Knowledge Representation Resolution and Unification
1. Resolution
It is an algorithm for proving facts true or false by virtue of contradiction. If we want to prove a theorem X is true, we have to show that the negation of X is not true.
Resolution theorem:
For any three clauses p, q and r,
p v r, q v ? r ? p v q
Modus Pones
It can be summarized as "P implies Q; P is asserted to be true, so therefore Q must be true." The history of modus ponens (implication elimination ) goes back to antiquity. Modus ponens allows one to eliminate a conditional statement from a logical proof or argument (the antecedents) and thereby not carry these antecedents forward in an ever-lengthening string of symbols; on other words, the rule of logic stating that if a conditional statement (“if p then q ”) is accepted, and the antecedent ( p ) holds, then the consequent ( q ) may be inferred. Such as:
If it is raining, I will meet you at the theater.
It is raining.
Therefore, I will meet you at the theater.
Modus ponens can be stated formally as:
The argument form has two premises (hypothesis). The first premise is the "if– then" or conditional claim, namely that P implies Q. The second premise is that P, the antecedent of the conditional claim, is true. From these two premises it can be logically concluded that Q, the consequent of the conditional claim, must be true as well. Inartificial intelligence, modus ponens is often called forward chaining.
An example of an argument that fits the form modus ponens:
If today is Tuesday, then John will go to work.
Today is Tuesday.
Therefore, John will go to work.
Example
Prove that
"Fido will die" from the statements: die(Fido)
"Fido is a dog",
"all dogs are animals"
"all animals will die", with applying modus ponens
1- All dogs are animals: ?X (dog(X) ? animal (X) )
2-Fido is a dog : dog (fido)
3-Modus Ponens and {fido / X} gives : animal(fido)
4- All animals will die : ?Y (animal(Y) ? die (Y))
5- Modus Ponens and {fido/Y} gives : die (fido).
Clause form:
~ dog(X) ? animal (X)
dog(fido)
~ animal(Y) ? die(Y)
~ die(fido)
2. Unification
Unification is a technique for taking two sentences in predicate logic and finding a substitu¬tion that makes them look the same.
• A variable can be replaced by a constant.
• A variable can be replaced by another variable.
• A variable can be replaced with a predicate, as long as the predicate does not contain that variable.
Unification Conditions:
1- The two predicate names must be the same.
2-The two predicates must have same no. of arguments.
Example:
Given the following set of predicates,
1.hates(X , Y)
2.hates(John, Football).
3. hates(Adam, Spinach).
Unify 1 and 2: S={john/X, football/ Y}
Unify 1 and 3: S={adam/X, spanich/Y}
If we introduce more complex unifications:
4. Like(X, season(Y))
5. Like(George, season(summer)).
6. Like(Z, summer)
Unify 4 and 6: S={Z/X, summer/Y}
Unify 4 and 5: S={george/X, summer/Y}
3-Frames
A frame is a collection of attributes which defines the state of an object and its relationship to other frames (objects).
Frames are called Slot-and-Filler data representations.
Slots are the data values,
Fillers are attached procedures.
Frames are often linked into a hierarchy to represent has-part and isa relationships.
المادة المعروضة اعلاه هي مدخل الى المحاضرة المرفوعة بواسطة استاذ(ة) المادة . وقد تبدو لك غير متكاملة . حيث يضع استاذ المادة في بعض الاحيان فقط الجزء الاول من المحاضرة من اجل الاطلاع على ما ستقوم بتحميله لاحقا . في نظام التعليم الالكتروني نوفر هذه الخدمة لكي نبقيك على اطلاع حول محتوى الملف الذي ستقوم بتحميله .
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