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More natural deduction and term sheet overview.

c-declarations
Joshua Potter 2024-07-22 10:58:42 -06:00
parent b498097731
commit 5dc598393e
6 changed files with 201 additions and 5 deletions
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notes/.obsidian/plugins/obsidian-to-anki-plugin/data.json
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@ -562,7 +562,7 @@
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"Basic": [

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notes/_journal/2024-06/2024-06-23.md
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@ -9,5 +9,5 @@ title: "2024-06-23"
- [ ] Korean (Read 1 Story)
* Read chapter 4 ("Numbers") of "An Introduction to Ontology".
* Notes on [[financing]] rounds.
* Notes on [[financing-rounds]] rounds.
* Additional notes on hash tables with [[closed-addressing#Chaining|chaining]] and independent uniform hashing.

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notes/_journal/2024-07-22.md
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- [ ] Korean (Read 1 Story)
* Beginning notes on [[natural-deduction|natural deduction]].
* Read chapter 3 "Overview of the Term Sheet" of "Venture Deals".

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notes/formal-system/proof-system/natural-deduction.md
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@ -68,6 +68,11 @@ Reference: Gries, David. *The Science of Programming*. Texts and Monographs in
<!--ID: 1721655978506-->
END%%
### Negation
For proposition $E1$, $$\neg{\text{-}}I{:} \quad \text{TODO}$$
and $$\neg{\text{-}}E{:} \quad \text{TODO}$$
### Conjunction
For propositions $E_1, \ldots, E_n$, $$\land{\text{-}}I{:} \quad \begin{array}{c} E_1, \ldots, E_n \\ \hline E_1 \land \cdots \land E_n \end{array}$$
@ -174,6 +179,135 @@ Reference: Gries, David. *The Science of Programming*. Texts and Monographs in
<!--ID: 1721656601613-->
END%%
### Implication
For propositions $E1$ and $E2$, $${\Rightarrow}{\text{-}}I: \quad \text{TODO}$$
and $${\Rightarrow}{\text{-}}E: \quad \begin{array}{c} E1 \Rightarrow E2, E1 \\ \hline E2 \end{array}$$
%%ANKI
Basic
In natural deduction, how is implication introduction denoted?
Back: As ${\Rightarrow}{\text{-}}I$.
Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
<!--ID: 1721665510225-->
END%%
%%ANKI
Basic
In natural deduction, how is implication elimination denoted?
Back: As ${\Rightarrow}{\text{-}}E$.
Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
<!--ID: 1721665541946-->
END%%
%%ANKI
Basic
*Modus ponens* is associated with which propositional logic operator?
Back: $\Rightarrow$
Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
<!--ID: 1721665541949-->
END%%
%%ANKI
Basic
Does *modus ponens* correspond to an introduction or elimination rule?
Back: Elimination.
Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
<!--ID: 1721665541951-->
END%%
%%ANKI
Cloze
Natural deduction rule {1:$\Rightarrow$}-{1:$E$} is also known as {modus ponens}.
Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
<!--ID: 1721665541953-->
END%%
%%ANKI
Basic
How is ${\Rightarrow}{\text{-}}E$ expressed in schematic notation?
Back: $$\begin{array}{c} E1 \Rightarrow E2, E1 \\ \hline E2 \end{array}$$
Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
<!--ID: 1721665510228-->
END%%
%%ANKI
Basic
How is *modus ponens* expressed in schematic notation?
Back: $$\begin{array}{c} E1 \Rightarrow E2, E1 \\ \hline E2 \end{array}$$
Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
<!--ID: 1721665541955-->
END%%
%%ANKI
Basic
Which natural deduction inference rule is used in the following? $$\begin{array}{c} P \Rightarrow Q, P \\ \hline R \end{array}$$
Back: N/A.
Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
<!--ID: 1721666244354-->
END%%
%%ANKI
Basic
Which natural deduction inference rule is used in the following? $$\begin{array}{c} P \Rightarrow Q, P \\ \hline Q \end{array}$$
Back: ${\Rightarrow}{\text{-}}E$
Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
<!--ID: 1721666244357-->
END%%
### Biconditional
For propositions $E1$ and $E2$, $${\Leftrightarrow}{\text{-}}I: \quad \begin{array}{c} E1 \Rightarrow E2, E2 \Rightarrow E1 \\ \hline E1 \Leftrightarrow E2 \end{array}$$
and $${\Leftrightarrow}{\text{-}}E: \quad \begin{array}{c} E1 \Leftrightarrow E2 \\ \hline E1 \Rightarrow E2, E2 \Rightarrow E1 \end{array}$$
%%ANKI
Basic
In natural deduction, how is biconditional introduction denoted?
Back: As ${\Leftrightarrow}{\text{-}}I$.
Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
<!--ID: 1721666244359-->
END%%
%%ANKI
Basic
In natural deduction, how is biconditional elimination denoted?
Back: As ${\Leftrightarrow}{\text{-}}E$.
Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
<!--ID: 1721666244361-->
END%%
%%ANKI
Basic
How is ${\Leftrightarrow}{\text{-}}I$ expressed in schematic notation?
Back: $$\begin{array}{c} E1 \Rightarrow E2, E2 \Rightarrow E1 \\ \hline E1 \Leftrightarrow E2 \end{array}$$
Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
<!--ID: 1721666244362-->
END%%
%%ANKI
Basic
Which natural deduction inference rule is used in the following? $$\begin{array}{c} P \Rightarrow Q, Q \Rightarrow P \\ \hline Q \Leftrightarrow P \end{array}$$
Back: ${\Leftrightarrow}{\text{-}}I$
Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
<!--ID: 1721666244367-->
END%%
%%ANKI
Basic
How is ${\Leftrightarrow}{\text{-}}E$ expressed in schematic notation?
Back: $$\begin{array}{c} E1 \Leftrightarrow E2 \\ \hline E1 \Rightarrow E2, E2 \Rightarrow E1 \end{array}$$
Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
<!--ID: 1721666244366-->
END%%
%%ANKI
Basic
Which natural deduction inference rule is used in the following? $$\begin{array}{c} P \Leftrightarrow Q \\ \hline Q \Rightarrow P \end{array}$$
Back: ${\Leftrightarrow}{\text{-}}E$
Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
<!--ID: 1721666244364-->
END%%
## Bibliography
* Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.

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---
title: Financing
title: Financing Rounds
TARGET DECK: Obsidian::H&SS
FILE TAGS: startups::financing
tags:

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---
title: Term Sheet
TARGET DECK: Obsidian::H&SS
FILE TAGS: startups::term-sheet
tags:
- startups
- term-sheet
---
## Overview
According to Feld et al., there are only two things VCs actually care about when making investments:
* **Economics**: the return investors ultimately get in a liquidity event;
* **Control**: mechanisms that allow investors to exercise control over the business and/or veto decisions the company can make.
%%ANKI
Basic
According to Feld et al. what two things do VCs *actually* care about when making investments?
Back: Economics and control.
Reference: Brad Feld and Jason Mendelson, _Venture Deals_, 3rd ed., n.d.
<!--ID: 1721667425673-->
END%%
%%ANKI
Basic
VCs care about the economics of an investment. What does that refer to?
Back: The return investors will receive in case of a liquidity event.
Reference: Brad Feld and Jason Mendelson, _Venture Deals_, 3rd ed., n.d.
<!--ID: 1721667425676-->
END%%
%%ANKI
Basic
What terms found in a term sheet relate to "economics"?
Back: Those related to the return investors receive in a liquidity event.
Reference: Brad Feld and Jason Mendelson, _Venture Deals_, 3rd ed., n.d.
<!--ID: 1721667425682-->
END%%
%%ANKI
Basic
VCs care about the control of an investment. What does that refer to?
Back: The ability to push and/or veto decisions made by the company.
Reference: Brad Feld and Jason Mendelson, _Venture Deals_, 3rd ed., n.d.
<!--ID: 1721667425684-->
END%%
%%ANKI
Basic
What terms found in a term sheet relate to "control"?
Back: Those that effect investors ability to push and/or veto decisions.
Reference: Brad Feld and Jason Mendelson, _Venture Deals_, 3rd ed., n.d.
<!--ID: 1721667425679-->
END%%
## Bibliography
* Brad Feld and Jason Mendelson, _Venture Deals_, 3rd ed., n.d.