Mar 26 Problem Solving

• Syllogisms: logical reasoning task often used in philosophy
• Syllogisms:

  1. Organize steps (premises) that represent "truth" in a given order

  2. Use those truths to determine if a conclusion is valid (logical)
• Syllogistic Fallacies: Incorrectly assessing syllogisms shows when we deviate from logical reasoning
• Conditional Reasoning: If some condition is true, then we will observe X

  • hypothesis testing
• Confirmation Bias: a tendency to seek confirmatory evidence for a hypothesis

  • Many information seeking and evaluation tasks are influenced by confirmation bias
• Falsification: look for situations that would falsify a rule
• Familiarity Affects Judgement
• Problem Solving: going from a problem to goal state

  • Problem solving is a multi-step cognitive process that involves three aspects:

  1. Recognizing and representing problem

  2. Analyzing and solving it

  3. Assessing the solution's effectiveness

  
• Analyzing and Solving It; The Problem Solving Cycle

  1. Recursive: Repeat this cycle as many times as necessary to find a solution

  2. Applicable: Apply successful cycles (solutions) to new problems (must be able to generalize)

  
• Problem Solving & Generalization: Involves storing specific solutions without detail to apply to new scenarios

  • Generalization is important for adaptive behavior
  • Memory for solutions should include 'essence' and not specific details for generalization to occur
• Problem Types

  1. Well Defined Problems: Requirements are unambiguous
  2. Ill Defined Problems: How to overcome problem / the goal is ambiguous
• Well-Defined Problems: all information needed to solve the problem is present

  • Defined goal state
  • Single, expected outcome
  • Clear steps
  • Represents an information processing approach to study problem solving

  
• Ill-Defined Problem: have few limitations (rules) for how to solve the problem

  • Ambiguous situations
  • Multiple solutions or expected outcomes
  • Social problem solving
• Ill-Defined Problems Carry a Load
• Moravec's Paradox: AI can solve well-defined problems well but not ill-defined problems and simple skills
• The Tower of Hanoi: move 3 discs from peg A to C so they are in the same initial order

  • well-defined problem

  
• Brute Force: Systematic algorithm that represents all the possible steps from the problem to goal state

  • guaranteed to find a solution, but inefficient
  • consider every possible set to find solution
  • can lead to combinatorial explosion (and decision fatigue)
• Heuristics: Strategies to select moves in a problem space to avoid combinatorial explosion

  • Trial and error
  • Hill climbing strategy
  • Means end analysis
• Trial & Error: Try out a number of solutions, rule out what doesn't work

  • Considered "lower-level thinking"
  • Good for limited outcome problems (E.g.; what color of my shirt matches these pants?)
  • Not good for multi-outcome problems (E.g.; solving a Rubik's Cube via trial and error doesn't work - rubik's cube best solved with algorithms)
• Hill Climbing Strategy: Select the operation that brings you closer to the goal without examining the whole problem space

  • can lead to a false outcome, a 'local maxima' (subgoal) is mistaken as the final goal
  • does not always work because some problems require you to move away from the goal in order to solve i
• Combinatorial Explosion: computing too many alternatives
• Means Ends Strategy: Determining the best strategy for attaining the goal given the current situation (What "means" do I have to make the current state look like the goal state I want to be in?)

  • Envisioning end or ultimate goal
  • Identifying subproblems to complete the goal
  • Includes forward and backward movements and constantly evaluating the difference between current and goal states
  • Highlights the importance of recursion (sub-goals and step-by-step approach to getting solution)
• Maier (1931) gave useless cues to people working on the two-string problem to demonstrate a lack of consciousness of the process of producing insight​
• Luchin (1942) gave a list of water jug problems to people to solve

  • The first several problems were all solvable using the same pattern
  • The last few problems were solvable using a much simpler pattern
  • Luchin found that participants kept using the same complex equation for the last few questions​