--- title: Predicate Logic description: Predicate logic, or first-order logic, extends propositional logic by incorporating quantifiers and variables to express complex relationships. You will understand how to formalize mathematical statements, construct proofs, and analyze the validity of arguments containing quantifiers. category: mathematics subcategory: mathematical-logic difficulty: beginner, intermediate, advanced url: /subject/predicate-logic --- # Predicate Logic Predicate logic, or first-order logic, extends propositional logic by incorporating quantifiers and variables to express complex relationships. You will understand how to formalize mathematical statements, construct proofs, and analyze the validity of arguments containing quantifiers. ## Available Resources 1 Books • 2 Courses • 4 Websites ## Websites ### 1. Stanford Encyclopedia of Philosophy - Classical Logic Stanford Encyclopedia of Philosophy entry presenting classical first-order logic: its formal language, a natural-deduction proof system, model-theoretic semantics, and the soundness, completeness and compactness theorems. Readers come away understanding how syntax and semantics of predicate logic relate. **Difficulty:** Beginner | **Price:** Free **Link:** https://plato.stanford.edu/entries/logic-classical/ **Tags:** predicate-logic, first-order-logic, model-theory, completeness-theorem, philosophy-of-logic ### 2. forall x Open Logic Project Free open-licensed textbook from the Open Logic Project, based on P.D. Magnus's forall x, teaching formal logic from truth-functional logic through first-order predicate logic, with natural deduction, translation exercises and semantics. Readers learn to symbolize English arguments and construct formal proofs. **Difficulty:** Beginner | **Price:** Free **Link:** https://forallx.openlogicproject.org/ **Tags:** predicate-logic, formal-logic, natural-deduction, truth-functional-logic, open-textbook ### 3. Wolfram MathWorld **Author:** Eric W. Weisstein MathWorld is an online mathematics encyclopedia from Wolfram Research offering detailed, browsable articles on topics across the math spectrum, including algebra, geometry, calculus, and number theory. Each entry includes definitions, theorems, formulas, diagrams, worked examples, and links to further reading. **Difficulty:** Intermediate | **Language:** English | **Price:** Free **Link:** https://mathworld.wolfram.com **Tags:** mathematics-reference, encyclopedia, abstract-algebra, number-theory, geometry ### 4. plato.stanford.edu The Stanford Encyclopedia of Philosophy is a peer‑reviewed online encyclopedia of philosophy featuring in‑depth, scholarly articles written and regularly updated by experts, including comprehensive coverage of logic topics. **Difficulty:** Intermediate | **Language:** English | **Price:** Free **Link:** https://plato.stanford.edu **Tags:** websites, mathematics-statistics, discrete-math ## Courses ### 1. Introduction to Logic This course is an introduction to Logic from a computational perspective. It shows how to encode information in the form of logical sentences; it shows how to reason with information in this form; and it provides an overview of logic technology and its applications - in mathematics, science, engineering, business, law, and so forth. **Difficulty:** Beginner | **Language:** English | **Duration:** 10 weeks of study, 4-8 hours/week | **Price:** Free **Link:** https://www.coursera.org/learn/logic-introduction **Tags:** courses, mathematics-statistics, discrete-math ### 2. Logic for Computer Science A Coursera course from BITS Pilani on computational logic: propositional and predicate logic, natural deduction, soundness and completeness, undecidability, LTL and CTL model checking, and Floyd-Hoare program verification. Learners can write formal proofs and verify properties of algorithms and systems. **Difficulty:** Intermediate | **Language:** English | **Price:** Free **Link:** https://www.coursera.org/learn/bits-logic-for-computer-science **Tags:** propositional-logic, predicate-logic, model-checking, temporal-logic, hoare-logic, program-verification ## Books ### 1. A Concise Introduction to Logic **Author:** Patrick J. Hurley Standard introductory logic textbook covering arguments and fallacies, categorical syllogisms, propositional logic with natural deduction, and predicate logic with quantifiers and relations. Readers learn to translate English statements into symbolic form and prove validity using quantifier rules. **Difficulty:** Intermediate | **Language:** English | **Price:** Paid **Link:** https://www.amazon.com/dp/0534585051?tag=edmonddante07-20 **Tags:** books, mathematics-statistics, mathematical-logic --- *This content is part of Dantes.io - Your Treasure Map to Knowledge* *Curated by humans at Dantes.io. Personal study use welcome; republishing this curation requires permission (team@dantes.io).* View this page online: https://dantes.io/subject/predicate-logic