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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
)
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
)
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