Agents That Reason Logically

Any intelligent system surely must take into account that not all the information that an agent uses is explicit. It seems likely therfor that an intelligent agent should be able to extract this implicit information.

There is a useful example to be drawn here from the way that Prolog works. A Prolog program is capable of answering a query such as

grandfather(abraham, X)
even though it has no explicit knowledge in the form
grandfather(abraham, joseph).

These pages cover various aspects of knowledge and reasoning. This one in particular sets the stage.

The Wumpus world example in the book shows a justification for agents that are capable of reasoning. One aspect of the situation that makes reasoning necessary is that not all knowldege about the world is expressed explicitly. In particular an agent may not know the full state of the world or even its own full state. Reasoning can be used to infer addtional information about the world.

Agents therefor need to be able to represent knowledge in some way. Alobng with search knowledge representation (KR) is a foundational part of AI. There are many methods of doing knowledge representation we will concentrate here on the use of logic.

Logic for KR

The major advantage that logic has for knowledge representation lies in its declarative nature. Sentences representing knowledge can be added to a knowledge base without havig to connect them to the rest of the knowledge. At least this is so as long as new knowledge does not contradict other knowledge. (This is the truth maintenance problem. It is quite difficult for humans as well as for machines!).

Proof and Truth

Given a Knowledge Base KB a model for the knowledge base is a represnetation of the objects in the knowledge base for which all the sentence in the knowledge base are true. If a is a sentence which has the property that a is true in every model of KB we say KB entails a (KB |= a). This is not the same as being able to prove a. Proofs are constructed using inference procedures. Given an inference procedure, which is no more than a set of rules for obtaining sentences from a given set of sentences if we can derive a from KB using these rules we say KB |- a.

Obviously we are looking for inference procedures that are both sound and complete.

Forms of Logic

We will consider two forms of logic
  1. Propositional Logic
  2. First Order Logic
These are the two classical logics. AI also makes use of various non standard logics which we will not go into at this point.

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Last Changed: 14 October 1995