  • Kevin is not in Edinburgh ( not-q)
  • Therefore Erica is not in Derby (not-p)
  • If p, then q
  • not-q,
  • therefore not-p

12
  • Denial of the Antecedent
  • (p) (q)
  • If Erica is in Derby, then Kevin is in Edinburgh
  • Erica is not in Derby ( not-p)
  • Therefore Kevin is not in Edinburgh (not-q)
  • If p, then q
  • not-p,
  • therefore not-q

13
  • Affirmation of the consequent
  • (p) (q)
  • If Erica is in Derby, then Kevin is in Edinburgh
  • Kevin is in Edinburgh (q)
  • Therefore Erica is in Derby (p)
  • If p, then q
  • q,
  • therefore p

14
Percentage of inferences drawn in conditional
reasoning experiments

15
Studying conditionals
  • 3 classic ways to study conditionals
  • 1. Conditional inference tasks
  • Conditional statement and premise
  • conclusion evaluation
  • conclusion generation
  • select conclusion from list
  • 2. Truth table tasks
  • asked to construct or evaluate truth tables

16
Experiment
  • RULE if there is an even number on one side of
    the card, then there is a vowel on the other
    side.
  • What cards MUST you turn over to see if the rule
    is true?

3
7
D
O
17
  • 3. The Wason Selection Task (Wason, 1966)
  • Abstract Version
  • 4 cards with a letter on one side and a number on
    the other.
  • You can see one side of each card
  • A (p), J (not-p), 3 (q), 7 (not-q)
  • Conditional rule that relates to those 4 cards
  • According to logical analysis the correct answer
    is
  • A (p card) and 7 (not-q card)
  • Few as 10 get correct answers (original abstract
    form)

18
  • Two types of error
  • 1. Selection of the unnecessary q card
  • 2. Failure to select the not-q card
  • Why do people get it wrong?
  • Evans Lynch (1973) - matching bias
  • Summary - abstract selection task
  • 1. Few people get it right
  • 2. Make 2 types of error
  • 3. Exhibit something called matching bias

19
  • Thematic version
  • Thematic facilitation effect - easier to reason
    with problems of concrete content
  • Wason Shapiro (1971) - Towns Transport
  • Every time I go to Manchester, I go by train
  • found facilitation
  • Johnson-Laird, Legrenzi Legrenzi (1972) -Postal
    Rule
  • If a letter is sealed then it has a 50 lire
    stamp on it
  • 81 facilitation effect

20
  • Manktelow Evans (1979) Food Drinks
  • Problem - failed to get facilitation with
    thematic content
  • Every time I eat haddock then I drink gin
  • No facilitation on Towns Transport
  • Suggested - postal rule material was test of
    memory.
  • Rule in England in PO higher value stamps were
    required on sealed letters, therefore Ss read
    rule as if a letter is sealed then it must have
    a 50 lire stamp on it
  • Memory-cue hypothesis (Griggs Cox, 1982)

21
  • Griggs Cox (1982) Drinking age rule
  • Clarified issues
  • Towns Transport - no facilitation
  • Postal rule on Florida Ss - no facilitation
  • Drinking age rule - 74 facilitation
  • Evans Pollard (1987) showed importance of
    police officer scenario
  • Summary - thematic content
  • 1. Early studies showed high facilitation
  • 2. Later contradicted, cant conclude that
    thematic materials make us reason better, other
    explanations put forward.

22
Is there an explanation for performance of the
selection task?
  • Theories fall into 2 categories
  • 1. General theories of reasoning
  • Formal rule theory (Rips, Braine, OBrien)
  • have mental inference rules (modus ponens), apply
    to tasks
  • have better representation of some of rules than
    others (e.g. modus tollens)
  • Mental models (Johnson-Laird, Byrne)
  • represent statement as model
  • due to incomplete model that lead to errors on
    task A 2 A 2
  • . . . 2

23
  • Heuristics and biases (Evans, Over)
  • Heuristic-analytic theory (Evans 1984,1989)
  • 2 stages of reasoning
  • heuristic stage - certain information is deemed
    relevant and selected for further processing
  • analytic stage - inference is generated from the
    selected information
  • Relevance theory (Evans and Over,1996) matching
    bias - cases more relevant when features match
    those named in conditional
  • attributed to the function of the If and
    not-heuristics
  • if - enhances relevance, directs attention to
    antecedent condition.
  • not - directs the attention to proposition it
    denies.

24
  • Expected Information Gain (Oaksford and Chater)
  • Cognitive behaviour is adapted to the structure
    of the environment, it does not depend on rule or
    models
  • Ss arent testing rules but seeking information
    that will help them update their beliefs
  • Gain information that decreases uncertainty
  • Card selections are based on information value of
    each card in the form of expected information
    gain
  • Choices are rational

25
  • 2. Domain specific theories
  • Pragmatic reasoning schemas (Cheng, Holyoak)
  • Schemas - generalised knowledge learnt from
    experience, can include rules for action or
    inference
  • Propose permission schema learnt from
    situations in which require permission to perform
    actions
  • can be applied to conditional in form
  • If action is to be taken, then the precondition
    must be satisfied

26
  • Permission schema produces 4 production rules
  • R1 If the action is to be taken then the
    precondition must be satisfied
  • R2 If the action is not to be taken then the
    precondition need not be satisfied
  • R3 If the precondition is satisfied then the
    action may be taken
  • R4 If the precondition is not satisfied then the
    action must not be taken
  • In selection task - p is action and q is
    condition
  • Drinking age - rules indicate selection of p
    (drinking beer) not-q (16 yrs old) (R1, R4)
  • No mistake of selecting q - R3 says can only
    drink if over age limit

27
Summary
  • Various different accounts have been put forward
    to try and give an understanding of how people
    reason on the selection task
  • they need to account for
  • competence
  • bias
  • content
  • Not all do this
  • References
  • Evans, J.ST.B.T., Newstead, S.E. Byrne, R.M.J.
    (1993). Human reasoning The psychology of
    deduction. Hove LEA
  • Evans, J.St.B.T. (1984). Heuristic and analytic
    processes in reasoning. British Journal of
    Psychology, 75, 451-468.
  • Evans, J.St.B.T. (1996). Deciding before you
    think Relevance and reasoning in the selection
    task. British Journal of Psychology, 87, 223-240.
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