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Logic
Notes
β
Semantics involves giving meaning to logical constants in a formal way. When we talk about truth table semantics, weβre 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.
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Intuitionistic logic is also known as βconstructive logic,β which is not a coincidence. And the Curry-Howard correspondence, which is also deeply related, connects computation to intuitionistic logic.
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Links
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Teach Yourself Logic: A Study Guide
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Logic Matters
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Logic Matters Study Guide
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GΓΆdelβs Theorems Books
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Introduction to Formal Logic
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forallx: Cambridge book
- Covers both truth-functional logic and first-order logic, introducing students to semantics and to a Fitch-style natural deduction system.
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The Haskell Road to Logic, Math and Programming
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Hoare Logic: Introduction to separation logic
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Great resources on learning logic
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Many-valued logic
(
HN
)
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An Introduction to Non-Classical Logic book
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Data Abstraction and Relational Program Logic (2020)
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Reinventing Formal Logic (2012)
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Univalence as a Principle of Logic (2016)
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POTL: A First-Order Complete Temporal Logic for Operator Precedence Languages (2019)
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Symbolic Logic (1897)
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Logic and Computation Intertwined
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An Introduction to Godel's Theorems
(
HN
)
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GΓΆdel Without Tears, slowly (2020)
(
Published book
)
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Logic, Explainability and the Future of Understanding (2018)
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Finite of Sense and Infinite of Thought (2018)
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What Godel Discovered
(
HN
)
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Logicomix: An Epic Search for Truth book (2009)
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Logic and Semantics @ Aarhus University
(
GitHub
)
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Propositional Dynamic Logic
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Ξ»Prolog: Logic programming in higher-order logic
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Dale Miller Research
- Focuses on Computational Logic.
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Logical Fallacies
- List of Logical Fallacies with Examples. (
HN
) (
Reddit
)
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Intensional Logic in Context β from philosophy to technology (2021)
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Open Logic Project
- Open Source, Customizable, Advanced Logic Text. (
Code
)
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Combinators: A Centennial View (2021)
(
HN
)
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Dana Scott: Looking Backward; Looking Forward (2018)
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Dana Scott's Research
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Retrospective review of GΓΆdel, Escher, Bach (1996)
(
HN
)
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Superposition for Lambda-Free Higher-Order Logic (2021)
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Logica
- Modern Logic Programming. (
Code
) (
Article
) (
HN
)
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Per Martin LΓΆf: How did 'judgement' come to be a term of logic? (2011)
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Clingo
- Grounder and solver for logic programs. (
Web
)
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Specifying State Machines with Temporal Logic (2021)
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Cqfd
- Why3 certified prover for the propositional logic.
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Standard Ternary Logic (2016)
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Relational
- Educational tool for relational algebra.
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Logic solver in Rust
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You Can't Prove Everything That's True (2021)
(
Lobsters
)
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Five Stages of Accepting Constructive Mathematics (2017)
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Master List of Logical Fallacies
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An Automated Approach to the Collatz Conjecture (2021)
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Designing Software with Predicate Logic (2021)
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1931: Kurt GΓΆdel shows limits of math, logic, computing, AI
(
HN
)
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Abductive vs. inductive reasoning
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Zorn's Lemma, Choice, & Well-ordering (2021)
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Logical Foundations
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Logic Deduction Course
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Mathematical Circles: Russian Experience
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Ask HN: Books that teach you logic building skills (2021)
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Inductive logic programming at 30: a new introduction (2020)
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PoincarΓ©, Heisenberg, GΓΆdel and the limits of scientific knowledge (2013)
(
HN
)
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Π‘Π΅ΠΌΠ°Π½ΡΠΈΡΠ΅ΡΠΊΠΈΠ΅ Π°ΡΠΏΠ΅ΠΊΡΡ ΠΈΠ½ΡΡΠΈΡΠΈΠΎΠ½ΠΈΡΡΡΠΊΠΎΠΉ Π»ΠΎΠ³ΠΈΠΊΠΈ (2021)
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ΠΠΎΠ³ΠΈΠΊΠ° Π΄Π»Ρ Π»ΡΠ΄Π΅ΠΉ
(
Code
)
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On the unity of logic
(
Tweet
)
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MA 210: Logic, Types and Spaces (2019)
(
Code
)
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History of Logic
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To H.B. Curry: Essays on Combinatory Logic, Lambda Calculus and Formalism (1980)
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