Logic 7 - First Order Logic | Stanford CS221: AI (Autumn 2021)

For more information about Stanford's Artificial Intelligence professional and graduate programs visit: stanford.io/ai
Associate Professor Percy Liang
Associate Professor of Computer Science and Statistics (courtesy)
profiles.stanford.edu/percy-l...
Assistant Professor Dorsa Sadigh
Assistant Professor in the Computer Science Department & Electrical Engineering Department
profiles.stanford.edu/dorsa-s...
To follow along with the course schedule and syllabus, visit:
stanford-cs221.github.io/autu...
0:00 Introduction
0:06 Logic: first-order logic
0:36 Limitations of propositional logic
5:08 First-order logic: examples
6:19 Syntax of first-order logic
12:55 Natural language quantifiers
15:47 Some examples of first-order logic
20:01 Graph representation of a model If only have unary and binary predicates, a model w can be represented as a directed graph
22:09 A restriction on models
24:16 Propositionalization If one-to-one mapping between constant symbols and objects (unique names and domain closure)

[@watermellon6125]

You don’t understand how much this helped

[@Aminakzyzz]

Great video, loved the explanation :)

[@manim4434]

Thank you so much, your video helped me a lot, it actually saved me. Thanks 🙏😊

[@MathCuriousity]

Hey love your channel and may I ask a question:
If in set theory, I can create a relation which takes a set of elements which are propositions (like set a is a subset of set b) and map it to a set of elements containing “true” and “false”, then why is it said that set theory itself can’t make truth valuations?
I ask this because somebody told me recently that “set theory cannot make truth valuations” Is this because I cannot do what I say above? Or because truth valuations happen via “deductive systems” and not actually within first order set theory ?

[@JDMaravelias]

The short answer is “no you cannot create a map from all propositions to { true , false }.”
The short explanation is that the map cannot exist. The easy way to explain this is that “you can’t capture ‘all propositions’” in a set: it’s simply too large a collection to be a set. You could take a finite set, or some ‘small’ infinite set, but I’m not sure that captures what you want!
The harder, and truer explanation is that if you were able to construct such a collection, you could not construct a map that is surjective into your set of true and false. Lawvere’s Fixed Point Theorem (perhaps annoyingly) boils this down to connectives in propositions and self reference. It’s another annoying case of a diagonalization proof!

[@MathCuriousity]

@@JDMaraveliasI see. What topic should I google or TH-cam to understand this better? I’ll admit I’m having trouble following your reasoning. Is there a specific topic I can search?

[@MathCuriousity]

@@JDMaravelias I’m having great trouble why any collection is too big for a set? Can you explain this conceptually intuitively for a beginner please?

[@kplers]

You are god, omg

[@studyaccount-ve7wr]

anyone counted how many (k) she is saying in a minute