Explain non-monotonic reasoning.

        • Non-monotonic reasoning (NMR) is based on supplementing absolute truth with beliefs.

        • These tentative beliefs are generally based on default assumptions that are made due to lack of evidence.

        • A NMR system tracks a set of tentative beliefs and revises them, when knowledge is observed or derived.

           • Conventional reasoning systems like first order predicate logic are designed to work with information that has 3 important properties –
                1. It is complete w.r.t domain of interest.
                2. It is consistent.
                3. The only way it can change is that new facts can be added as they become available.

        • NMR systems are designed to be able to solve problems in which the above 3 properties are missing.

        • This can be done using the following 2 approaches –
                1. Non-monotonic logic
                2. Default logic

        • Two common kinds of NMR that can be defined in these two logics are –
                1. Abduction

                2. Inheritance

        • Thus, NMR is of the type –

                1. Non-monotonic logic and default logic

                2. Circumscription

                3. Truth maintenance systems

Non-monotonic logic and default logic:

        • Default reasoning is a very common form of NMR. Conclusions are drawn, based on what is most likely to be true.

        • Non-monotonic logic states that “The truth of a proposition may change when new information are added, and a logic may be built to allow the statement to be retracted.”

        • Default logic initiates a new inference rule: A:B where C

A is known as the Pre-requisite

B is the Justification

C is the Consequent

Circumscription:

    • It is a non-monotonic logic to formalize common sense assumption.

    • It is a formalized rule of conjecture that can be used along with the rules of inference of first order logic.

Truth maintenance systems:

        •   Reasoning Maintenance Systems (RMS) are a critical part of the reasoning system.

        •   Its purpose is to assure that inferences made by the reasoning system are valid.

        • The reasoning system provides the RMS with information about each inference it performs, and in return, the RMS provides it with information about the whole set of inferences.