**Artificial Intelligence**

**History and Application**

**Types of AI**

**Agents in AI**

**Types of AI Agents**

**Agent Environment**

**Turing Test in AI**

**Search Algorithms**

**Adversarial Search**

**Mini-Max Algorithm**

**Alpha-Beta Pruning**

**Knowledge-based Agent**

**Knowledge Representation**

**Knowledge Representation Techniques**

**Propositional Logic**

**Rules of Inference**

**The Wumpus World**

**Knowledge Base for Wumpus World**

# Knowledge-base for Wumpus world in Artificial intelligence

**In this page we will learn about Knowledge-base for Wumpus world in Artificial intelligence |
Knowledge-base for Wumpus world in Artificial intelligence |Atomic proposition variable for Wumpus world | Some Propositional Rules for the wumpus world | Representation of Knowledgebase for Wumpus world | Prove that Wumpus is in the room (1, 3) **

## Knowledge-base for Wumpus world in Artificial intelligence

We studied about the wumpus world and how a knowledge-based agent evolves the world in the previous topic. Now, in this topic, we'll establish a knowledge base for the Wumpus world and use propositional logic to deduce some Wumpus-world facts.

The agent begins his visit in the first square [1, 1], and we already know that the agent is secure in this room. We'll utilize certain rules and atomic propositions to create a knowledge base for the wumpus world. For each place in the wumpus world, we need the symbol [I j], where I stands for row location and j for column location.

## Atomic proposition variable for Wumpus world:

- Let P
_{i,j}be true if there is a Pit in the room [i, j]. - Let B
_{i,j}be true if agent perceives breeze in [i, j], (dead or alive). - Let W
_{i,j}be true if there is wumpus in the square[i, j]. - Let S
_{i,j}be true if agent perceives stench in the square [i, j]. - Let V
_{i,j}be true if that square[i, j] is visited. - Let G
_{i,j}be true if there is gold (and glitter) in the square [i, j]. - Let OK
_{i,j}be true if the room is safe.

**[Note: There will be 7*4*4= 122 propositional variables for a 4 * 4 square board.
]**

#### Some Propositional Rules for the wumpus world:

**[Note: Lack of variable gives similar rules for each cell.
]**

#### Representation of Knowledgebase for Wumpus world:

The Simple KB for wumpus world when an agent moves from room [1, 1], to room [2,1] is as follows:

We mentioned propositional variables for room[1,1] in the first row, indicating that the room has no wumpus (¬W_{11}), no smell (¬S_{11}), no Pit (¬P_{11}), no breeze (¬P_{11}), no gold (¬G_{11}), has been visited (V_{11}), and is safe (OK_{11}).

We mentioned propositional variables for room [1,2] in the second row, indicating that there are no wumpus, stink, or breeze because an agent has not visited room [1,2], no Pit, and the room is safe.

We mentioned a propositional variable for room[2,1] in the third row, which shows that there are no wumpus(¬W_{21}), no stink (¬S_{21}), no Pit (¬P_{21}), Perceives breeze(B_{21}), no glitter(¬G_{21}), visited (V_{21}), and the room is secure (OK_{21}).

**Prove that Wumpus is in the room (1, 3)**

We can prove that wumpus is in the room (1, 3) using propositional rules which we have derived for the wumpus world and using inference rule.

**Apply Modus Ponens with ¬S11 and R1:**At first we will apply MP rule with R1 which is ¬S_{11}→ ¬W_{11}^ ¬W_{12}^ ¬W_{21}, and ¬S_{11}which will give this output ¬ W_{11}^ W_{12}^ W_{12}**Apply And-Elimination Rule:**After we apply And-elimination rule to ¬W_{11}∧ ¬W_{12}∧ ¬W_{21}, we will see three statements:

¬W_{11}, ¬W_{12}, and ¬W_{21}.**Apply Modus Ponens to ¬S**We will now apply Modus Ponens to ¬S_{21}, and R2:_{21}and R2 which is ¬S_{21}→ ¬W_{21}∧¬ W_{22}∧ ¬W_{31}, which will give the Output as ¬W_{21}∧ ¬W_{22}∧ ¬W_{31}**Apply And -Elimination rule:**Again we will now apply And-elimination rule to ¬ W21 ∧ ¬ W22 ∧¬ W31, We will see three statements:

¬W_{21}, ¬W_{22}, and ¬W_{31}.**Apply MP to S**Apply Modus Ponens to S_{12}and R4:_{12}and R4 which is S_{12}→ W_{13}∨. W_{12}∨. W_{22}∨. W_{11}, we will get the output as W_{13}∨ W_{12}∨ W_{22}∨ W_{11}.**Apply Unit resolution on W**After applying Unit resolution formula on W_{13}∨ W_{12}∨ W_{22}∨ W_{11}and ¬W_{11}:_{13}∨ W_{12}∨ W_{22}∨ W_{11}and ¬W_{11}we will see W_{13}∨ W_{12}∨ W_{22}**Apply Unit resolution on W**After applying Unit resolution formula on W_{13}∨ W_{12}∨ W_{22}∨ W_{11}and ¬W_{11}:_{13}∨ W_{12}∨ W_{22}∨ W_{11}and ¬W_{11}we will see W13 ∨ W12 ∨ W22.**Apply Unit resolution on W**After applying Unit resolution on W_{13}∨ W_{12}∨ W_{22}and ¬W_{22}:_{13}∨ W_{12}∨ W_{22}, and ¬W_{22}, we will get W_{13}∨ W_{12}as output.**Apply Unit Resolution on W**After Applying Unit resolution on W_{13}∨ W_{12}and ¬W_{12}:_{13}∨ W_{12}and ¬W_{12}, we will see W_{13}as an output, therefore, it is proved that the Wumpus is in the room [1, 3].

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