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CompSci37: AI > Lec 1 | Knowledge > Flashcards

Lec 1 | Knowledge Flashcards

Terms lang

1
Q

Agents that reason by operating on internal representations of knowledge

A

Knowledge Based Agents

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2
Q

An assertion about the world in a knowledge representation language

A

Sentence

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3
Q

It is based on propositions; statements about the world that can be either true or false

A

Propositional logic

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4
Q

What are propositional symbols?

A

Propositional symbols are most often letters (P, Q, R) that are used to represent a proposition.

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5
Q

What are the logical connectives?

A

not, and, or, implication, and biconditional

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6
Q

Logical Connectives:

Inverses the truth value of the proposition.

A

Not

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7
Q

Logical Connectives:

Connects two different propositions

A

And

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8
Q

Logical Connectives:

It is true as long as either one of its arguments is true

A

Or

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9
Q

Logical Connectives:

Represents a structure of “if P then Q.” Where P is the antecedent and Q is called the consequent

A

Implication

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10
Q

Logical Connectives:

An implication that goes both directions. You can read it as “if and only if.”

A

Biconditional

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11
Q

It is an assignment of a truth value to every propositional symbol (a “possible world”).

A

Model

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12
Q

It is the truth-value assignment that provides information about the world.

A

Model

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13
Q

A set of sentences known by a knowledge-based agent

A

Knowledge Base (KB)

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14
Q

This is knowledge that the AI is provided about the world in the form of propositional logic sentences that can be used to make additional inferences about the world.

A

Knowledge Base (KB)

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15
Q

In every model or world in which sentence α is true, sentence β is also true

A

Entailment

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16
Q

The process of deriving new sentences
from old ones

A

Inference

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17
Q

What is the Model Checking algorithm?

A

To determine if KB ⊨ α (in other words, answering the question: “can we conclude that α is true based on our knowledge base”)
* Enumerate all possible models.
* If in every model where KB is true, α is true as well, then KB entails α (KB ⊨ α).
* Otherwise KB does not entail α

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18
Q

Is the model checking algorithm efficient?

A

Model Checking is not an efficient algorithm because it has to consider every possible model before giving the answer (a reminder: a query R is true if under all the models (truth assignments) where the KB is true, R is true as well).

19
Q

What is the difference between the Model Checking Algorithm and the Inference Rules?

A

Inference rules allow us to generate new information based on existing knowledge without considering every possible model.

20
Q

What are needed to run the Model Checking algorithm?

A
  • Knowledge Base, which will be used to draw inferences
  • A query, or the proposition that we are interested in whether it is entailed by the KB
  • Symbols, a list of all the symbols (or atomic propositions) used (in our case, these are rain, hagrid, and dumbledore)
  • Model, an assignment of truth and false values to symbols
21
Q

The process of figuring out how to represent propositions and logic in AI.

A

Knowledge Engineering

22
Q

What are the Inference Rules?

A

Modus Ponens, Elimination, Double Negation Elimination, Biconditional Elimination, De Morgan’s Law, and Distributive Property

23
Q

Theorem Proving

A
  • Initial state: starting knowledge base
  • Actions: inference rules
  • Transition model: new knowledge base after inference
  • Goal test: checking whether the statement that we are trying to prove is in the KB
  • Path cost function: the number of steps in the proof
24
Q

A powerful inference rule that states that if one of two atomic propositions in an Or proposition is false, the other has to be true.

A

Resolution

25
Q

What does Resolution rely on?

A

Complementary Literals

26
Q

Two of the same atomic propositions where one is negated and the other is not, such as P and ¬P.

A

Complementary Literals

27
Q

It is a disjunction of literals (a propositional symbol or a negation of a propositional symbol, such as P, ¬P)

A

Clause

28
Q

Consists of propositions that are connected with an Or logical connective (P ∨ Q ∨ R)

A

Disjunction

29
Q

Logical sentence that is a conjunction of clauses. for example: (A ∨ B ∨ C) ∧ (D ∨ ¬E) ∧ (F ∨ G)

A

Conjunctive Normal Form (CNF)

29
Q

Consists of propositions that are connected with an And logical connective (P ∧ Q ∧ R)

A

Conjunctions

30
Q

What are the steps in Converting Propositions to CNF?

A
  1. Eliminate biconditionals
    * Turn (α ↔ β) into (α → β) ∧ (β → α).
  2. Eliminate implications
    * Turn (α → β) into ¬α ∨ β.
  3. Move negation inwards until only literals are being negated (and not clauses), using De Morgan’s Laws.
    * Turn ¬(α ∧ β) into ¬α ∨ ¬β
31
Q

What process is used when a clause contains the same literal twice?

A

Factoring. The duplicate literal is removed.

32
Q

Proof by contradiction

A 
To determine if KB ⊨ α:
    Check: is (KB ∧ ¬α) a contradiction?
        If so, then KB ⊨ α.
        Otherwise, no entailment.
33
Q

Another Resolution Algorithm

A 
To determine if KB ⊨ α:
    - Convert (KB ∧ ¬α) to Conjunctive Normal Form.
    - Keep checking to see if we can use resolution to produce a new clause.
    - If we ever produce the empty clause (equivalent to False), a contradiction has been reached, thus proving that KB ⊨ α.
    - However, if contradiction is not achieved and no more clauses can be inferred, there is no entailment.
34
Q

Another type of logic that allows us to express more complex ideas more succinctly than propositional logic.

A

First Order Logic

35
Q

What are the two types of Symbols used in First Order Logic?

A

Constant Symbols and Predicate Symbols.

36
Q

What do constant symbols represent?

A

objects

37
Q

What are predicate symnols?

A

Predicate symbols are like relations or functions that take an argument and return a true or false value.

38
Q

It is a tool that can be used in first order logic to represent sentences without using a specific constant symbol.

A

Quantification

39
Q

What symbol is used in Universal Quantification?

A

Universal quantification uses the symbol ∀ to express “for all.”

40
Q

It is an idea parallel to universal quantification.

A

Existential Quantification

41
Q

It is used to create sentences that are true for at least one x.

A

Existential Quantification

42
Q

What symbol is used in Existential Quantification?

A

It is expressed using the symbol ∃.

43
Q

Can the Existential and Universal Quantification be used in the same sentence?

A

Yes. For example, the sentence ∀x. Person(x) → (∃y. House(y) ∧ BelongsTo(x, y)) expresses the idea that if x is a person, then there is at least one house, y, to which this person belongs. In other words, this sentence means that every person belongs to a house.

CompSci37: AI (7 decks)

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