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Propositional Logic (Internet Encyclopedia of Philosophy)

by Kevin C. Klement · Internet Encyclopedia of Philosophy, University of Tennessee at Martin

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.

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Wolfram MathWorld

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.

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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.

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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.

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Mathematics for Computer Science (MIT 6.042J)

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.

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Propositional Logic (Stanford Encyclopedia of Philosophy)

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.

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Stanford Introduction to Logic

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.

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