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Logic & Applications

@LogicPractice

Logic and applications of logic from @JohnDCook

 Houston, TX
JohnDCook.com/logic
Joined September 2016
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Big logic johndcook.com/blog/applied-l…
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“I wish my wish would not be granted!” — Douglas Hofstadter
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Intuitionistic implication A ⇒ B can be represented in linear logic as !A ⊸ B.
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Gödel proved in 1932 that intuitionistic logic has no interpretation as a finite-valued logic. The proof was only two pages long.
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A Timeline for Logic, λ-Calculus, and Programming Language Theory by Dana Scott fm.csl.sri.com/SSFT15/Timeli… [pdf]
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Understanding SAT by Implementing a Simple SAT Solver in Python sahandsaba.com/understanding…

Understanding SAT by Implementing a Simple SAT Solver in Python

SAT is often described as the "mother of all NP-complete problems." This post goes over what SAT is and why it is considered to be so important. A simple SAT solver is implemented using Python in the...

sahandsaba.com
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Linear logic analogies to arithmetic johndcook.com/blog/2022/01/1…

Linear logic additive, multiplicative, and exponential

Why are linear logic operators called additive, multiplicative, and exponential? Why are some called positive and some negative?

johndcook.com
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“Computer-aided cryptography is an active area of research that develops and applies formal, machine-checkable approaches to the design, analysis, and implementation of cryptography.” eprint.iacr.org/2019/1393
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An order preserving map on a complete lattice has a fixed point.
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Continuum hypothesis -- whether there a set with cardinality greater than the integers and less than the reals -- is independent of ZFC.
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Seven normal forms in logic johndcook.com/blog/seven-nor…

Logic normal forms negation, conjunction, Skolem, Blake, etc

This post discusses seven normal forms: Negation normal form Conjunctive normal form Disjunctive normal form Algebraic normal form Prefix normal form Skolem normal form Blake canonical form The photo...

johndcook.com
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All human beings are different. All apathetic people are indifferent. Therefore, no apathetic people are human beings. -- Solomon Golomb
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Kurt Godel Created a hurdle For the truths of a system: You just can't list 'em! -- Steven Cushing
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The equivalence A ≡ B in linear logic means the formula (A ⊸ B) & (B ⊸ A) is derivable.
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Software Foundations cis.upenn.edu/~bcpierce/sf/c… #coq
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'You can sway a thousand men by appealing to their prejudices quicker than you can convince one man by logic.' -- Robert A. Heinlein
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How much can Boolean expressions be simplified? johndcook.com/blog/2020/11/1…

How much does Boolean expression minimization shorten?

If you have a Boolean function with n variables, how long can a minimized version of the expression be? How much does minimization save?

johndcook.com
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Logic & Applications retweeted
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little grey mouse 🐭@mouse_mathOct 13
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'Logic, like whiskey, loses its beneficial effect when taken in too large quantities.' -- Edward Plunkett
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Where did combinators come from? writings.stephenwolfram.com/…
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TLA: Temporal Logic of Actions research.microsoft.com/en-us…
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