Best intro on the subject i could find. Gonna subscribe and keep digging into your logic content!

Best explanation I have ever heard.

Put them in a playlist, very interesting

10:36 Just KT5 will suffice in fact, as T and 5 together show that B is true.

Dear Marc (if I may), your videos on logic are just spot on - you got yourself a new subscriber! Your explanation for Euclidean models was especially helpful to me; it was the one I had always been baffled about. Do you know why Euclidean frames are called "Euclidean"? The triangle situation reminds me of Euclidean geometry but that's everything I know. I'll make sure to recommend you and your channel :)

Hey Mark, Let me ask you something. Suppose your model is Euclidean and transitive, and you have a frame looking like that triangle you showed in your video. Can I say, or even better, when can I say that the bottommost arrow equals the composition (that's not well defined right?) of the two other arrows? There is a key notion in quantum dynamics, that goes by the name of Markovianity (or divisibility), and that expresses something very similar to this property. Simply put, a particular dynamics is represented by a set of arrows whose origin are at the same point - just like the white arrows in your diagram. The dynamics is said to be divisible, or Markovian, whenever there are intermediate arrows (like the blue ones) such that the diagram commutes, in other words, such that the composition holds true (A -f-> B and A -g- > C is markovian iff there exists B -h-> C such that g=h \circ f).

euclidean requires a bidirected relation, which is a stricter criterion for all connected nodes. this is stronger than a directional node, so symetry + directional + reflex = symmetry + (directional relation + symetry) -- okay that was the "easy part" for the connectivity, if for all connections every relation is symetric, then for any node k, in model m, node j would have to be connected for [0,k] this entails fully connected graphs okay, so now presume we have a model space (universe?), we know that for all nodes which are connected are fully connected -> but we haven't shown all worlds are fully connected. so we'll create a model X and X-not, world X has X as true world X not has X not as true. world X cannot draw valid inferences contining X as an .... what's a relation -> negation is a relation -> scratch that we have shown that for nodes which are connected connect a fully formed graph, we have not shown implication, as counter example presume to nodes which are merely reflexive. these are fully connected graphs which satisfy our critereon. Draw some diagrams and formalize, that's why partitions exist as fully connected graphs within a Universe or Model (?) and how they exist separately. This is fun! tho i'm confused on a couple of items (i have seen model logic twice now XD -> both from your videos!)

@AtticPhilosophy The Euclidian Relation expressed as ∀x∀y∀z(Rxy ∧ Rxz → Ryz) the conclusion of the implication inside the bracket only has Ryz which kind of makes me think one way arrow only between y and z. But the diagrammatic explanation is a two way arrow does this not then mean Ryz ∧ Rzy ? I am battling a bit relating the diagram to the statement / sentence. If I look at the diagram in the video I am thinking ∀x∀y∀z(Rxy ∧ Rxz → Ryz Ryz ∧ Rzy ∧ Ryz ∧ Rzz ∧ Ryy) where am I going wrong in my interpretation of the diagram o the mathematical / logical expression ? PS Thanks for the great videos. The explanations and simplicity makes it very easy to understand and apply the material.

Is the serial relation for modelling induction?

In the symmetrical relation, why it's a if-then implication instead of iff implication? i.e: ¿¿¿for all x,y(Rx→Ry and Ry→Rx)???

i like

q : I watch one of your modal logic videos M, w1 |= ◻️q