knowledge type

8/8/2019 Knowledge Type

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Knowledge Representation

Artificial Intelligence

Resolution

Goes from conclusions to the given facts.

It gains its efficiency from the fact that it operates on statements that havebeen converted to a very convenient standard form.

To prove a statement, resolution attempts to show that the negation of thestatement produces a contradiction with the known statements ( i.e. that itis unsatisfiable.)


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Conversion to Clause Form in case of proposition logic

Eliminate using the fact that ab is equivalent to a V b

Reduce each by using the fact that (p) =p

x : P(x) V x : Q(x) then x : P(x) V y : Q(y)

(a b) V c = (a V c) (b V c)

Winter V summer means winter V cold

(a b) = a V b and (a V b) = a b


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Limitations of Resolution ( Evolution of Natural Deduction)

The previous method of resolution brings uniformity, everything looks thesame. Hence at times, it becomes very difficult to pick the statement thatmay be useful in solving the problem.

As we convert everything into clause form, we loose important heuristicinformation.

Eg. We believe that all judges who are not crooked are well-educated

x : judge(x) crooked (x) educated(x)

In the clause form it will take the following shape judge (x) V crooked(x) V educated(x)


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Natural Deduction

Another problem with the use of resolution is that people do not think inresolution.

Computers are still poor at proving very hard things, hence we need a

practical standpoint. ( focus is on interaction)To facilitate it we led to Natural Deduction.

It describes a blend of techniques, used in combination to solve problemsthat are not traceable by any one method alone.

One common technique is to talk about objects involved in the predicateand not the predicate itself.


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Procedural v/s Declarative Knowledge

A Declarative representation is one in which knowledge is specified butthe use to which that knowledge is to be put in, is not given.

A Procedural representation is one in which the control information that is

necessary to use the knowledge is considered to be embedded in theknowledge itself.

To use a procedural representation, we need to augment it with aninterpreter that follows the instructions given in the knowledge.

The difference between the declarative and the procedural views of

knowledge lies in where control information resides.


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Consider the example

man(Marcus)

man (Ceaser)

Person(Cleopatra)

Vx : man(x) person(x)

Now we want to extract from this knowledge base the ans to the question:

y : person (y)

Marcus, Ceaser and Cleopatra can be the answers


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As there is more than one value that satisfies the predicate, but only onevalue is needed, the answer depends on the order in which the assertionsare examined during the search of a response.

If we view the assertions as declarative, then we cannot depict how theywill be examined. If we view them as procedural, then they do.

Let us view these assertions as a non deterministic program whose outputis simply not defined, now this means that there is no difference betweenProcedural & Declarative Statements

The focus is on working on the control model.


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man(Marcus)

man (Ceaser)

Vx : man(x) person(x)

Person(Cleopatra)

If we view this as declarative then there is no difference with the previousstatement. But viewed procedurally, and using the control model, we used togot Cleopatra as the answer, now the answer is marcus.

The answer can vary by changing the way the interpreter works.The distinction between the two forms is often very fuzzy. Rather then tryingto prove which technique is better, what we should do is to figure out what theways in which rule formalisms and interpreters can be combined to solveproblems.


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Logic Programming

Logic programming is a programming language paradigm in which logicalassertions are viewed as programs, e.g : PROLOG

A PROLOG program is described as a series of logical assertions, each ofwhich is a Horn Clause.

A Horn Clause is a clause that has at most one positive literal.

Eg p, p V q etc are also Horn Clauses.

The fact that PROLOG programs are composed only of Horn Clausesand not of arbitrary logical expressions has two important consequences.

Because of uniform representation a simple & effective interpretercan be written.

The logic of Horn Clause systems is decidable.


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Logic Programming

Even PROLOG works on backward reasoning.

The program is read top to bottom, left to right and search is performeddepth-first with backtracking.

There are some syntactic difference between the logic and the PROLOGrepresentations

The key difference between the logic & PROLOG representation is thatPROLOG interpreter has a fixed control strategy, so assertions in thePROLOGprogram define a particular search path to answer any question.

Where as Logical assertions define set of answers that they justify,there can be more than one answers, it can be forward or backwardtracking .


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Forward VS Backward

reasoning Forward ,from the start state.

Backward, from the goal state.

To reason forward ,the left sides are matched againstthe current state and right sides are used to generate

new nodes until goal is reached. to reason backward ,the

right sides are matched against the current node and left

sides are used to generate new nodes representing new

goal states to be achieved.

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Factor to decide reasoning style

Are there more start sates or goal states-move from small states to large states.

In which direction is branching factorproceed in direction with lower branching factor.

Will the program be asked to justify its

reasoning process to user.-closely to way the

user think

What kind of event is going to trigger a

problem solving

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