Knowledge Representation in Logic

The modern version of Logic are capable of representing any factual information that can be stated precisely in any language, natural or artificial. Natural languages display the widest range of knowledge that can be expressed, and logic enables the precisely formulated subset to be expressed in a computable form.

Perhaps there are some kinds of knowledge that cannot be expressed in logic. But if such knowledge exists, it cannot be represented or manipulated on any digital computer in any other notation. The expressivel power of logic includes every knd of Intormation that can be stored or programmed on any digital computer.

Here is mainly knowledge can be represented in three types:

(1) PROPOSITIONAL LOGIC

As an illustration of the issues in translating language to logic, consider a sample sentencc in Lnglish that could be mapped to various notations for logic:

(a)Every trailer truck has 18 wheels. 

The simplest knowledge representation language is propositional logic, which is a modern variation of Boolean algebra. 

In propositional logic, the sentence about trailer trucks can be represented by a single letter: "P"

This is the simplest possible way of representung the sentence, but it cannot represent any detals about the traler truck, the wheels, the number 18, or their interrelationships. That loss of detail may be an advantage in some applications where the main concern is not the internal structure of propositions, but the patterns of implications between them. For those applications, the absence of distracting detail makes propositional loglc an attractive choice of representation.

(2) SUBJECT AND PREDICATE

To show the internal structure of a proposition, the sentence must be broken down into smaller parts that can be represented, separately. For his syllogisms, Aristotle divided the sentence into two parts: the subjet and the predicate. In the example of the trailer truck seatence could be used as the major premise: 

 A: All trailer trucks are eighteen wheelers. 

I: Some Peterbilt is a trailer truck. 

I:Thereore, some Peterbilt is an eighteen wheeler.

In each statement, the phrase betorc the verb, such as "all trailer trucks",  is the subject; the rest of the sentence, which includes the verb and its object, is the predicate. The conncction between the two premises is established by havng the term trailer truck, which is called the mddle term, appear in the subject of one premise and the predicate of the other premise.

(3) CHOICE OF PREDICATES

The division of a sentence into subject and predicate is an Important step, but more detall is needed to show how the wheels are  related to the truck and how the number 18 is related to the wheels. An important advantage of predicate logic over Aristotles syllogisms Is the ability to support the analysis and representation of a proposition at any level of detail. Any feature of a sentence that happens to be significant can be emphasized by an appropriate choice of predicates.

The number 18, for example, could be shown explicitly by replacing. the predicate eighteen Wheeler(x) with a dyadic or two-place predicate that relates  a vehicle x to a number n.

 (a.) NumberOfWheels(x,m) 

(b.) The number of wheels of x is n.