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Grundlagen KI

When is a variable **arc consistent ?**

Consistency between **X_k** and **X_a**:

- Every
**Value**in domain**D_k**has**value**in**D_a**, that satisfy**constraint**in arc**(X_k,X_a)**

Arc consistency is **not commutative**!

Grundlagen KI

What does **Interference **mean

**Draw **(logical, new) **conclusions **from given **premises**

Grundlagen KI

What is **Direct arc consistency ?**

- Only feasible if there are
**no loops**in the graph - A graph is
**direct arc consistent**iif- every
**X_i**is arc-consistent**with each**directly following**neighbor j > i**

- every

Grundlagen KI

When is a CSP-**graph **arc consistent?

**Every **variable is **arc-consistent** with **every other **variable

Grundlagen KI

What is **Conditioning **?

[Context: Nearly tree-structured CSPs]

For graph with loops:

- Remove subset S, such that the graph becomes a tree
- fix S to specific value
- update neighbors
- reorder CSP as tree

Grundlagen KI

which possibilites are there to gain knowledge?

- inference
- declarative approach
- perception

levels agents can be viewed at:

- knowledge level
- implementation level

Grundlagen KI

Is **Backward **Chaining...

Depth-First

Breadth-First

None of the above

Grundlagen KI

when to use theorem proving?

which concepts are required?

which concepts are required?

if the number of models are large but the lengths of proof is short

- logical equivalence: a implies b and b implies a
- validity: sentence is valid if its true in all models, also known as tautologies
- satisfiability: if a sentence is true in some model

Grundlagen KI

What are the** main steps** of the **Arc-Consistency-Algorithm**?

- Init
**FIFO**queue- as
**pre-processing**: all arcs - as
**interference**: All**neighboring**arcs**of assigned**var

- as
**queue.pop()**- remove inconsistent vals
- if
**none**: repeat queue.pop() - if
**some**: Check if domain is empty**yes**: backtrack**no**: add all**neighbors**of this Var**to queue**[**except**: “partner” of current arc]- repeat queue.pop()

- if

- remove inconsistent vals

Grundlagen KI

What are the** main steps** of the **forward checking consistency **algorithm?

- Assign
**Value**to**Variable** **Check**all**neighbors**of that Var**Remove inconsistent Values**of their domains- (no assignment happens here)

- Check if
**a domain is empty****No**: assign next var**Yes**: backtrack

Grundlagen KI

What is the** Least Constraining Value**** **heuristic

- Heuristic for choosing
**order**of**values** - Choose
**value**that rules out**fewest**choices of neighbors - “Fail-last”-approach

Grundlagen KI

What's the **benefit **of a **fail-first variable selectio****n** like **MRV**

**Prunes **the search-tree for first iterations

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