--- title: Propositional Logic description: Propositional logic is the branch of logic that studies truth-functional combinations of statements. You will understand how to construct truth tables, evaluate logical equivalence, and use inference rules to analyze the validity of arguments without analyzing internal sentence structure. category: mathematics subcategory: mathematical-logic difficulty: beginner, intermediate, advanced url: /subject/propositional-logic --- # Propositional Logic Propositional logic is the branch of logic that studies truth-functional combinations of statements. You will understand how to construct truth tables, evaluate logical equivalence, and use inference rules to analyze the validity of arguments without analyzing internal sentence structure. ## Available Resources 4 Courses • 6 Websites ## Websites ### 1. 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 ### 2. Propositional Logic (Stanford Encyclopedia of Philosophy) **Author:** Curtis Franks Peer-reviewed survey of propositional logic. Covers truth-functional completeness, decidability and SAT, axiomatic and natural deduction systems, Gentzen sequent calculi, and proofs of completeness and compactness, then turns to many-valued, intuitionistic, relevance and linear logics. Covers the deeper metatheory the topic still lacks: completeness and compactness proofs, the proof systems compared, and non-classical variants. It is the step after the textbook and course. **Difficulty:** Advanced | **Language:** English | **Price:** Free **Link:** https://plato.stanford.edu/entries/logic-propositional/ **Tags:** propositional-logic, metatheory, proof-systems, non-classical-logic, completeness-theorem ### 3. Propositional Logic (Internet Encyclopedia of Philosophy) **Author:** Kevin C. Klement Peer-reviewed encyclopedia article on truth-functional logic: the formal language, tautologies and logical equivalence, rules of inference and replacement, an axiomatic propositional calculus, and metatheoretic results including soundness, completeness and decidability, with historical context from the Stoics onward. **Difficulty:** Intermediate | **Language:** English | **Price:** Free **Link:** https://iep.utm.edu/propositional-logic-sentential-logic/ **Tags:** propositional-logic, truth-functional-logic, rules-of-inference, metatheory ### 4. Carnap — Formal Logic in the Browser **Author:** Graham Leach-Krouse, Jake Ehrlich Browser-based logic courseware that machine-checks propositional proofs line by line in Fitch, Kalish-Montague and Hardegree styles, plus truth tables, symbolization and truth trees. Instant feedback on exactly where a derivation breaks. Free and open source. Propositional logic is learned by doing proofs and being told precisely which line is wrong. Carnap is the only free tool that checks derivations across several standard proof styles rather than just evaluating truth tables, so it is the practice layer the textbooks need. **Difficulty:** Beginner | **Language:** English | **Price:** Free **Link:** https://carnap.io/ **Tags:** natural-deduction, fitch-proofs, proof-checker, truth-tables, propositional-logic ### 5. 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 ### 6. 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. Mathematics for Computer Science (MIT 6.042J) **Author:** Tom Leighton, Marten van Dijk Discrete mathematics for computer science with an emphasis on definitions and proofs: logic, induction, sets and relations, graph theory, modular arithmetic, asymptotics, counting and discrete probability. 25 lecture videos, problem sets and exams with solutions build fluency in writing proofs. **Difficulty:** Intermediate | **Price:** Free **Link:** https://ocw.mit.edu/courses/6-042j-mathematics-for-computer-science-fall-2010/ **Tags:** discrete-mathematics, mathematical-proofs, induction, graph-theory, combinatorics, discrete-probability ### 2. Stanford Introduction to Logic **Author:** Michael Genesereth, Eric Kao Free self-paced Stanford course with an online text, interactive exercises and a built-in Fitch proof editor. Covers propositional syntax and semantics, truth tables, satisfiability, validity, logical entailment and formal proofs, then moves on to relational logic. A structured course where learners get instant feedback on truth tables and proofs. It approaches logic from the computer-science side (satisfiability, entailment, circuits), which complements the philosophy angle of forall x and IEP. **Difficulty:** Beginner | **Language:** English | **Price:** Free **Link:** http://intrologic.stanford.edu/homepage/index.html **Tags:** propositional-logic, truth-tables, formal-proofs, satisfiability, relational-logic ### 3. 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 ### 4. 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 --- *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/propositional-logic