Notes by Lex Toumbourou

Logical Reasoning refers to the process of arriving at conclusions based on some premises. The premises and conclusions are supported by Propositions, statements that are either true or false. It is the foundation of Symbolic AI, which makes inferences using logic and knowledge systems

There are three main types of Logical Reasoning:

• Abduction - conclusion is a plausible explanation, but not necessarily a fact.
• Deduction - conclusion is guaranteed to be correct.
• Induction - a generalisation based on the data, that needs to be verified. ML is primarily based on inductive reasoning.

Abduction

Abduction, or Abductive Reasoning, refers to making the most plausible explanation based on a rule or set of rules.

The conclusion is not necessarily correct, only a plausible explanation.

The format is: if P then Q; Q is observed; P is a possible explanation.

Rule: All men are mortal Observation: Socrates is mortal Plausible Conclusion: Socrates is a man

Sherlock Holmes' "deductive method" is actually abductive reasoning, as Holmes typically observes clues (effects) and infers the most likely cause or explanation for those observations.

Deduction

On the other hand, Deduction, or Deductive Reasoning, takes an observation that fits the general rule to create a conclusion that is guaranteed to be correct (if the general rule is indeed true).

Format: If P then Q; P is true; Therefore Q is true.

Rule: all men are mortal. Observation: Socrates is a man. Conclusion: Socrates is mortal.

Deductive reasoning moves from the general to the specific and provides certainty when the premises are true.

Induction

Finally, Induction takes a set of facts and aims to build a general conclusion that may or may not be true. Machine Learning is primarily based on Inductive Reasoning, though modern ML systems may also incorporate deductive and abductive elements.

Format: Specific observations -> General rule/pattern

Example: - Fact: Socrates is a man - Fact: Socrates is mortal - Fact: Plato is a man - Fact: Plato is mortal - Fact: Aristotle is a man - Fact: Aristotle is mortal - Possible rule: All men are mortal

Inductive reasoning moves from specific observations to general principles. The strength of the conclusion depends on the number and variety of observations. Unlike deduction, inductive conclusions are probabilistic rather than certain, which is why they require verification through further testing or observation.