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Formal Logic in AI

Logics are formal languages with well defined rules for manipulation of representations.

A knowledge base (KB) is a set of sentences in a given logic language.

The family of logics vary on expressivity.

More expressivity comes at the cost of increasing computational complexity.

Logics





Reasoning :

The manipulation of symbols in a meaningful manner.

Maths is replete with algorithms we use -
  • Addition and multiplication of multi-digit numbers 
  • Long division
  • Solving systems of linear equations
  • Fourier transformation, convolution...
Soundness and completeness

Given a knowledge base and a reasoning algorithm -
  • Entailment : which other sentences in the language are necessarily true ?
  • Proof : which other sentences in the language can one produce by the reasoning algorithm ?

Soundness (of the reasoning algorithm) :
  • A logic is sound if only true statement in the language can be proved.
Completeness (of the reasoning algorithm) :
  • A logic is complete if all true statements in the language can be proved.


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