First Order Logic

All objects described are fixed or unique

"John is a student" student(john)

Here John refers to one unique person.

First order predicate logic

Objects described can be unique or variables to stand for a unique object

"All students are poor"

ForAll(S) [student(S) -> poor(S)]

Here S can be replaced by many different unique students. This makes programs much more compact:

eg. ForAll(A,B)[brother(A,B) -> brother (B,A)] replaces half the possible statements about brothers

• Temporal

Represents truth over time.

• Modal

Represents doubt

• Higher order logics

Allows variable to represent many relations between objects

• Non-monotonic

Represents defaults

Propositional is one of the simplest systems of logic.

Propositional Logic

In propositional logic (PL) an user defines a set of propositional symbols, like P and Q.

User defines the semantics of each of these symbols. For example,

o P means "It is hot"

o Q means "It is humid"

o R means "It is raining"

UNIT III

KNOWLEDGE REPRESENTATION

Knowledge Representation and Reasoning

Intelligent agents should have capacity for:

• Perceiving, that is, acquiring information from environment,

• Knowledge Representation, that is, representing its understanding of the world,

• Reasoning, that is, inferring the implications of what it knows and of the choices

it has, and

• Acting, that is, choosing what it want to do and carry it out.

Representation of knowledge and the reasoning process are central to the entire field of

artificial intelligence. The primary component of a knowledge-based agent is its

knowledge-base. A knowledge-base is a set of sentences. Each sentence is expressed in a

language called the knowledge representation language. Sentences represent some

assertions about the world. There must mechanisms to derive new sentences from old

ones. This process is known as inferencing or reasoning. Inference must obey the primary

requirement that the new sentences should follow logically from the previous ones.

Logic is the primary vehicle for representing and reasoning about knowledge.

Specifically, we will be dealing with formal logic. The advantage of using formal logic as

a language of AI is that it is precise and definite. This allows programs to be written

which are declarative - they describe what is true and not how to solve problems. This

also allows for automated reasoning techniques for general purpose inferencing.

This, however, leads to some severe limitations. Clearly, a large portion of the reasoning

carried out by humans depends on handling knowledge that is uncertain. Logic cannot

represent this uncertainty well. Similarly, natural language reasoning requires inferring

hidden state, namely, the intention of the speaker. When we say, "One of the wheel of the

car is flat.", we know that it has three wheels left. Humans can cope with virtually infinite

variety of utterances using a finite store of commonsense knowledge. Formal logic has

difficulty with this kind of ambiguity.

A logic consists of two parts, a language and a method of reasoning. The logical

language, in turn, has two aspects, syntax and semantics. Thus, to specify or define a

particular logic, one needs to specify three things:

Syntax: The atomic symbols of the logical language, and the rules for constructing wellformed,

non-atomic expressions (symbol structures) of the logic. Syntax specifies the

symbols in the language and how they can be combined to form sentences. Hence facts

about the world are represented as sentences in logic.

Semantics: The meanings of the atomic symbols of the logic, and the rules for

determining the meanings of non-atomic expressions of the logic. It specifies what facts

in the world a sentence refers to. Hence, also specifies how you assign a truth value to a

sentence based on its meaning in the world. A fact is a claim about the world, and may be

true or false.