10: Logic and Inference Rules Flashcards
Why is DL (Descriptive Logic) used in AI (Artificial Intelligence)?
To describe and reason about the relevant concepts of an application domain (known as terminological knowledge)
In intelligent systems, knowledge needs to be ____, ____, and ____.
In intelligent systems, knowledge needs to be captured, communicated, and processed.
Agents are ____ and have their own ontology and ____ with one another through such systems.
Agents are autonomous** and have their own ontology and **communicate with one another through such systems.
On what two components are DL’s knowledge representation systems based?
- TBOX
- ABOX
note: T stands for terminology and A stands fo assertion
What is the difference between “some” (∃) and “only” (∀)?
- “only” is about closure and closes off extra options
- “some” does not
Assuming T is a top concept, translate the following to English:
Parent≡∃parentOf.T
Persons who are parents
Assuming T is a top concept, translate the following to English:
∃parentOf.Female
Persons who have some daughter(s)
Assuming T is a top concept, translate the following to English:
∀parentOf.Female
Those who are the parents of only daughters, if any
Assuming T is a top concept, translate the following to English:
(∀.parentOf.Female)∩∃parent.Female
Those who are the parents of only daughters
Write the DL equivalent of the following Protege statement:
ParentOf Some Female
∃parentOf.Female
Write the DL equivalent of the following Protege statement:
ParentOf Only Female
∀parentOf.Female
Write the DL equivalent of the following Protege statement:
hasGivenName value “Matthew”
∃hasGivenName. {Matthew}
Assume you have 3 classes of Team, Player, and Position. Also, assume you have 2 properties of employs and plays:
team1 employs player1
player1 plays position1
Write a descriptive logic statement in Protege that returns the teams which have employed at least 3 players who play as striker or rightBack position.
Team and employs min 3 (Player and hasPosition some {striker, rightBack})
Translate the following to a descriptive logic statement:
You have a class DogLike and you intend to state that if something runs like a Dog and smells like a Dog, then it is in DogLike class.
((runsLike some Dog) and (smellsLike some Dog)) SubClassOf DogLike
In a nutshell, in a General Class Axiom, you say things about complex descriptions of entities without using any ____.
In a nutshell, in a General Class Axiom, you say things about complex descriptions of entities without using any naming.
What will the Debugger prevent if you add the following statement to General Class Axiom?
Disease and (causedBy some A) SubClassOf: (hurts only B)
The Debugger will prevent inconsistency by not allowing a disease caused by some A to hurt somewhere outside B
Assume three colors:
Colors:{red, white, blue}
And in the set Flower, each flower can have one or more color(s). The following DL query:
Flower and hasColor value red
does return any flower with red color but NOT every flower with ONLY red color. Even changing it to
Flower as (hasColor only {red})
does not solve the problem. Why is this?
Because OWL uses the open world assumption.
If we know that a flower has a red color, it does not mean that it does not have other colors, e.g. it can have other colors in the dataset.
Logic helps in the challenging task of representing knowledge in www in a consistent and uniform manner so that it is ____ ____ to humans and ____ ____ by machines.
Logic helps in the challenging task of representing knowledge in www in a consistent and uniform manner so that it is easily comprehensible to humans and effectively inferable by machines.
Descriptive Logic (DL) helps us to build ____ ____ from atomic concepts.
Descriptive Logic (DL) helps us to build complex concepts from atomic concepts.
In DL, a domain can be described in terms of different classes, properties, and instances.
In this way, DL can facilitate generating answers to queries through ____ ____, improving future semantic search engines.
In this way, DL can facilitate generating answers to queries through logical reasoning, improving future semantic search engines.
What is the intersection of Horn Logic and OWL called?
DLP (Description Logic Program)
Fill in the blanks of the DLP diagram.
What are the equivalent terms in Description Logic for the following OWL terms?
class, property, Object
- class = concept
- property = role
- Object = individual
What is the importance of logic?
- high-level language for expressing knowledge
- high expressive power
- well-understood formal semantics
- precise notion of logical consequence
- proof systems that can automatically derive statements syntactically from a set of premises
The languages of RDF and OWL can be viewed as ____ of predicate logic (first order logic).
The languages of RDF and OWL can be viewed as specializations of predicate logic (first order logic).
Predicate logic and its special cases are ____, in the sense that, if a conclusion can be drawn, it remains valid even if new knowledge becomes available.
Predicate logic and its special cases are monotonic, in the sense that, if a conclusion can be drawn, it remains valid even if new knowledge becomes available.
How is a rule represented in Horn Logic?
A1, …, An -> B
Deductive Rules
(Horn Logic)
If A1, …, An are known to be true, then B is also true
Reactive Rules
(Horn Logic)
If the conditions A1, …, An are true, then carry out the action B
Description Logic vs Horn Logic
- Neither of them is a subset of the other
- Impossible to assert that a person X who is a brother of Y is uncle of Z (where Z is child of Y) in OWL
- But using rules, it can be represented as brother(X, Y), childOf (Z, Y) -> uncle (X, Z)
-
On the other hand, rules cannot assert the information that a person is either a man or a woman
- In OWL, this can be expressed using a disjoint union
Give an example of a chain of properties using circle notation.
- hasGrandParent is a chain of properties of hasParent o hasParent
- hasSibling is a chain of properties of hasParent o hasChild
Assuming you have hasParent, hasSister, hasSibling, hasBrother, and hasChild properties, build the concept of a cousin based on the chain of properties through defining hasCousin.
hasCousin is a chain of properties of
hasParent o hasSibling o hasChild
Give a monotonic and a non-monotonic rule for the following:
An online vendor wants to give a special discount if it is a customer’s birthday.
- Monotonic: If birthday, then special discount
-
Non-monotonic: If birthday is not known, then not special discount
- Applicable when available information is incomplete
The Semantic Web approach is to express the knowledge in a ____ way using one of the Web languages already discussed.
The Semantic Web approach is to express the knowledge in a machine-accessible way using one of the Web languages already discussed.
