- published: 17 Apr 2007
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In mathematical logic, predicate logic is the generic term for symbolic formal systems like first-order logic, second-order logic, many-sorted logic, or infinitary logic. This formal system is distinguished from other systems in that its formulae contain variables which can be quantified. Two common quantifiers are the existential ∃ ("there exists") and universal ∀ ("for all") quantifiers. The variables could be elements in the universe under discussion, or perhaps relations or functions over that universe. For instance, an existential quantifier over a function symbol would be interpreted as modifier "there is a function". The foundations of predicate logic were developed independently by Gottlob Frege and Charles Sanders Peirce.
In informal usage, the term "predicate logic" occasionally refers to first-order logic. Some authors consider the predicate calculus to be an axiomatized form of predicate logic, and the predicate logic to be derived from an informal, more intuitive development.
Logic (from the Ancient Greek: λογική, logike) is the branch of philosophy concerned with the use and study of valid reasoning. The study of logic also features prominently in mathematics and computer science.
Logic was studied in several ancient civilizations, including Greece, India, and China. In the West, logic was established as a formal discipline by Aristotle, who gave it a fundamental place in philosophy. The study of logic was part of the classical trivium, which also included grammar and rhetoric. Logic was further extended by Al-Farabi who categorized it into two separate groups (idea and proof). Later, Avicenna revived the study of logic and developed relationship between temporalis and the implication. In the East, logic was developed by Hindus, Buddhists and Jains.
Logic is often divided into three parts: inductive reasoning, abductive reasoning, and deductive reasoning.
The concept of logical form is central to logic. The validity of an argument is determined by its logical form, not by its content. Traditional Aristotelian syllogistic logic and modern symbolic logic are examples of formal logic.
Summary of the basic symbolization forms for predicate logic. Please see www.ifpthenq.net for more info and online quizzes.
Now we're going to "upgrade" our logic to predicate logic, which lets us have a good bit more flexibility in how we describe various situations, including the use of quantifiers. http://www.polymathlectures.org/
This lecture explains how to write first order logic statements given English statements
"propositional logic" universal existential instantiation generalization "rules of inference" "mathematical deductions"
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What kind of logic can we find inside sentences? How do we calculate the meaning from what we hear? In this week's episode, we talk about predicate logic: why we need it, how it differs from sentential logic, and how we can combine it with quantifiers to capture the full meaning of our language. This is Topic #50! Wow. This week's tag language: Albanian! Watching our previous video about logic will be pretty helpful for this one: https://youtu.be/lw4ykgRtv3Q Other of our semantics and pragmatics videos: Scoping Out the Truth: http://youtu.be/XC-MGuj75zQ Clues to Meaning: http://youtu.be/N9OdeDQKnR4 The Rules of Conversation: http://youtu.be/rzxyjFHh-y8 Find us on all the social media worlds: Tumblr: http://thelingspace.tumblr.com/ Twitter: https://twitter.com/TheLingSpace Facebook: ht...
This first E-Lecture on Predicate Logic is meant as a gentle introduction. It first points out why propositional logic alone is not sufficient for the formalization of sentence meaning and then introduces the central machinery of predicate logic using several examples with which the students can practice.
This E-Lecture builds upon Predicate Logic I and discusses the main principles of quantification. Prof. Handke explains how to use and interpret the universal, the existebntial and the negative quantifier and uses several examples for illustration.
MIT 6.042J Mathematics for Computer Science, Spring 2015 View the complete course: http://ocw.mit.edu/6-042JS15 Instructor: Albert R. Meyer License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
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8 1 Predicate Logic Symbols & Translation