Logic & Applications @LogicPractice Twitter profile

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Logic & Applications

@LogicPractice

2 years

Big logic

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Logic & Applications

@LogicPractice

1 year

When a logician receives a wedding invitation

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Logic & Applications

@LogicPractice

1 year

"What is a tautology?" "A tautology is a tautology."

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@LogicPractice

3 years

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Logic & Applications

@LogicPractice

2 years

Ran across an author who says “precisely when” rather than “if and only if.” I kinda like that.

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Logic & Applications

@LogicPractice

1 year

Gödel's completeness theorem (1929) isn't as famous as his incompleteness theorem (1931).

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Logic & Applications

@LogicPractice

2 years

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Logic & Applications

@LogicPractice

11 months

'Ex falso quodlibet.' From a false assumption, anything follows.

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Logic & Applications

@LogicPractice

2 years

Gödel's completeness theorem (1929) isn't as famous as his incompleteness theorem (1931).

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Logic & Applications

@LogicPractice

8 years

"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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Logic & Applications

@LogicPractice

1 year

All consistent axiomatic formulations of number theory include undecideable propositions. -- Kurt Gödel

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Logic & Applications

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8 years

"Logic has turned out to be signiﬁciantly more effective in computer science than it has been in mathematics."

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Logic & Applications

@LogicPractice

1 year

'Logic has turned out to be significantly more effective in computer science than it has been in mathematics.' [pdf]

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Logic & Applications

@LogicPractice

8 years

Tarski's undefinability theorem

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Logic & Applications

@LogicPractice

2 years

“One should never try to prove anything that is not almost obvious.” ― Alexander Grothendieck

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Logic & Applications

@LogicPractice

11 months

Modal logic axiom cube

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Logic & Applications

@LogicPractice

4 years

Q: How many modal logicians does it take to change a lightbulb? A: In which world?

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Logic & Applications

@LogicPractice

1 year

Gödel's compactness theorem: A first order theory T is satisfiable iff every finite subset of T is satisfiable.

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Logic & Applications

@LogicPractice

1 year

'Induction makes you feel guilty for getting something out of nothing ... but it is one of the greatest ideas of civilization.' -- Herbert Wilf

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Logic & Applications

@LogicPractice

1 year

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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Logic & Applications

@LogicPractice

1 year

Peirce's law: ((P => Q) => P) => P. Holds in classical logic but not intuitionistic logic.

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Logic & Applications

@LogicPractice

3 years

'Logic has turned out to be significantly more effective in computer science than it has been in mathematics.' [pdf]

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Logic & Applications

@LogicPractice

11 months

'It requires a very unusual mind to undertake the analysis of the obvious.' -- Alfred North Whitehead

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Logic & Applications

@LogicPractice

2 years

“It wouild be very discouraging if somewhere down the line you could ask a computer if the Riemann hypothesis is correct and it said, `Yes, it is true, but you won’t be able to understand the proof.’” — Ronald Graham

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Logic & Applications

@LogicPractice

1 year

“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

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Logic & Applications

@LogicPractice

11 months

“It is not easy, and perhaps not even useful, to explain briefly what logic is.' -- E. J. Lemmon

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Logic & Applications

@LogicPractice

2 years

"No science can defend its own first principles." -- Aristotle (384–322 BC)

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Logic & Applications

@LogicPractice

1 year

Incomplete and Utter Introduction to Modal Logic

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Logic & Applications

@LogicPractice

6 years

An introduction to existential types

An Introduction to Existential Types

Parametric polymorphism is now widely known in the programming community (often by the alternate name generics). They allow one to create…

stephenebly.medium.com

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Logic & Applications

@LogicPractice

1 year

Logic and linear algebra

Logic and linear algebra: an introduction

We give an introduction to logic tailored for algebraists, explaining how proofs in linear logic can be viewed as algorithms for constructing morphisms in symmetric closed monoidal categories with...

arxiv.org

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Logic & Applications

@LogicPractice

1 year

'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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Logic & Applications

@LogicPractice

1 year

'Logic, like whiskey, loses its beneficial effect when taken in too large quantities.' -- Edward Plunkett

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Logic & Applications

@LogicPractice

1 year

'A proof tells us where to concentrate our doubts.” — Morris Kline

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Logic & Applications

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2 years

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Logic & Applications

@LogicPractice

3 years

The linear logic connectives ⊕ and & are called additive, ⊗ and ⅋ are called ``multiplicative,'' and ! and ? are called ``expontentials.'' The equations below are analogous to the equation exp(a + b) = exp(a) exp(b).

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Logic & Applications

@LogicPractice

2 years

'Induction makes you feel guilty for getting something out of nothing ... but it is one of the greatest ideas of civilization.' -- Herbert Wilf

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Logic & Applications

@LogicPractice

4 years

"Logic, like whiskey, loses its beneficial effect when taken in too large quantities." Edward Plunkett

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Logic & Applications

@LogicPractice

3 years

Logic gate symbols for AND, OR, and XOR on top row. Their negations NAND, NOR, and XNOR on bottom row.

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Logic & Applications

@LogicPractice

1 year

Introduction to Categories and Categorical Logic

The aim of these notes is to provide a succinct, accessible introduction to some of the basic ideas of category theory and categorical logic. The notes are based on a lecture course given at...

arxiv.org

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Logic & Applications

@LogicPractice

5 years

"It requires a very unusual mind to undertake the analysis of the obvious." -- Alfred North Whitehead

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Logic & Applications

@LogicPractice

3 years

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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Logic & Applications

@LogicPractice

3 years

Logicians put their assumptions on the left side of a turnstile symbol. Statisticians put their assumptions on the right side of a vertical bar.

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Logic & Applications

@LogicPractice

4 years

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Logic & Applications

@LogicPractice

2 years

Introduction to Categories and Categorical Logic

The aim of these notes is to provide a succinct, accessible introduction to some of the basic ideas of category theory and categorical logic. The notes are based on a lecture course given at...

arxiv.org

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Logic & Applications

@LogicPractice

3 years

Gödel's compactness theorem: A first order theory T is satisfiable iff every finite subset of T is satisfiable.

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Logic & Applications

@LogicPractice

2 years

“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

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Logic & Applications

@LogicPractice

1 year

Glivenko's theorem: If φ is a propositional formula, then φ is a classical tautology if and only if ¬ ¬ φ is an intuitionistic tautology.

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Logic & Applications

@LogicPractice

5 years

'Ex falso quodlibet.' From a false assumption, anything follows.

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Logic & Applications

@LogicPractice

2 years

The linear logic connectives ! and ? are pronounced 'of course' and 'why not'.

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Logic & Applications

@LogicPractice

5 years

'Informal proofs are algorithms; formal proofs are code.'

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Logic & Applications

@LogicPractice

3 years

“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

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Logic & Applications

@LogicPractice

6 years

"Logic has turned out to be significantly more effective in computer science than it has been in mathematics." [pdf]

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Logic & Applications

@LogicPractice

1 year

The linear logic connectives ! and ? are pronounced 'of course' and 'why not'.

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Logic & Applications

@LogicPractice

3 years

Glivenko's theorem: If φ is a propositional formula, then φ is a classical tautology if and only if ¬ ¬ φ is an intuitionistic tautology.

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Logic & Applications

@LogicPractice

3 years

“One should never try to prove anything that is not almost obvious.” ― Alexander Grothendieck

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Logic & Applications

@LogicPractice

11 months

Classic papers in programming languages and logic

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Logic & Applications

@LogicPractice

3 years

'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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Logic & Applications

@LogicPractice

7 years

“Before functorality, people lived in caves.” -- B. Conrad Category theory is a great source of arrogant quotes, sometimes tongue-in-cheek.

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Logic & Applications

@LogicPractice

2 years

Gödel's completeness theorem (1929) isn't as famous as his incompleteness theorem (1931).

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Logic & Applications

@LogicPractice

7 years

'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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Logic & Applications

@LogicPractice

2 years

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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Logic & Applications

@LogicPractice

3 years

'Ex falso quodlibet.' From a false assumption, anything follows.

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Logic & Applications

@LogicPractice

1 year

The Algebra of Logic

The Algebra of Logic by Louis Couturat

Free kindle book and epub digitized and proofread by volunteers.

gutenberg.org

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Logic & Applications

@LogicPractice

2 years

'It requires a very unusual mind to undertake the analysis of the obvious.' -- Alfred North Whitehead

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Logic & Applications

@LogicPractice

1 year

Kurt Gödel Created a hurdle For the truths of a system: You just can't list 'em! -- Steven Cushing

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@LogicPractice

8 years

Hacker-Proof Code

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@LogicPractice

3 years

Linear logic analogies to arithmetic

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Logic & Applications

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2 years

'Every good idea will be discovered twice: once by a logician and once by a computer scientist.' -- @PhilipWadler

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Logic & Applications

@LogicPractice

11 months

In linear logic, the implication A -> B can be read 'consuming A produces B.' Sometimes written with the 'lollipop' symbol for linear implication.

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Logic & Applications

@LogicPractice

3 years

“Attempts to form social judgments by aggregating individual expressed preferences always lead to the possibility of paradox.” — Kenneth Arrow

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Logic & Applications

@LogicPractice

10 months

'Logic, like whiskey, loses its beneficial effect when taken in too large quantities.' -- Edward Plunkett

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Logic & Applications

@LogicPractice

2 years

'A proof tells us where to concentrate our doubts.” — Morris Kline

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Logic & Applications

@LogicPractice

7 years

Ask three modal logicians what modal logic is, and you are likely to get at least three different answers. -- Blackburn et al

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Logic & Applications

@LogicPractice

6 years

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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Logic & Applications

@LogicPractice

8 years

'Informal proofs are algorithms; formal proofs are code.'

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Logic & Applications

@LogicPractice

2 years

'Induction makes you feel guilty for getting something out of nothing ... but it is one of the greatest ideas of civilization.' -- Herbert Wilf

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Logic & Applications

@LogicPractice

1 year

History of modal logic [pdf]

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2 years

Karnaugh maps are a way to simplify boolean algebra expressions.

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8 years

Formal verification and The Martian

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Logic & Applications

@LogicPractice

5 years

“I wish my wish would not be granted!” — Douglas Hofstadter

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Logic & Applications

@LogicPractice

5 years

'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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1 year

A Timeline for Logic, λ-Calculus, and Programming Language Theory by Dana Scott [pdf]

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5 years

Gödel, Leibniz, and God

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Logic & Applications

@LogicPractice

2 years

'Logic, like whiskey, loses its beneficial effect when taken in too large quantities.' -- Edward Plunkett

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Logic & Applications

@LogicPractice

2 years

Peirce's law: ((P => Q) => P) => P. Holds in classical logic but not intuitionistic logic.

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Logic & Applications

@LogicPractice

5 years

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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Logic & Applications

@LogicPractice

1 year

The halting problem: You cannot write a program that can tell whether an arbitrary program will complete or run forever.

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Logic & Applications

@LogicPractice

6 years

Logic in Computer Science, Engineering and Industry

Yuri Gurevich, Microsoft Researchhttps://simons.berkeley.edu/talks/yuri-gurevich-11-10-2016{Symmetry, Logic, Computation}

www.youtube.com

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Logic & Applications

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11 months

Logic in physical form

Insight 1: Logic in Physical Form

Learn More:- Professor Carver Mead: http://carvermead.caltech.edu/- Carver Mead Channel: https://www.youtube.com/channel/UCPZvrtffxEZ7KZQ9dYCG0xg

www.youtube.com

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@LogicPractice

2 years

Triangles of dots in LaTeX

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2 years

“One should never try to prove anything that is not almost obvious.” ― Alexander Grothendieck

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1 year

A modal logic is monotone if □(p∧q) → □p.

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8 years

'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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3 years

Modal logic duality

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2 years

Why people don't use formal methods

Why Don't People Use Formal Methods?

I saw this question on the Software Engineering Stack Exchange: What are the barriers that prevent widespread adoption of formal methods? The question was closed as opinion-based, and most of the...

www.hillelwayne.com

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Logic & Applications

@LogicPractice

1 year

Formal Verification: History and Methods

In the first part of our series about formal verification, we discuss the roots of formal verification in fields such as mathematical logic and theoretical computer science.

serokell.io

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Logic & Applications

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4 years

“It cannot be a complete coincidence that several outstanding logicians of the twentieth century found shelter in asylums at some time in their lives.” — Gian-Carlo Rota

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1 year

Löb's theorem regarding Peano arithmetic is taken as an axiom in Gödel–Löb modal logic. □(□p → p) → □p.

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Logic & Applications

@LogicPractice