There is no precise distinction between defeasible and non-monotonic reasoning, except that one tends to speak of the latter if one considers explicit logical arguments that may fail if further premisses are added.

1. Consequence relations: If we write the assertion that C is a logical consequence of premisses P as 'P |- C', where P is a set of premisses and C a conclusion there is in deductive logic the standard consequence relation of

(1) monotonicity: If P |- C then P U Q |- C

that is: If C is a consequence of P, C also is a consequence of P together with Q.

Usually this is justified with the argument that if C does follow from P, then it must keep following from P whatever further information is added, and this can be argued by reference to valid formulas in standard bi-valent propositional logic, such as
(P --> C) --> (P --> (Q --> C)).

However, as soon as one considers less simple systems than standard bi-valent propositional logic, such as probability theory, it may happen that adding a premiss Q considerably weakens the probability of P, and thereby the probability of C.

And this also is true for empirical arguments involving contingent implications, such as 'If this is a bird, then it can fly', and the additional premiss 'This bird is a penguin'. Also, it is true of much empirical argumentation of any kind: Adding (or deleting) premisses changes the truth-status or probability of the rest of the system.

Hence non-monotonic logics result as soon as (1) is given up or qualified. There are good reasons to do so wherever one argues about empirical facts. For more, see Reasoning - defeasible.