4.1 - Abstraction and Automation

• logical reasoning = to reach a conclusion or logical consequence from premises using deductive, inductive and/or abductive reasoning.
  • Requires putting models into action to solve problems
    • create algorithm
    • implement algorithms in program code
    • implementing models in data structures
    • executing the code
• logic
  • argument = actual statements
  • compound proposition: if X then Y
  • deduction
    • \(P \implies Q\) = P implies Q
      • P is the hypothesis/antecedent/premise
      • Q is the conclusion/consequence
      • If P is true then Q is true.
    • argument form: \(P \therefore Q\)
    • Logical reasoning
      • if P then Q, if Q then R, therefore, if P then R
      • \[P \implies Q, Q \implies R \vdash P \implies R\]
  • induction
    • Netwon’s Principle: Whatever is true of everything before our eyes is true of everthing in the universe.
    • Inductive reasoning kinda the opposite of deductive reasoning (look for rules from facts):
      • E.g: If John Smith is a footballer, then he wears football boots when playing football.
      • can then generalise using Newton’s Principle:
      • If x is a footballer, then x wears football boots when playing football.
      • AKA: All footballers wear football boots when playing football.
• problem solving = process of finding a solution
• automation = the technology by which a process or procedure is performed with minimum human assistance.
• abstraction
  • representational abstraction
    • unnecessary details removed (only info required to solve problem remains)
    • ‘looking at the big picture’
  • abstraction by generalisation/categorisation = putting similar aspects of problem into hierarchal categories
    • procedural abstraction = solutions broken down into procedures or subroutines
    • functional abstraction = breaking down a complex problem into reusable functions