Anyway, I found it reasonable but must admit I've been doing tonnes of ND proofs.

My guess between 75 - 80%]]>

A late night looms, anyone writing in Benoni?]]>

I'm also looking for more material around the k-validity i.e. its proof.

i.m using COS261C Fitch to practice natural deduction for propositional and predicate logic. But would like more material to practice ND for modals]]>

W = { X4, X5, X6 }

R = { (X4,X4), (x4,X5), (X5,X5), (X5,X6), (X6,X6) }

so each world as a relation to itself and apart form X6 not linking back to X4 the rest of the relations are transitive.

The books states that this frame does not satisfy []p -> [][]p

... here's my thinking ...

for X4, []p is true as p is true @ X4 and X5 (only worlds accessible via single step relation from X4)

for X4, [][]p is true as [] is true @ X4 and []p is true @ X5 (for the same reasons as X4, i.e. with itself and next world )

for X5, []p is true as already seen above

for X5, [][]p is true as same approach as X4 (i.e. []p is true @ X6 because of its reflexive relation)

for X6, []p is true because of the reflexive relation

but what about [][]p - my understanding is that []p must be true from all worlds accessible from X6 via single step relation, and in my view that relation is (X6,X6)

as pointed out the book says that this is not so i.e. []p -> [][]p is false, and the only what this can be false is if []p is true and [][]p is false - I can't get [][]p false

Any takers?]]>

I can't seem to get past page 310/311

Think I got used to 2year text book that kept the pace really slow...]]>

I'm not sure how to start the proof so any help/hints/pointers would be awesome :)

I know that I need to prove that ~K1~K1(p & q) -> K1(p &q) and then visa versa, but I'm just not sure what to do with the ~K1~K1...]]>

For 9.1, how does one change the 'not P' into a 'P' in the goal? I feel like I'm missing something simple here because it's only supposed to be 5 marks...

Any advice would be awesome :) Thanks]]>

This is kind of what I am thinking for question 6 and was hoping that someone could comment on it to tell me if I'm on the right track.

The formula says that for all x, it is not the case that P(x,x). And I assume that we have to come up with a meaning for P? So then, a model where the formula is true is if P means 'greater than' and a model where the formula is false is if P is equality.

Is that right? Is that the idea to give P different meanings? Or is it x that we are supposed to assign meaning to?

Thanks]]>

I have an identity which would suite me changing with DeMorgans law, but I dont know if I am allowed to use "DeMorgan" as a reason, or if I have to put the whole DeMorgan proof in (This would be crap because it would increase the size of the proof by 5 times.)]]>

Hopefully someone can help me - for some reason I cannot understand exactly what they are asking with question 4.

Do we have to prove that: 11

I don't quite understand what they mean then they say: "is 'n multiple of 7 ..."

Thanks in advance]]>

Q1

(p -> ~q) ...1

(p ^ r) ...2

s ...3

Will it be (1 v 2) ->3 or 1 v (2 -> 3)

Q6

Must we place the brackets to make the two semantically equivalent?

I did email cos361@.......

I will wait for a response.]]>

I always say if there is a lot of feedback on this, I may one day complete the last hree chapters :-)

As always, corrections are welcome.]]>