{"id":2280,"date":"2022-04-15T12:05:30","date_gmt":"2022-04-15T12:05:30","guid":{"rendered":"https:\/\/mdr.foobrdigital.com\/?p=2280"},"modified":"2022-04-15T12:05:30","modified_gmt":"2022-04-15T12:05:30","slug":"rules-of-inference-in-artificial-intelligence","status":"publish","type":"post","link":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/2022\/04\/15\/rules-of-inference-in-artificial-intelligence\/","title":{"rendered":"Rules of Inference in Artificial intelligence"},"content":{"rendered":"\n<h2 class=\"wp-block-heading\">Inference:<\/h2>\n\n\n\n<p>In artificial intelligence, we need intelligent computers which can create new logic from old logic or by evidence,&nbsp;<strong>so generating the conclusions from evidence and facts is termed as Inference<\/strong>.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Inference rules:<\/h2>\n\n\n\n<p>Inference rules are the templates for generating valid arguments. Inference rules are applied to derive proofs in artificial intelligence, and the proof is a sequence of the conclusion that leads to the desired goal.<\/p>\n\n\n\n<p>In inference rules, the implication among all the connectives plays an important role. Following are some terminologies related to inference rules:<\/p>\n\n\n\n<ul><li><strong>Implication:<\/strong>&nbsp;It is one of the logical connectives which can be represented as P \u2192 Q. It is a Boolean expression.<\/li><li><strong>Converse:<\/strong>&nbsp;The converse of implication, which means the right-hand side proposition goes to the left-hand side and vice-versa. It can be written as Q \u2192 P.<\/li><li><strong>Contrapositive:<\/strong>&nbsp;The negation of converse is termed as contrapositive, and it can be represented as \u00ac Q \u2192 \u00ac P.<\/li><li><strong>Inverse:<\/strong>&nbsp;The negation of implication is called inverse. It can be represented as \u00ac P \u2192 \u00ac Q.<\/li><\/ul>\n\n\n\n<p>From the above term some of the compound statements are equivalent to each other, which we can prove using truth table:<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/static.javatpoint.com\/tutorial\/ai\/images\/rules-of-inference-in-ai.png\" alt=\"Rules of Inference in Artificial intelligence\"\/><\/figure>\n\n\n\n<p>Hence from the above truth table, we can prove that P \u2192 Q is equivalent to \u00ac Q \u2192 \u00ac P, and Q\u2192 P is equivalent to \u00ac P \u2192 \u00ac Q.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Types of Inference rules:<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">1. Modus Ponens:<\/h3>\n\n\n\n<p>The Modus Ponens rule is one of the most important rules of inference, and it states that if P and P \u2192 Q is true, then we can infer that Q will be true. It can be represented as:<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/static.javatpoint.com\/tutorial\/ai\/images\/rules-of-inference-in-ai2.png\" alt=\"Rules of Inference in Artificial intelligence\"\/><\/figure>\n\n\n\n<p><strong>Example:<\/strong><\/p>\n\n\n\n<p>Statement-1: &#8220;If I am sleepy then I go to bed&#8221; ==&gt; P\u2192 Q<br>Statement-2: &#8220;I am sleepy&#8221; ==&gt; P<br>Conclusion: &#8220;I go to bed.&#8221; ==&gt; Q.<br>Hence, we can say that, if P\u2192 Q is true and P is true then Q will be true.<\/p>\n\n\n\n<p><strong>Proof by Truth table:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/static.javatpoint.com\/tutorial\/ai\/images\/rules-of-inference-in-ai3.png\" alt=\"Rules of Inference in Artificial intelligence\"\/><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">2. Modus Tollens:<\/h3>\n\n\n\n<p>The Modus Tollens rule state that if P\u2192 Q is true and&nbsp;<strong>\u00ac Q is true, then \u00ac P<\/strong>&nbsp;will also true. It can be represented as:<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/static.javatpoint.com\/tutorial\/ai\/images\/rules-of-inference-in-ai4.png\" alt=\"Rules of Inference in Artificial intelligence\"\/><\/figure>\n\n\n\n<p><strong>Statement-1:<\/strong>&nbsp;&#8220;If I am sleepy then I go to bed&#8221; ==&gt; P\u2192 Q<br><strong>Statement-2:<\/strong>&nbsp;&#8220;I do not go to the bed.&#8221;==&gt; ~Q<br><strong>Statement-3:<\/strong>&nbsp;Which infers that &#8220;<strong>I am not sleepy<\/strong>&#8221; =&gt; ~P<\/p>\n\n\n\n<p><strong>Proof by Truth table:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/static.javatpoint.com\/tutorial\/ai\/images\/rules-of-inference-in-ai5.png\" alt=\"Rules of Inference in Artificial intelligence\"\/><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">3. Hypothetical Syllogism:<\/h3>\n\n\n\n<p>The Hypothetical Syllogism rule state that if P\u2192R is true whenever P\u2192Q is true, and Q\u2192R is true. It can be represented as the following notation:<\/p>\n\n\n\n<p><strong>Example:<\/strong><\/p>\n\n\n\n<p><strong>Statement-1:<\/strong>&nbsp;If you have my home key then you can unlock my home.&nbsp;<strong>P\u2192Q<\/strong><br><strong>Statement-2:<\/strong>&nbsp;If you can unlock my home then you can take my money.&nbsp;<strong>Q\u2192R<\/strong><br><strong>Conclusion:<\/strong>&nbsp;If you have my home key then you can take my money.&nbsp;<strong>P\u2192R<\/strong><\/p>\n\n\n\n<p><strong><u>Proof by truth table:<\/u><\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/static.javatpoint.com\/tutorial\/ai\/images\/rules-of-inference-in-ai6.png\" alt=\"Rules of Inference in Artificial intelligence\"\/><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">4. Disjunctive Syllogism:<\/h3>\n\n\n\n<p>The Disjunctive syllogism rule state that if P\u2228Q is true, and \u00acP is true, then Q will be true. It can be represented as:<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/static.javatpoint.com\/tutorial\/ai\/images\/rules-of-inference-in-ai7.png\" alt=\"Rules of Inference in Artificial intelligence\"\/><\/figure>\n\n\n\n<p><strong>Example:<\/strong><\/p>\n\n\n\n<p><strong>Statement-1:<\/strong>&nbsp;Today is Sunday or Monday. ==&gt;P\u2228Q<br><strong>Statement-2:<\/strong>&nbsp;Today is not Sunday. ==&gt; \u00acP<br><strong>Conclusion:<\/strong>&nbsp;Today is Monday. ==&gt; Q<\/p>\n\n\n\n<p><strong>Proof by truth-table:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/static.javatpoint.com\/tutorial\/ai\/images\/rules-of-inference-in-ai8.png\" alt=\"Rules of Inference in Artificial intelligence\"\/><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">5. Addition:<\/h3>\n\n\n\n<p>The Addition rule is one the common inference rule, and it states that If P is true, then P\u2228Q will be true.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/static.javatpoint.com\/tutorial\/ai\/images\/rules-of-inference-in-ai9.png\" alt=\"Rules of Inference in Artificial intelligence\"\/><\/figure>\n\n\n\n<p><strong>Example:<\/strong><\/p>\n\n\n\n<p><strong>Statement:<\/strong>&nbsp;I have a vanilla ice-cream. ==&gt; P<br><strong>Statement-2:<\/strong>&nbsp;I have Chocolate ice-cream.<br><strong>Conclusion:<\/strong>&nbsp;I have vanilla or chocolate ice-cream. ==&gt; (P\u2228Q)<\/p>\n\n\n\n<p><strong>Proof by Truth-Table:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/static.javatpoint.com\/tutorial\/ai\/images\/rules-of-inference-in-ai10.png\" alt=\"Rules of Inference in Artificial intelligence\"\/><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">6. Simplification:<\/h3>\n\n\n\n<p>The simplification rule state that if&nbsp;<strong>P\u2227 Q<\/strong>&nbsp;is true, then&nbsp;<strong>Q or P<\/strong>&nbsp;will also be true. It can be represented as:<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/static.javatpoint.com\/tutorial\/ai\/images\/rules-of-inference-in-ai11.png\" alt=\"Rules of Inference in Artificial intelligence\"\/><\/figure>\n\n\n\n<p><strong>Proof by Truth-Table:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/static.javatpoint.com\/tutorial\/ai\/images\/rules-of-inference-in-ai12.png\" alt=\"Rules of Inference in Artificial intelligence\"\/><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">7. Resolution:<\/h3>\n\n\n\n<p>The Resolution rule state that if P\u2228Q and \u00ac P\u2227R is true, then Q\u2228R will also be true.&nbsp;<strong>It can be represented as<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/static.javatpoint.com\/tutorial\/ai\/images\/rules-of-inference-in-ai13.png\" alt=\"Rules of Inference in Artificial intelligence\"\/><\/figure>\n\n\n\n<p><strong>Proof by Truth-Table:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/static.javatpoint.com\/tutorial\/ai\/images\/rules-of-inference-in-ai14.png\" alt=\"Rules of Inference in Artificial intelligence\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Inference: In artificial intelligence, we need intelligent computers which can create new logic from old logic or by evidence,&nbsp;so generating the conclusions from evidence and facts is termed as Inference. Inference rules: Inference rules are the templates for generating valid arguments. Inference rules are applied to derive proofs in artificial intelligence, and the proof is [&hellip;]<\/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\/2280"}],"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=2280"}],"version-history":[{"count":0,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/2280\/revisions"}],"wp:attachment":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/media?parent=2280"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/categories?post=2280"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/tags?post=2280"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}