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II.1 Introduction

Logic [Slide 18]

Logic is a tool for careful reasoning.

  • Software and hardware development
    • Formal logic can lead to defect-free products
    • Heavily used in chip design (since Pentium disaster)
    • Used in safety-critical software design
    • Positive influence on all software development
  • Foundation for programming languages (PL)
    • Together with Functions (Lambda calculus) form the semantic base for all PLs
    • Type checking and type inference - basis in logic
    • Computation model - limits of expressiveness
  • Artificial intelligence, database systems
    • Grounded in formal logic

Propositional Logic [Slide 19]

  • Proposition - atomic entity, true or false
    • letters P,Q,... denote propositional variables standing for specific propositions P,Q, specific propositions - value: true or false
    • letters f,f1,f2, are meta-variables denoting propositional variables or formulae f,f1,f2, value: proposition, such as P, (P Q)
  • Propositional Calculus
    • Scheme for calculating with logic formulae
  • Three different propositional calculi
    • semantics-based reasoning - truth table
    • syntax-based reasoning - inference rules
    • equational reasoning - Boolean algebra

Logical Operators [Slide 20]

Logical operators provide ways to combine propositions for calculation. These are:

  • (And)
    • P Q, (P Q) R,
  • (Or)
    • P Q,P (Q R),
  • ¬ (Not)
    • ¬P, ((¬P) Q),
  • (Implication)
    • P Q, (P Q) Q,
  • (Equivalence)
    • P Q, (P Q) (Q P),







2018-03-10
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