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Introduction to Reasoning in Machines: Basic Concepts

Syllogisms

What is it?	A form of deductive argument/reasoning in which a conclusion is drawn from 2 given or assumed propositions (premises / statements). The premises and the conclusion are simple declarative statements constructed using only three simple terms between them, each term appearing twice (as a subject and as a predicate) E.g. all dogs are animals; all animals have four legs; therefore all dogs have four legs. The argument in such syllogisms is valid by virtue of the fact that it would not be possible to assert the premises and to deny the conclusion without contradicting oneself. (Based on Oxford Dictionary and Encyclopedia Britannica)
3 types	Categorical, conditional and disjunctive.
Categorical	The traditional type is the categorical syllogism in which both premises and the conclusion are simple declarative statements that are constructed using only three simple terms between them, each term appearing twice. Assumes all premises are true.
Conditional	Implies an `if` in the premises. E.g. You are injured. I am qualified to assist with injuries. I can heal you.
Disjunctive	Uses an either/or premise. If it is known that at least one of two statements is true, and that it is not the former that is true; we can infer that it has to be the latter that is true.

Moduls Ponens	If a conditional statement ‘if P then Q’ is accepted, and the antecedent P holds, then the consequent Q may be inferred. E.g. If it's raining then its cloudy. It is raining. Then it's cloudy.
Moduls Tollens	A mixed syllogism that takes the form of 'If P, then Q. Not Q. Therefore, not P.' It is an application of the general truth that if a statement is true, then so is its contrapositive (“if not-B then not-A ” is the contrapositive of “if A then B”).