I've solved "One Step Off".

Just one addition I noticed just now: You can stack blockers in Winlemm.

3) A is false. B may be true or false.  This is neither evidence for nor against the statement.  These irrelevant cases have no bearing on someone's confidence on the truthfulness of the statement.

It's an interesting point to see conditionals in a way of verification or falsification. The classical logical principle follows then the rule that if it can't be falsified it's true. Whereas intuition from your view (as I understand it) says that only what can be verified (or falsified) can be true. This is a very demanding view of truth which combines truth with the possibility of determining it.
It could be seen as problematic to mix up the logical conditional with natural language intuitions of "if-then" but since it's about formalization of natural language it's a valid point to question those formalizations. (The same applies maybe to the concept of truth.)

If you take the empty set that contains no elements: The fact that it contains no elements can be used with the logical principle discussed here:
E.g. You get to the conclusion that the empty set is a subset (or identical) of every other set.
This is because subset is defined in the following way:
Be x,y sets:
x is a subset (or identical) of y iff For all z (z € x then z € y). ('€' means "is element of")
Since z € empty set is always false, the whole universal sentence is (for x = the empty set) always true no matter which set y is.
Insofar I have a problem in calling such things irrelevant.

That leads to the question what is the consequence of the intuition that there is a "not sure"-value. Do we introduce this third value and how does our logic then look like? Does it have consequences for mathematics (in a very wide sense) as well or only for natural language?

It seems to me that there probably can't be a universal rewrite for this sentence, because there's insufficient context to determine the exact bounds of the subset "the frogs."

"The frogs are green" can be true or false depending on what "the frogs" refers to. We need context to determine that. Suppose there is a box containing frogs. I point to it and say, "The frogs are green." This extra context removes the ambiguity as to which frogs we are referring to - now it's the frogs that are in the hypothetical box, rather than an unspecified group subset of frogs. But now we must check to see if the statement is actually correct. It is possible for all the frogs in the box to be green^[1][2]. However, it is also possible that at least one of the frogs in the box is NOT green^[3][4]. For this reason, I can create a set of frogs for which the statement "The frogs are green" is false.

That's a very good point. Yeah, the statement is dangling without context. So formalization is probably not complete without catching somehow the context or that there is further context.

This is where I can no longer really work with the given information without more background knowledge. I am unsure of the exact meaning of "For all X, if X is a frog, then X is green." Is this statement defining the object selection, to state that all the frogs under consideration are green (i.e. if an object is a frog, and it is not green, it is not X)? Or is it a statement that, for any given object X, if X is a frog, it is green (i.e. stating that all frogs are green)?

I'm not fully sure if I can pinpoint what you say there.

Generally "For all X, if X is a frog, then X is green." is an universal statement and is meant to formalize "All frogs are green.". One remark: This statement is equivalent to "For all x it is not the case that x is a frog and x is not green." Another remark: "For all X, if X is a frog, then X is green." doesn't imply in modern formal logic that there are frogs.

One point is that if one talks about all objects still the question remains for truth or falsehood what is the set of objects and how are expression like "frogs" and "green" defined or what objects are assigned to them.

In formal logics you have model-theoretic semantics, where a model has a set of objects as a domain and an interpretion function that e.g. assigns subsets of the domain to the one-place predicates (like "frogs" and "green"). Depending on the model the sentence is true or false in that model unless it's a logical truth, which the given sentence is not.

But in general if you formalize a sentence of natural language one has the model that fits to our understanding of the world in the back of their minds I would say since that's the background people are formulating these sentences.

I think generally formalization mainly tries to catch the logical structure of the sentence, is on the syntactical side and most of such sentences will be logically indetermined.

Concerning recognizability of buttons:

The flip/mirror horizontally button has a symbol that looks rather like flip/mirror vertically.
But the latter function doesn't have a button at all (, although you can achieve this effect by mirroring horizontally and rotating twice.)

Only two issues that are connected to points mentioned here:

To copying pieces:

That copied pieces spawn a bit below the original can lead to the problem that they spawn outside of the reachable map if the original is too low on the screen edge. You can still reach them by increasing the lower map size though.

Apart from that it makes them easier to select that they spawn a bit below and not directly on the original.

To background colors:

The brazier for example has a black rectangle around the fire, which can be seen on non-black background. I attached a picture to demonstrate.

Apart from that I actually like the possiblity to choose different background colors because certain tiles(ets) seem to work better with brighter colors.

While we're on this topic, what are your thoughts on the difference (if any) between

A dog is a mammal.

and

Dogs are mammals.

Is the usage of singular versus plural meaningful?

My feeling says no concerning logical analysis.

I would formalize both as: For all x: if x is a dog then x is a mammal

Edit: I assumed for the first sentence that you want to make a general statement about dogs and not to say that some dog happens to be a mammal.

Some cuber edge cases:

1. Climber climbs in cube: If you assign a cuber it lasts some time until the cube is created and so lix can get into the cube in the process of cubing. So far so usual. But if you have a climber and cube near a wall it will start to climb and climb up within the created cube. (Showcase replay: cube3.txt)

2. Blocker within cube: In the above mentioned creating process of the cube you can assign a blocker to a lix, which will remain within the cube. Since the cube is created at first in layers, a lix that gets into that process pulls itself up the already created layer. If you assign blocker then, it is not only in the cube but also a bit heightened.
If you free that blocker with a walker you can assign basher which destroys the upper part of the cube. You have a small step then (Showcase replay: cube1.txt) (You can achieve that of course with assigning basher instead of blocker in first place as well.)  But the blocker must have been assigned at the very edge else there remains to one side a thin wall. (Showcase replay: cube2.txt)

3. Lix can get caught within the cube: As long as the cube is in creation process the lix can normally climb out of the already created parts of the cube. But if you delay a lix until the process is finished then the lix gets caught.  You can still assign destructive skills like the basher. The delay can be achieved, e.g. with assigning a batter or having a stunned lix. (Showcase replay with batter: cube5.txt)
A more unusual case is that even a faller if it is timed right can get caught. (Showcase replay: cube4.txt)
If the hatch is low enough then lix can spawn within the cube and get caught as well.

All replays were made in the level Any Way You Want.