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.

The manipulation of symbols in a meaningful manner.

Maths is replete with algorithms we use -

Given a knowledge base and a reasoning algorithm -

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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