{"id":2284,"date":"2022-04-16T19:06:23","date_gmt":"2022-04-16T19:06:23","guid":{"rendered":"https:\/\/mdr.foobrdigital.com\/?p=2284"},"modified":"2022-04-16T19:06:23","modified_gmt":"2022-04-16T19:06:23","slug":"knowledge-base-for-wumpus-world","status":"publish","type":"post","link":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/2022\/04\/16\/knowledge-base-for-wumpus-world\/","title":{"rendered":"Knowledge-base for Wumpus world"},"content":{"rendered":"\n
As in the previous topic we have learned about the wumpus world and how a knowledge-based agent evolves the world. Now in this topic, we will create a knowledge base for the wumpus world, and will derive some proves for the Wumpus-world using propositional logic.<\/p>\n\n\n\n
The agent starts visiting from first square [1, 1], and we already know that this room is safe for the agent. To build a knowledge base for wumpus world, we will use some rules and atomic propositions. We need symbol [i, j] for each location in the wumpus world, where i is for the location of rows, and j for column location.<\/p>\n\n\n\n<\/figure>\n\n\n\n
Atomic proposition variable for Wumpus world:<\/h3>\n\n\n\n
Let Pi,j<\/sub><\/strong> be true if there is a Pit in the room [i, j].<\/li>
Let Bi,j<\/sub><\/strong> be true if agent perceives breeze in [i, j], (dead or alive).<\/li>
Let Wi,j<\/sub><\/strong> be true if there is wumpus in the square[i, j].<\/li>
Let Si,j<\/sub><\/strong> be true if agent perceives stench in the square [i, j].<\/li>
Let Vi,j<\/sub><\/strong> be true if that square[i, j] is visited.<\/li>
Let Gi,j<\/sub><\/strong> be true if there is gold (and glitter) in the square [i, j].<\/li>
Let OKi,j<\/sub><\/strong> be true if the room is safe.<\/li><\/ul>\n\n\n\n
Note: For a 4 * 4 square board, there will be 7*4*4= 122 propositional variables.<\/h4>\n\n\n\n
Some Propositional Rules for the wumpus world:<\/h3>\n\n\n\n<\/figure>\n\n\n\n
Note: lack of variables gives us similar rules for each cell.<\/h4>\n\n\n\n
Representation of Knowledgebase for Wumpus world:<\/h3>\n\n\n\n
Following is the Simple KB for wumpus world when an agent moves from room [1, 1], to room [2,1]:<\/p>\n\n\n\n<\/figure>\n\n\n\n
Here in the first row, we have mentioned propositional variables for room[1,1], which is showing that room does not have wumpus(\u00ac W11<\/sub>), no stench (\u00acS11<\/sub><\/strong>), no Pit(\u00acP11<\/sub><\/strong>), no breeze(\u00acB11<\/sub><\/strong>), no gold (\u00acG11<\/sub><\/strong>), visited (V11<\/sub><\/strong>), and the room is Safe(OK11<\/sub><\/strong>).<\/p>\n\n\n\n
In the second row, we have mentioned propositional variables for room [1,2], which is showing that there is no wumpus, stench and breeze are unknown as an agent has not visited room [1,2], no Pit, not visited yet, and the room is safe.<\/p>\n\n\n\n
In the third row we have mentioned propositional variable for room[2,1], which is showing that there is no wumpus(\u00ac W21), no stench (\u00acS21<\/sub><\/strong>), no Pit (\u00acP21<\/sub><\/strong>), Perceives breeze(B21<\/sub><\/strong>), no glitter(\u00acG21<\/sub><\/strong>), visited (V21<\/sub><\/strong>), and room is safe (OK21<\/sub><\/strong>).<\/p>\n\n\n\n
Prove that Wumpus is in the room (1, 3)<\/h2>\n\n\n\n
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.<\/p>\n\n\n\n
Apply Modus Ponens with \u00acS11 and R1:<\/strong><\/li><\/ul>\n\n\n\n
We will firstly apply MP rule with R1 which is \u00acS11<\/sub> \u2192 \u00ac W11<\/sub> ^ \u00ac W12<\/sub> ^ \u00ac W21<\/sub>, and \u00acS11<\/sub><\/strong> which will give the output \u00ac W11<\/sub> ^ W12<\/sub> ^ W12<\/sub>.<\/p>\n\n\n\n<\/figure>\n\n\n\n
After applying And-elimination rule to \u00ac W11<\/sub> \u2227 \u00ac W12<\/sub> \u2227 \u00ac W21<\/sub>, we will get three statements: \u00ac W11<\/sub>, \u00ac W12<\/sub>, and \u00acW21<\/sub><\/strong>.<\/p>\n\n\n\n
Apply Modus Ponens to \u00acS21<\/sub>, and R2:<\/strong><\/li><\/ul>\n\n\n\n
Now we will apply Modus Ponens to \u00acS21<\/sub> and R2 which is \u00acS21<\/sub> \u2192 \u00ac W21<\/sub> \u2227\u00ac W22<\/sub> \u2227 \u00ac W31<\/sub>, which will give the Output as \u00ac W21<\/sub> \u2227 \u00ac W22<\/sub> \u2227\u00ac W31<\/sub><\/strong><\/p>\n\n\n\n<\/figure>\n\n\n\n
Apply And -Elimination rule:<\/strong><\/li><\/ul>\n\n\n\n
Now again apply And-elimination rule to \u00ac W21<\/sub> \u2227 \u00ac W22<\/sub> \u2227\u00ac W31<\/sub><\/strong>, We will get three statements: \u00ac W21<\/sub>, \u00ac W22<\/sub>, and \u00ac W31<\/sub><\/strong>.<\/p>\n\n\n\n
Apply MP to S12<\/sub> and R4:<\/strong><\/li><\/ul>\n\n\n\n
Apply Modus Ponens to S12<\/sub><\/strong> and R4<\/sub><\/strong> which is S12<\/sub> \u2192 W13<\/sub> \u2228. W12<\/sub> \u2228. W22<\/sub> \u2228.W11<\/sub><\/strong>, we will get the output as W13<\/sub>\u2228 W12<\/sub> \u2228 W22<\/sub> \u2228.W11<\/sub><\/strong>.<\/p>\n\n\n\n<\/figure>\n\n\n\n
Apply Unit resolution on W13<\/sub> \u2228 W12<\/sub> \u2228 W22<\/sub> \u2228W11<\/sub> and \u00ac W11<\/sub> :<\/strong><\/li><\/ul>\n\n\n\n
After applying Unit resolution formula on W13<\/sub> \u2228 W12<\/sub> \u2228 W22<\/sub> \u2228W11<\/sub> and \u00ac W11<\/sub> we will get W13<\/sub> \u2228 W12<\/sub> \u2228 W22<\/sub>.<\/p>\n\n\n\n<\/figure>\n\n\n\n
Apply Unit resolution on W13<\/sub> \u2228 W12<\/sub> \u2228 W22<\/sub> and \u00ac W22<\/sub> :<\/strong><\/li><\/ul>\n\n\n\n
After applying Unit resolution on W13<\/sub> \u2228 W12<\/sub> \u2228 W22<\/sub><\/strong>, and \u00acW22<\/sub><\/strong>, we will get W13<\/sub> \u2228 W12<\/sub><\/strong> as output.<\/p>\n\n\n\n<\/figure>\n\n\n\n
Apply Unit Resolution on W13<\/sub> \u2228 W12<\/sub> and \u00ac W12<\/sub> :<\/strong><\/li><\/ul>\n\n\n\n
After Applying Unit resolution on W13<\/sub> \u2228 W12<\/sub> and \u00ac W12<\/sub><\/strong>, we will get W13<\/sub><\/strong> as an output, hence it is proved that the Wumpus is in the room [1, 3].<\/p>\n\n\n\n<\/figure>\n","protected":false},"excerpt":{"rendered":"
As in the previous topic we have learned about the wumpus world and how a knowledge-based agent evolves the world. Now in this topic, we will create a knowledge base for the wumpus world, and will derive some proves for the Wumpus-world using propositional logic. The agent starts visiting from first square [1, 1], and […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[885],"tags":[],"_links":{"self":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/2284"}],"collection":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/comments?post=2284"}],"version-history":[{"count":0,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/2284\/revisions"}],"wp:attachment":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/media?parent=2284"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/categories?post=2284"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/tags?post=2284"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
![\"Knowledge-base](\"https:\/\/static.javatpoint.com\/tutorial\/ai\/images\/ai-knowledge-base-for-wumpus-world.png\")
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