Fundamentals of Formalisation level 1: Basic Logic

Fol­lowup to Soon: a weekly AI Safety pre­req­ui­sites mod­ule on LessWrong

(note: we have a study group run­ning a week ahead of this se­ries that adds im­por­tant con­tent. It turns out that to get that con­tent ready on a weekly ba­sis, we would have to cut cor­ners. We pre­fer qual­ity over speed. We also like pre­dictabil­ity. So we de­cided to cut us some slack and pub­lish ev­ery 2 weeks in­stead for the time be­ing)

(re­lat­edly, the challenges sec­tion of this week is not yet com­plete at the time of post­ing, so com­plet­ing those will not yet im­ply a full un­der­stand­ing of the con­tent)

Ba­sic logic

The big ideas:

  • Sen­ten­tial Logic

  • Truth Tables

  • Pred­i­cate Logic

  • Meth­ods of Math­e­mat­i­cal Proof

To move to the next level you need to be able to:

  • Trans­late in­for­mal ar­gu­ments into for­mal logic.

  • Eval­u­ate an ar­gu­ment as ei­ther valid or in­valid.

  • Ex­plain how to prove an im­pli­ca­tion/​con­di­tional, a con­junc­tion, a dis­junc­tion, and a nega­tion and know what this looks like in­for­mally (i.e. in words and not sym­bols).

Why this is im­por­tant:

This builds the ba­sic knowl­edge you need to be able to pro­duce and un­der­stand math­e­mat­i­cal proof. A firm foun­da­tion in how log­i­cal ma­chin­ery op­er­ates is the best way to be as­sured that a proof you pro­duce or read is cor­rect. This also teaches the ba­sic meth­ods by which a proof is pro­duced.

Without fur­ther ado: you can find the first les­son on our course plat­form.

Every week you have 2 op­tions: do the whole thing, or skip to the “challenges” in the end. The lat­ter op­tion is for those peo­ple that sus­pect they already know the sub­ject. It serves as a means of ver­ify­ing that as­sump­tion.

We hope this track will fa­cil­i­tate as­piring AI Safety re­searchers in their stud­ies. If it leads to even one suc­cess story, it will have been worth it. Maybe that suc­cess story is you!

Happy studying