Decision Making: Choosing a specific course of actions from many choices.

12.1 Reasoning

Reasoning: Drawing conclusions from given info.

• Beliefs / Premises: Estimates of whether certain propositions about the world are true.
• Propositions: Statements that can be true or false. (e.g. "I don't have keys" or "I remember leaving them on the counter")

Deduction

Deduction: Draw conclusion from initial premises.

Field of logic: What kinds of inferences can be made from some statements (Aristotle)

Syllogism: Conclusion derived from two or more propositions.

• Categorical Syllogism: Two premises and one conclusion (e.g. "All A are B, all B are C, therefore all A are C": $A\sub B, B\sub C \Rightarrow A\sub C$) (e.g. $A\sub B, (A \cup C \neq \empty) \Rightarrow (B \cup C \neq \empty)$)
• Valid Syllogism: Conclusion follows directly from premises. (Not necessarily true) Truth depended on premises. If any premise is false, conclusion is false.
• 256 possible categorical syllogisms using all, some, or no qualifiers. Only 24 are valid.

Fallacies: People do not analyze syllogisms by logical rules

• Belief Bias: Tend to judge a syllogism's validity based on conclusion's truthfulness. Declines when more time is given to make the decision (Evans 2005)
• Atmosphere Effect: Tend to rate a syllogism valid if qualifiers match in premises and conclusions. (e.g. "Some A are B, some A are C $\Rightarrow$ some B are C" is invalid)
• Mental Models: Models for evaluating syllogisms (Phillip Johnson-Laird 1983) Visualizations of the sentences and mentally explore whether the model breaks down.
• Syllogism Confirmation Bias: People identify valid syllogisms correctly more often than invalid

Conditional/Hypothetical Syllogisms: Syllogisms with a conditional claim (If P, then Q) Test by either proving $P \Rightarrow Q$ or $\neg Q \Rightarrow \neg P$

• Affirming the Antecedent / Modus Ponens: When P is true, we can conclude Q is true.
• Denying the Consequent / Modus Tollens: When Q is false, we can conclude P is false.