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)