Thank you in advance]]>

May I ask for past material for the following subject, I will be taking these modules in 2012. Please kindly send to sedeya@gmail.com

(COS2621) Computer organization (Computer Science 221)

(COS2661) Formal logic 2 (Computer Science 261)

(INF3705) Advanced systems development (Information Systems 305)

(COS3701) Theory of computer science 3 (Computer Science 301)

(COS3711) Advanced programming (Computer Science 311)

(COS3721) Operating systems and architecture (Computer Science 321)

(COS3712) Computer graphics (Computer Science 340)

(COS3761) Formal logic 3 (Computer Science 361)

(COS3751) Techniques of artificial intelligence (Computer Science 351)

Thanks in advance.

Regards

Rutendo.]]>

> Hi 4c and 4d kind of got me..

>

> I have thoughts on them but not quite sure:

>

> 4c)

>

> 1.not ForAllx not P(x) --premise

>

>

> BOX1----------------------------------------------

> -----------------------

> 2. not ThereExists P(x) --assumption

>

> 3 .BOX2 with x0

> ---------------------------------

>

> BOX3----------------------------------------------

> ---------------

> 4 .P(x0)

> --assumption

> 5. ThereExists P(x0) -- ThereExists

> intro Line 4

> 6. contradiction -- not elim

> line 2

>

> BOX3----------------------------------------------

> ----------------

> 7. not P(x0) --

> contradiction elim line 6

>

> BOX2----------------------------------------------

> -------------------

>

> 8. ForAllx Not P(x) -- ForALl

> intro 3-7

> 9. Contradiction -- Line 1

>

> --------------------------------------------------

> ---------------------------

> 10.ThereExistsx P(x)

Yep, I'd say that looks about right... had me stumped for quite some time there. I haven't done 4d yet, since I haven't got to going over proofs with modal logic yet...

Going to get me some practise on these other proofs quick... then off to do some mathematical induction :)]]>

QUESTION 7A:

BLOCKp -> p

Its satisfiable, since it is true in this particular model. Every world that has a p, can be reached from a world that has a p.

Its not valid, since it does not hold for every world in every model.

QUESTION 7B:

(i)

Holds - world c makes this true.

(ii)

Does not hold - after "processing" the first 2 BLOCKS, world c is reached. DIAMOND states that "there is one world reachable", but there are no worlds reachable from c, thus this statement is false, regardless of what appears after the DIAMOND.

(iii)

Does not hold - d does not satisfy q, and the second conjunct requires that either a or c have at least one world that is reachable that satisfies q. This is not the case for a, and there are no worlds reachable from c (making this false in that world anyway).

(iv)

Holds - there are no worlds reachable from c (the only world reachable from b), and the statement is thus vacuously true.]]>

I have thoughts on them but not quite sure:

4c)

1.not ForAllx not P(x) --premise

BOX1---------------------------------------------------------------------

2. not ThereExists P(x) --assumption

3 .BOX2 with x0 ---------------------------------

BOX3-------------------------------------------------------------

4 .P(x0) --assumption

5. ThereExists P(x0) -- ThereExists intro Line 4

6. contradiction -- not elim line 2

BOX3--------------------------------------------------------------

7. not P(x0) -- contradiction elim line 6

BOX2-----------------------------------------------------------------

8. ForAllx Not P(x) -- ForALl intro 3-7

9. Contradiction -- Line 1

-----------------------------------------------------------------------------

10.ThereExistsx P(x)]]>

QUESTION 4A:

1 (p OR (q -> p)) AND q premise 2 p OR (q ->p) AND ELIM 1 3 q AND ELIM 1 4 | p assumption 5 | p copy 4 6 | q->p assumption 7 | p -> e 6,3 8 p OR ELIM 2, 4-5, 6-7

QUESTION 4B:

1 FORALLx (S(x) OR T(x)) premise 2 FORALLx (S(x) -> T(x)) premise 3 EXISTSx (NOT C(x)) premise 4 |x0 NOT(C(x0)) assumption 5 | S(x0) OR T(x0) FORALLx ELIM 1 6 | S(x0) -> T(x0) FORALLx ELIM 2 7 | | S(x0) assumption 8 | | C(x0) ->e 6,7 9 | | CONT NOT ELIM 4,8 10 | | T(x0) CONT ELIM 9 11 | 12 | | T(x0) assumption 13 | | T(x0) copy 12 14 | T(x0) OR ELIM 5, 7-10, 12-13 15 | EXISTSx(T(x)) EXISTS INTRO 14 16 EXISTSx (T(x)) EXISTS ELIM 3, 4-15]]>

Cant redraw the diagram here, so I'm not answering (i) and (ii) here.

(iii)

No. The free occurrences of y (two of them, namely the B(x,y) and A(y) formulas ) in the formula are both under the scope of a quantifier on x. Thus, substituting f(x) with the free occurrences of y will place the substituted x values under the scope of the quantifier, which is not intended.

Thus f(x0 is not free for y.]]>

In propositional logic, the atoms making up some formula @ can be assigned truth values, which can be used to obtain a truth value for @. The statement provided is a tautology, and will always evaluate to true no matter the truth value of its atoms. It can be shown to do as such by constructing a truth table, for example. Therefore, it has a decided 'output', regardless of the input.

With predicate logic though, the use of variables to represent actual objects means that the objects represented by the variables are required to be known before deciding whether a particular formula is valid or not. Thus a tautology is based on a particular set of concrete objects that can be represented by the specified variables. Hence a formula is dependent on this additional knowledge, and can then be said to be undecidable in a general context.]]>

QUESTION 1(a):

(i)

(r AND s) -> q

(ii)

If he drives a BMW and drank too much, then he will drive slowly (ie: not drive very fast).

QUESTION 1(b):

(i)

FORALLx [ (P(x) AND G(m,x) AND NOT( G(f(m),x) ) ) -> E(m,x) ]

(ii)

Maggie's mother did not enjoy a party she went to with Maggie

QUESTION 1(c):

(i)

(K1p OR NOT K1p) AND (K2p OR NOT K2p) AND (K3p OR NOT K3p)

(ii)

Agent 1 knows p but does not know whether Agent 2 knows p or not.]]>

To be honest, I don't think that we have to know the table (Table 5.7) by heart, but more use it as a tool to understand the content... From my understanding of the scope of the situation, the table is used to indicate the different meanings of the modal connectives in the different modes of truth. In other words, simply showing that by changing the meaning of the mode of truth that block and diamond represent, a formula that may be valid in one mode of truth is not necessarily valid in another.

I've had a quick look through the table, and it may be helpful to understand what the differences are, how the validity differs between the various modes of truth, etc. But I don't see how learning the differences is going to be helpful...]]>

some feedback on the exam paper. Would like your inputs

1a i) Only if is read as P --> Q = P only if Q

Thus q --> r and S

1a) ii) if he drank to much AND drives a BMW, then he does not drive too fast

1b) i)

FORALLx (P(x) and (not G(f(m),x)) and G(m,x) --> E(m,x)

1b) ii) THEREEXISTS an x, such that x is a party AND Mary goes to the part AND Mary's mother goes to the party AND mary's mother enjoys the party

1 c) i) K1p ^ K2p ^ K3p ^ K4p (ie. Each agent knows p)

1 c) ii) Agent 1 knows p AND

Agent 1 does NOT know that / if Agent 2 knows p or does not know P

in better english: Agent 1 knows p, but does not know if Agent 2 knows P or not.

Question 2:

Grive propositional Logic, we can dsign a truth table and assign T or F to each term and then finally get the result of the formula in 2^n steps. If predicate logic, we are unable to devise a truth table, because we might have infinite number of variables to consider via FORALLx. Propositional logic will terminate in 2^n, predicate logic might not terminate for all worlds (unless the world only has 4 instances of the variable).

Question 3: i and ii

x under a is bound - left branch of -->

x under B is bound - left branch of -->

y under B is bound - right branch of -->

3 iii)

if f(x) free for Y?

Y under right branch does not get replaced, because it is bound

2x Y's under left branch are free of Y quantifier, thus

substituting with F(x) would create problem, it would introduct x under THEREEXISTS x

THus it is NOT free.

Question 4

a)

1. p OR (q --> p) AND q --premise

2. p OR (q --> p) --or elim 1

3. q --or elim 1

BOX1

4. p --assumption

5. p --copy 4

BOX2

6. q -->p --assumption

7 q --copy 3

8. p -- --> elim 6

9. p OR elim, 2, 4-5, 6-8

4b)

1. ForALLx S(x) OR T(x) premise

2. ForALLx S(x) --> C(x) premise

3. ThereExistsx not C(x)

BOX1 x0

4. not C(x0) Assumption (actually by elim ThereExists of line 3, but the book says assumption for the reason)

5. S(x0) OR T(x0) -- forAll elim line 1

6. S(x0) --> C(x0) --for all elim line 2

BOX 2

7. S(x0) -- assumption

8. C(x0) -- --> elim line 6

9. CONTADICTION -- not elim line 4,8

10. T(x0) -- CONTRADICTION elim line 9

BOX 3

11. T(x0) assumption

12. T(x0) Copy line 11

13. T(x0) OR elim lines 5, 7-10, 11-12 still inside BOX1

14. ThereExists T(x) -- There exists INTRO, Lines 4 - 13

4(c) NOT QUITE SURE

still busy with the rest]]>

if BLOCK p then BLOCK BLOCK p (axiom 4)

if NOT BLOCK p then BLOCK NOT BLOCK p (axiom 5)

I assume, these work the other way around as well...

if BLOCK BLOCK p, then BLOCK p?

it was used like this in the last proof of assignment 3.

My logic behind the above assumption is the following

If I know something, then I know that I know it.

If I know that I know something, then I must know it.

you agree?]]>

we're given 3 valid formulas on page 314 . THey are always true in all worlds in all models.

Then on page 218 we are given formulas which are not valid, but should hold for certain interpretations of BLOCK and DIAMOND

now the decision on whether these hold, seem very very subjective.

for instance: It ought to be true

it says that if things ought to be true, then it should be permitted. hence saying if BLOCK p --> DIAMOND p (ie. if all should be permitted, then we should have at least one)

Are these interpretations fixed, should we know them based on the table on p 318. Or are they just given to help us understand the reasoning behind them?

many thanks]]>

However,

LS says that There exists x such that [not R(x)] OR [not Q(x)]. Meaning is not in the one OR its not in the other... (perhaps i got this wrong, but using de morgan I get, ~(R(x) ^ Q(x)) Meanings its never in both, just in one at a time and now im thinking perhaps its not in either one at all. meaning can be T&F, F&T or F&F

where as the RS says for all x we have either R(x) or Q(x),

this means that we can never have F&F. One of the two has got to be True.

THus I choose my model as such

A (of m) = 1 2 3 4 5 6

R (of m) = 1 3

Q (of m) = 2 4

In this model we have 1 and 3 only in R and 2 and 4 only in Q. 4 and 5 are nowehere. Thus LS satisfied.

the RH says all in A have got to be in R or in Q, which it is not, thus thie RH evaluates to False.

Is my reasoning correct?]]>

I had the whole "study over the weekend" idea planned, only to have the weekend pass me by and I still have not opened a book. And work carries on, through to tomorrow afternoon. Which leaves me with Monday evening and Tuesday. Guess what I'm going to be doing then...

I'm not sure that there is that much work to get through, although then again, the last time I opened my textbook was long over a month ago. Chapter 1 pretty much carries through the principles and ideas introduced in the second year module, COS261 (from back in the day), again, assuming that I'm remembering COS261 correctly. Chapter 2 takes us to predicate logic, again with the same look and feel as Chapter 1, but now with a slightly different "logic set" to work with. Chapter 5 is just the understanding that there are different types of logics, and introduces 2 more symbols.

All in all, its primarily about practising the rules, etc. I had this module last year and couldn't end up writing exams on it, so had to leave it to this year (end up skipping it during the first semester this year, and now here I am). From what I remember, along with the idea I got from the past papers, is that one needs to focus on a couple of specific areas in the text.

For example (and not a complete list):

Proof Rules from Chapter 1.

Induction Proofs from Chapter 1.

Proof Rules from Chapter 2.

Something else from Chapter 2, which I can't remember right now.

What K is, and how to apply it/use it/do something with it, from Chapter 5. Essentially, ensure that you understand and can work with K, and specifically K45 (if I recall correctly).

Something else from Chapter 5.

I'll get back to the something else's tomorrow. For the most part though, the practical stuff would seem to be the most important. Just my perspective. The theory shouldn't be that much, since you need to know most of the theory and then apply the theory in the practical aspects. For the most part anyway.

Guess I'll be back tomorrow evening :D]]>

Yeah I spent last week going through all the theory / reading material. Spending today and the next 2 on practicing.

The exam letter says study everything except that specified to be left out in tut 102, however, I find it to be a lot of work. Not a lot to be left out.

The last chapter (5), seems to have my brain going haywire and Id really like to know whats important in there. Letter 102 seems to be less specific on what to do here.

anyways, will most probably claim another few posts on this topic. chat later]]>

Any thoughts on the final expectations, necessary bits, etc? I'm planning on spending the weekend going over this one, so I'll probably have more info to post then. Just thought I would start the discussion (I get the first post :D)...]]>

¡Esstett still appears, though!

¿And Spanish question marks? Åll right what's göing ön Here?]]>

d]]>

Is there signs of life out there but the life-form is unintelligent, or is there no sign of any life-form out there?

(:P)

Just to spice up your day...]]>

Haven't allowed myself to worry about this, but somewhere beneath consciousness the worry will always find a way to churn. Yeeehah!]]>