Logic & Applications
@LogicPractice
Logic and applications of logic from @JohnDCook
The linear logic connectives ⊕ and & are called additive, ⊗ and ⅋ are called multiplicative, and ! and ? are called expontential.
“When you have eliminated the impossible, whatever remains is often more improbable than your having made a mistake in one of your impossibility proofs.” -- Steven Kass
Can construct a fixed point M for a lambda term L by defining M = (λx.L(xx))(λx.L(xx)).
Every lambda term L has a fixed point. That is, for every lambda term L there exists a term M such that LM is β-convertible to M.
'Logic has turned out to be significantly more effective in computer science than it has been in mathematics.' cs.rice.edu/~vardi/papers/… [pdf]
Following an idea to its logical conclusion johndcook.com/blog/2018/12/1…
Boole’s expansion theorem en.wikipedia.org/wiki/Boole%27s…
Lambda calculi with types home.ttic.edu/~dreyer/course… [193-page PDF]
Gödel's compactness theorem: A first order theory T is satisfiable iff every finite subset of T is satisfiable.
When Howard met Curry antitypical.com/posts/2021-07-…
Logic symbols: Unicode, HTML entities, and LaTeX commands johndcook.com/blog/logic-sym…
Peirce's law: ((P => Q) => P) => P. Holds in classical logic but not intuitionistic logic.
Proof General: Emacs front end for proof assistants proofgeneral.github.io
Three reasons TLA+ is hard to learn surfingcomplexity.blog/2018/12/24/tla…
'A proof tells us where to concentrate our doubts.” — Morris Kline
Typesetting modal logic johndcook.com/blog/2018/10/2…
Logic and linear algebra arxiv.org/abs/1407.2650