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    Rule of Inference: Fundamentals and Applications
    Rule of Inference: Fundamentals and Applications
    Rule of Inference: Fundamentals and Applications
    Ebook65 pages33 minutesArtificial Intelligence

    Rule of Inference: Fundamentals and Applications

    By Fouad Sabry

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    About this ebook

    What Is Rule of Inference


    In the field of logic, a rule of inference, inference rule, or transformation rule is a logical form that consists of a function that takes premises, analyzes their syntax, and produces a conclusion. Other names for this type of rule include rule of inference, rule of transformation, and rule of inference. For instance, the rule of inference known as modus ponens starts with two premises, the first of which is of the form "If p then q," and the second of which is of the form "p," and then it draws the conclusion "q." In accordance with the semantics of traditional logic, the rule is sound in the sense that if the premises are accurate, then the conclusion must also be accurate.


    How You Will Benefit


    (I) Insights, and validations about the following topics:


    Chapter 1: Rule of Inference


    Chapter 2: Modus Ponens


    Chapter 3: Modus Tollens


    Chapter 4: Disjunctive Syllogism


    Chapter 5: Immediate Inference


    Chapter 6: Hypothetical Syllogism


    Chapter 7: Constructive Dilemma


    Chapter 8: Destructive Dilemma


    Chapter 9: Biconditional Introduction


    Chapter 10: Biconditional Elimination


    (II) Answering the public top questions about rule of inference.


    (III) Real world examples for the usage of rule of inference in many fields.


    (IV) 17 appendices to explain, briefly, 266 emerging technologies in each industry to have 360-degree full understanding of rule of inference' technologies.


    Who This Book Is For


    Professionals, undergraduate and graduate students, enthusiasts, hobbyists, and those who want to go beyond basic knowledge or information for any kind of rule of inference.

    LanguageEnglish
    PublisherOne Billion Knowledgeable
    Release dateJun 29, 2023
    Rule of Inference: Fundamentals and Applications

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      Book preview

      Rule of Inference - Fouad Sabry

      Chapter 1: Rule of inference

      A rule of inference, also known as an inference rule or transformation rule, is a kind of logical form that may be found in the philosophy of logic. This form consists of a function that accepts premises, examines their syntax, and then provides a conclusion (or conclusions). For instance, the rule of inference known as modus ponens starts with two premises, the first of which is of the form If p then q, and the second of which is of the form p, and then it draws the conclusion q. The rule is sound with regard to the semantics of classical logic (in addition to the semantics of a great number of other non-classical logics), in the sense that if the premises are true (according to an interpretation), then the conclusion is also true.

      Typically, The truth may be preserved via a rule of inference, a characteristic that relates to meaning.

      In the logic of multiple values, it keeps a broad designation.

      On the other hand, the operation of a rule of inference is entirely syntactic, in addition, it is not required to maintain any semantic properties: A rule of inference may be established using any function that goes from sets of formulas to formulae.

      In most cases, only recursive rules should be considered relevant; i.e.

      rules in such a way that there is an efficient technique for assessing whether or not a certain formula is the conclusion of a particular set of formulas according to the rule.

      An example of a rule that is not effective in this sense is the infinitary ω-rule.

      In propositional logic, the principles of inference known as modus ponens, modus tollens, and contraposition are three of the most common. In first-order predicate logic, the treatment of logical quantifiers is handled by the application of rules of inference.

      In formal logic, as well as many other fields closely connected to it, rules of inference are often presented in the standard form shown below:

      Premise#1Premise#2...Premise#nConclusion

      The meaning of this term is that anytime, in the process of some logical deduction, the supplied premises have been acquired, the conclusion that was indicated may also be assumed to be true. The real environment in which the derivations are being carried out dictates the precise formal language that is utilized to explain both the premises and the conclusions. In a simple scenario, one might make use of logical equations like in:

      A\to B\underline {A\quad \quad \quad }\,\!B\!

      In propositional logic, this is referred to as the modus ponens rule. Inference rules are often presented in the form of schemata that make use of metavariables. In the rule (schema) that was just shown, the metavariables A and B may be instantiated to any part of the universe (or sometimes, by convention, a limited subset like propositions), which allows for

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