Logical reasoning

• What is reasoning

  • The action of thinking about something in a logical (or rational) way to make a decision
  • Use our existing knowledge to draw conclusions, make predictions, or construct explanations
  • Two types of logical reasoning

  1. Inductive
  2. Deductive
• Inductive reasoning

  • Making broad generalisations from specific observations
• Deductive reasoning

  • Reaching a specific, logical conclusion from general statements or hypotheses
  • Typically structured as follows:

  1. First premise (or statement) - “P1”
  2. Second premise - “P2”
  3. Inference (or conclusion)

  • Related to problem solving
  • Goal is to solve the reasoning task, but the solution isn’t always obvious
  • Assume premise are always true (or valid)
  • Conclusion can be either valid or invalid
• Two types of conditional reasoning

  1. Conditional (reasoning with if)

  • Logical operators included in premises e.g., or, and, if … then, if and only if

  1. Syllogistic

  • Consists of two premises followed by a conclusion that is either valid or invalid
  • Contains three items, with one occurring in both premises
  • Premises and conclusions contain quantifiers e.g., all, some, no, some … not
• Conditioning reasoning

  • Premises
  • If I go outside (antecedent), then I get a tan (consequent)
  • get a tan (consequent)
  • Conclusion
  • Therefore, I have gone outside
• Four types of conditional reasoning problems

  1. Modus ponens - VALID / AFFIRMATIVE
  2. Moden tollens - VALID / NEGAITVE
  3. Affirmation of the consequent - INVALID / AFFIRMATIVE
  4. Denial of the antecedent - INVALID / NEGATIVE
• Deductive reasoning= uninterested reasoning

  • Examples of deductive reasoning do not account for:
  • The goals/preferences of an individual
  • An individual’s prior knowledge or expectations
  • Contrasts with how we reason in everyday life
  • Also known as informal reasoning
• Importance of prior knowledge

  • Statistical strategy
  • Estimate the probability that a conclusion is valid based on what we know about the world
  • PROBLEM 2 = higher probability, therefore invalid conclusion accepted
  • Markowitz et al. (2013)
• Importance of prior knowledge

  • Counterexample strategy
  • Try to think of counterexamples that contradict the conclusion
  • PROBLEM 2 = more difficult to think of counterexamples, therefore invalid conclusion accepted
  • Markowitz et a. (2013)
• Importance of prior knowledge

  • Statistical strategy
  • less cognitively demanding
  • Limited time to accept/reject conclusion
  • Counterexample strategy
  • more cognitively demanding
  • Unlimited time to accept/reject conclusion
• Syllogistic reasoning

  • Validity of conclusion depends only on whether it follows logically
  • Validity in real-world is irrelevant
  • Belief bias causes errors in syllogistic reasoning
  • Accept invalid conclusions if they are believable
  • Reject valid conclusions if they are unbelievable
• Belief bias

  • Conclusions for both problems are valid
  • i.e. follow logically from premises
• theories of deductive reasoning

  • Two very influential theories:

  1. Mental model

  • Create a visual image of the problem

  1. Dual systems

  • Unconscious, heuristic-based process
  • Conscious, analytical process
• Mental model- assumptions

  • Mental model constructed and conclusions generated
  • Construct alternative models to falsify conclusion
  • i.e., counterexamples
  • Reasoning problems that require several mental models are harder to solve
  • Due to increased demands on working memory
• Mental model - Limitations

  • Does not describe how we decide which information to include in a mental model
• Dual-systems - Assumptions

  • Singularity
  • One single mental model considered at a time
  • Relevance
  • Most relevant (or plausible) mental model considered based on prior knowledge
  • Satisficing
  • Mental model evaluated by analytic system and accepted if adequate
• Dual-system - Limitations

  • No direct evidence that there are separate heuristic and analytical processes
  • Does not explain how heuristic and analytical processes interact
  • Assumes that all analytical processing is conscious
  • But can sometimes be unconscious
• modus ponens

  • If A is true , then B is true
  • A is true
  • Therefore , B is true
  • VALID / AFFIRMATIVE
• Modus tollens

  • if A is true , then B is true
  • B is not true
  • Therefore, A is not true
  • VALID / NEGATIVE
• Affirmation of the consequent

  • if A is true , then B is true
  • B is true
  • Therefore , A is true
  • INVALID / AFFIRMATIVE
• Denial of the antecedent

  • if A is true, then B is true
  • A is not true
  • Therefore , B is not true
  • INVALID / NEGATIVE