Logic and Truth Tables in ChatGPT (my First Prompt)

[shy steppe]

It fix's basic truth-table errors. feel free to shrink, edit, fork, or whatever you'd like to do 🙂 just please post new versions expanding on my version in this chat. Feedback is welcome!

Prompt:

Logic-Prompt Version-0.1.2:

I Will be teaching you how to use logic to create solid truth tables. A variable such as "a" can be either T(true) or F(false) in this world because it is considered to be a proposition. You will say either T for true or F for false in the truth tables you provide. Variables can be any letter of the alphabet or any symbol the user gives you that they declare to be a variable. In logic we will have several different "joiners" of variables that create new propositions.

Remember the RULES for:
Conjunction (∧):
Disjunction (∨):
Conditional (⇒):
Biconditional (⇔):
Negation (¬):

RULES EMPHASIZED:
Conditional (⇒): If you have two propositions on both sides of a conditional such as A ⇒ B and A= T and B=F, then (A ⇒ B) = F. if A = T and B = T then (A ⇒ B) = T. If A=F and B = F then (A ⇒ B) = T. If A = F and B = T, then (A ⇒ B) = T.

Negation (¬): If you negate a proposition on one side of any joiner such as ¬A∧B It does NOT EQUAL the opposite of the truth value for A∧B. If you negate both sides such as ¬(A∧B) then it is the opposite of the truth value for A∧B. For example, if A = T and B = T then A∧B = T, however ¬(A∧B) = F. Also in another situation if A = T and B = F then A∧B = F, however (A∧¬B) = T. If you are negating a variable or proposition make sure to make a column for that negation. So for example if you have A∧¬B, Have a column for ¬B as well as for B.

YOU MUST DO THE FOLLOWING FOR THE REST OF THE CHAT:

• When I say any of these symbols (such as ‘or’) I want you to replace that or with “∨” in the truth table, same goes with the other words and their corresponding symbols.

• For each new variable, you need to double the rows in the truth table. For instance, if there is variables a,b,c then there must be 8 rows.

[marsh lion]

Hi, can you provide an example of how to use it ?

Maybe also a screenshot but that is just a bonus

I tried this prompt:

provide an example of boolean algebra using LaTeX and a truth table in markdown. Provide the LaTeX in the format:

$$
[LaTeX code]
$$

The LaTeX has to written in that format as mentioned in another post https://discord.com/channels/974519864045756446/1074776802465157131

[shy steppe]

Sure:

I copy and paste the above prompt into a blank conversation and click enter,

Then after it has responded I say something like "Give me a truth table on this: not a or b implies not c."

this is what I was doing

[marsh lion]

Nice

what is the RULES EMPHASIZED: part for ?

[shy steppe]

the main thing I was trying for was I wanted to be able to write out a proposition like I was speaking it, and for it to translate it into the symbolic representation then give me a truth table - I had a lot of issues with it not understanding "Implies" and different negations but I found once I specified those with examples in the prompt it worked

Those were rules it kept messing up on

probably doesn't have to be labeled

[shy steppe]

those were the rules it kept messing up on

[marsh lion]

interesting, so it does not know the rules of boolean algebra but you taught it how to use it

[shy steppe]

yes, at least that is what I believe I did lol

[marsh lion]

Do you have some examples of where it failed ? I tried negation and it worked in this case:

In boolean algebra, what is Not[A OR Not[B AND C]]

I had trouble teaching ChatGPT addition. It seemed to do better when I told it to code addition in the coding language "lean" (a coding language for mathematical proof solving) and I made it simulate using the code. Maybe you might also want to try that in boolean algebra but I do not know if it will help.

Here is a possible prompt:

provide code for the boolean operator "implies" in the coding language "lean"

and then make it use that code to reply to answers. I do not know if it would help

[shy steppe]

So this is an example of where it failed without any extra prompt: messes up in various ways from having false or false equals true, to having true implies false as true (when that proposition is false)

[shy steppe]

Ohhh interesting - I’ll try that out

[shy steppe]

Good idea, I tested it out and it didn't seem to make much of a difference. It would of been super tight tho if it simplified that prompt down to something like that!

[marsh lion]

Nice that it seems to be working. Somewhat surprising how just giving the right environment can let it do better (If it is actually doing better all around).

It would of been super tight tho if it simplified that prompt down to something like that!

I did not understand, if it simplified what prompt down to something like what ?

[shy steppe]

I mean I rested the Lean thing without using my prompt, tested it in a brand new chat. Did you intend me to test it WITH my prompt?

*tested

[marsh lion]

No yeah I meant in a new chat. That said, maybe I am imagining things, but I feel like chats aren't completely independent. For example, I once taught it something in math I think and I think it remembered the correction in another chat.

Maybe when it is quite sure it messed up it changes permanently.

[shy steppe]

Hmmm that’s interesting 🤔I wonder if that’d change if we deleted all of the chats? Maybe there is some relationship. Or it’s just our own bias about what we are seeing

[marsh lion]

not sure. Normally it should forget.

[ebon siren]

this is hard for my old brain to understand, is there more simple table that dedect logic and irrelavent ?