Logic
Notes
- Semantics involves giving meaning to logical constants in a formal way. When we talk about truth table semantics, we’re talking about a way to formally interpret (or give meaning to) sentences in the logical language using truth tables. Similarly, algebraic semantics does the same, but using algebras. Proof-theoretic semantics attempts to give meaning in terms of proof rather than truth conditions.
- Intuitionistic logic is also known as “constructive logic,” which is not a coincidence. And the Curry-Howard correspondence, which is also deeply related, connects computation to intuitionistic logic.
Links
- Teach Yourself Logic: A Study Guide
- Logic Matters
- Logic Matters Study Guide
- Gödel’s Theorems Books
- Introduction to Formal Logic
- forallx: Cambridge book - Covers both truth-functional logic and first-order logic, introducing students to semantics and to a Fitch-style natural deduction system.
- The Haskell Road to Logic, Math and Programming
- Hoare Logic: Introduction to separation logic
- Great resources on learning logic
- Many-valued logic (HN)
- An Introduction to Non-Classical Logic book
- Data Abstraction and Relational Program Logic (2020)
- Reinventing Formal Logic (2012)
- Univalence as a Principle of Logic (2016)
- POTL: A First-Order Complete Temporal Logic for Operator Precedence Languages (2019)
- Symbolic Logic (1897)
- Logic and Computation Intertwined
- An Introduction to Godel's Theorems (HN)
- Gödel Without Tears, slowly (2020) (Published book)
- Logic, Explainability and the Future of Understanding (2018)
- Finite of Sense and Infinite of Thought (2018)
- What Godel Discovered (HN)
- Logicomix: An Epic Search for Truth book (2009)
- Logic and Semantics @ Aarhus University (GitHub)
- Propositional Dynamic Logic
- λProlog: Logic programming in higher-order logic
- Dale Miller Research - Focuses on Computational Logic.
- Logical Fallacies - List of Logical Fallacies with Examples. (HN) (Reddit)
- Intensional Logic in Context – from philosophy to technology (2021)
- Open Logic Project - Open Source, Customizable, Advanced Logic Text. (Code)
- Combinators: A Centennial View (2021) (HN)
- Dana Scott: Looking Backward; Looking Forward (2018)
- Dana Scott's Research
- Retrospective review of Gödel, Escher, Bach (1996) (HN)
- Superposition for Lambda-Free Higher-Order Logic (2021)
- Logica - Modern Logic Programming. (Code) (Article) (HN)
- Per Martin Löf: How did 'judgement' come to be a term of logic? (2011)
- Clingo - Grounder and solver for logic programs. (Web)
- Specifying State Machines with Temporal Logic (2021)
- Cqfd - Why3 certified prover for the propositional logic.
- Standard Ternary Logic (2016)
- Relational - Educational tool for relational algebra.
- Logic solver in Rust
- You Can't Prove Everything That's True (2021) (Lobsters)
- Five Stages of Accepting Constructive Mathematics (2017)
- Master List of Logical Fallacies
- An Automated Approach to the Collatz Conjecture (2021)
- Designing Software with Predicate Logic (2021)
- 1931: Kurt Gödel shows limits of math, logic, computing, AI (HN)
- Abductive vs. inductive reasoning
- Zorn's Lemma, Choice, & Well-ordering (2021)
- Logical Foundations
- Logic Deduction Course
- Mathematical Circles: Russian Experience
- Ask HN: Books that teach you logic building skills (2021)
- Inductive logic programming at 30: a new introduction (2020)
- Poincaré, Heisenberg, Gödel and the limits of scientific knowledge (2013) (HN)
- Семантические аспекты интуиционистской логики (2021)
- Логика для людей (Code)
- On the unity of logic (Tweet)
- MA 210: Logic, Types and Spaces (2019) (Code)
- History of Logic
- To H.B. Curry: Essays on Combinatory Logic, Lambda Calculus and Formalism (1980)
- Thesis on the π-calculus, a formal language for distributed computing
- Gödel's Incompleteness Theorem in Bash (2022) (HN)
- Foundations of Dawn: The Untyped Multistack Concatenative Calculus (2022) (Lobsters)
- Literature for logical reasoning
- Why are you being constructive? (2022)
- The Context And The Logic (2022)
- The countable reals - Topos in which the reals are countable (2022) (Reddit)
- Surprises in Logic (2016)
- Grothendieck's Approach to Equality (2022)
- Goedel Machines: Self-Referential Universal Problem Solvers Making Provably Optimal Self-Improvements (2003)
- SHACL: A Description Logic in Disguise (2021)
- Open Logic Project (HN)
- Formalizations of Gödel's Ontological Proof of God's Existence
- Logic as algebra (Lobsters)
- Reconfigurable Asynchronous Logic Automata
- KalkulierbaR - Learning Framework for Logic Calculi. (Code)
- Confusion in the Church-Turing Thesis (2014) (Lobsters)
- ABC: System for Sequential Logic Synthesis and Formal Verification
- Separation Logic (2019) (Lobsters)
- Gödel, Escher, Bach: an in-depth explainer (HN)
- Selected Papers of Dana S. Scott
- Explanation-Gödel and Plausibility-Gödel (HN)
- Gödel’s first incompleteness theorem – an interactive tutorial (HN)
- W-types in setoids (2018) (Code)
- The Logic of Logical Necessity (2022)
- What logic can teach us, Scala programmers (2022)
- Logic at its Limit: The Grelling-Nelson Paradox (2023) (Lobsters)
- Mathematical Logic through Python
- The Temperley-Lieb categories and skein modules (2014)
- Logic and Proof
- Ask HN: What happened to fuzzy logic? (2023)