Formal Reasoning [pdf] • Hacker News Board

Re: Formal Reasoning [pdf]

#31

Post by rramadass » Mon, Oct 27, 2025, 4:35 AM UTC

tannhaeuser wrote: post #24

rramadass wrote: post #6

Earlier quoted context omitted.

People are already using Prolog for this; 1) A series of excellent and detailed blog posts by Eugene Asahara Prolog in the LLM Era - https://eugeneasahara.com/category/prolog-in-the-llm-era/ 2) Previous HN discussion Use Prolog to improve LLM's reasoning - https://news.ycombinator.com/item?id=41831735 3) User "bytebach" gives a nice example of using Prolog as an intermediate DSL in the prompt to an LLM so as to trans…

There's also [1], containing further bibliography references along with practical applications in discrete planning. Prolog is quite popular and successful as a target for LLMs. And it's no accident considering Prolog was introduced to represent natural language statements in (predicate) logic. [1]: https://quantumprolog.sgml.net/llm-demo/part1.html

That is pretty neat!

Re: Formal Reasoning [pdf]

#32

Post by rramadass » Mon, Oct 27, 2025, 4:25 PM UTC

chrisweekly wrote: post #19

rramadass wrote: post #9

Earlier quoted context omitted.

Well said. Also i highly recommend everybody to read the great logician Alfred Tarski's classic book Introduction to Logic: And to the Methodology of Deductive Sciences to really understand "Logic" which is what Formal Reasoning is based on.

Agreed. Also, I feel strongly that logic should be part of the core curriculum in liberal arts colleges if not high school. I took a Logic class as an undergrad, in a course that covered Sentential, Predicate, and Aristotelian (syllogistic) Logic, then became a paid tutor the next semester. It was profoundly useful, and applicable to nearly every other field of study. So many otherwise well-educated people frequently…

Logic should be taught from the intuitive aspects first before turning it formal; With lots of domain examples to show how sentences often have a common Form (i.e. structure) which can then be generalized as Symbolic Logic ranging over a Domain of Discourse/Domain of Interpretation. Once this distinction between "Structure/Form"(i.e. Syntax) and "Meanings"(i.e. Semantics) is grasped then mechanical manipulation strictly following rules, starts to make sense.

Instead, what is taught is starting with truth tables for logical operators and thus students simply don't learn to think/understand. For example, almost everybody is thrown off by the "implication" logical operator (evaluates to True when the antecedent is False irrespective of the consequent). But if you use some actual domain examples then it becomes clear why it is so.

Alfred Tarski's classic book mentioned above does a good job of building up logic from the first principles and hence is a great companion to any standard textbook.

Re: Formal Reasoning [pdf]

#33

Post by sn9 » Mon, Oct 27, 2025, 11:39 PM UTC

MarcelOlsz wrote: post #28

sn9 wrote: post #27

Earlier quoted context omitted.

You should check out Math Academy. It'll give you as much math background as any engineering student and they aim to provide the equivalent of a full undergrad math degree in the next few years.

I've also had a lot of success with the Art Of Problem Solving text-books, the regular ones not the competition ones. As someone who's starting from the ground up with arithmetic.

Yeah they're great too!

I think of Math Academy as ideal for efficiently mastering subjects at a level slightly deeper than a typical education in a shorter amount of time, and AoPS is for taking your time to go much deeper into the topics.

Doing them both is probably best, but doing one or the other would still work.

Re: Formal Reasoning [pdf]

#34

Post by MarcelOlsz » Tue, Oct 28, 2025, 8:34 AM UTC

sn9 wrote: post #33

MarcelOlsz wrote: post #28

Earlier quoted context omitted.

I've also had a lot of success with the Art Of Problem Solving text-books, the regular ones not the competition ones. As someone who's starting from the ground up with arithmetic.

Yeah they're great too! I think of Math Academy as ideal for efficiently mastering subjects at a level slightly deeper than a typical education in a shorter amount of time, and AoPS is for taking your time to go much deeper into the topics. Doing them both is probably best, but doing one or the other would still work.

>I think of Math Academy as ideal for efficiently mastering subjects at a level slightly deeper than a typical education in a shorter amount of time, and AoPS is for taking your time to go much deeper into the topics.

I've been searching hi and lo for the ultimate beginner resource and nothing comes close to AoPS for the exact reason you mentioned. I started with principia mathematica by bertrand russel because I thought math worked like a big tree all stemming from one trunk. Boy was that a bad move lol. I'd be reading some textbook and I have an infinite amount of why's that would block me on the most basic of things, tons of assumed knowledge. AoPS treats you like a caveman who first discovered fire, and then discovered their books, in that order.

I'll give MathAcademy a go too, I heard lots of great things.