Maths - Propositional Logic

A proposition is a statement which is either true or false, but it cannot be both true and false at the same time.
A question, exclamation or a command are all not propostions.

Logical Operators:

Unary Operator (Works with one value)   NOT  ¬    e.g      ¬P
^ AND
˅ OR
͢ ͢    Conditional (Always false when Q is false (When P͢  Q)) otherwise it is always true

<-> Only true if both are true or if both are false.



Implications relating to P -> Q

Implication: P->Q
If a student is female, then the student has brown hair.

Converse: Q->P
If a student has brwn hair, then they are female.

Inverse: ¬P->¬Q
If a student is not female, then they do not have brown hair

Contrapositive: ¬Q->¬P
If a student is not brown haired, they are not female.

TRUTH TABLES

P                Q                   P->Q                 ¬Q                  ¬P              ¬Q->¬P

T                T                      T                        F                    F                    T
T                F                      F                        T                     F                   F
F                T                      T                        F                     T                   T
F                F                      T                        T                     T                   T







Argument Validity

An argument is a set of compound propositions called premises together with another compound proposition that is suggested follows from the premises.
This is called a conclusion at the end.

The general form of an argument is  p1^p2^p3...pN) = Conclusion.

The conjunction of premises (and gate) is only true if all the premises are to be true. The argument is only valid when each premise is true!!

p1    p2    p3          C
T      T      T           T
at least one F      T or F


Example:
P - You read alot                                    Q - You are a brilliant conversationalist
R - You have many friends

The argument put forward is:
'If you read alot' = P, 'you will become a brilliant conversationalist' = Q. If you become a brilliant conversationalist, 'you will have many friends' = R. Therefore if you don't have many friends, you dont read alot.

The premises taken from the above arguments are:
p1 - If you read alot, you will become a brilliant conversationalist.    P->Q
p2 - if you are a brilliant conversationalist, you will have many friends.    Q->R
C - If you dont have many friends, you dont read alot.    ¬R->¬Q

p1^p2 = C
or
(p->q)^(q->r) = (¬r->¬p)


TRUTH TABLE


Where premises are true.
                                                    p1                      p2                                      C
P           Q              R                 P->Q                Q->R       ¬R     ¬P          ¬R->¬P

T           T             T                        T                    T             F          F               T
F          T             T                         T                    T             F         T               T
F           F              T                       T                     T           F          T                T
F          F               F                       T                    T             T         T                 T

To see if an argument is valid we must look at the rows of the truth table for which the premises are all true, and when all the conclusions are also true. If this happens (as above) we know that the argument is valid.





Contingency
e.g. (P v Q) -> ¬P

Propostions that are sometimes true and sometimes false, depending on P and Q values. With at least one T and at least one F appearing.
(P  v  Q) -> ¬P
      F
      F
      T
      T
Contains both True and False values in the conclusion.

Taughtology :
A taughtology is when all values in conclusion are True
e.g. P->( P  v  Q)
                    T
                    T
                    T
                    T
All final value ares true.


Contradiction:
 Is when all the final values are false.
P ^ (¬P  ^  Q)
            F
            F
            F
            F

Each final value is false. 

Security Technology

I am currently studying a module on Security Technology at university and will share what I am learning and understanding on here, it may or may not interest you but it will also help me with revision for my courses. It may appear basic to begin with but that is because we are all beginners to the course and they are breaking us in gently :P

If you have a read you may find that you do infact enjoy what you are reading and could ask me questions about it and find that you may want to do something similar to myself as I find it a rather interesting subject.

BioMetrics

BioMetrics litterally means the 'measure of life' which therefore means a way in which you can measure life, there are many different ways of doing this and it has been around for centuries - for example in the 14th century in China they stamped both palm and footprints onto paper in order to indentify people and used mainly to distinguish children.
In 1890 a man called Alponse Bertillon invented a way of keeping track of criminals by taking multiple body measurements, such as length of arm, skull etc. The problem was that Bertillonage was measured by many different people and with many different measuring tools, which made it near impossible to standardize the measurements in which would be taken and therefore result in lack of accuracy when the results when be taken from the same person again. It also had the issue that some people who attempted the technique would round up, whilst others would round down therefore could mean that the same person being measured by two different people could end up with completely different results, which therefore leads to mistaken indentity.

        An example of one of the measurements taken whilst using the Bertillonage technique


 Sir Edward Henry - Edward Henry worked for the Bengal police and was eventually promoted to Commissioner at Scotland Yard after using the Bertillonage technique throughout his career, but then introducing the fingerprint taxonomy which was the identification of others by their finger prints.

Along with the work of others such as Galton he realised that the constancy of peoples fingerprints could be used much like the Bertillonage technique, he noticed that each fingerprint of every person was different and had many features (also called minutia) such as loops, whorls and arches which refer to the patterns in which the skin on your fingers reflect.




There are also many other ways in which the biometrics of something can be recorded that arent neccesarily connected to human life, in order to roughly work out the age of a tree you can count the rings inside the tree and also with clams you can count the shell rings.

Use of Biometrics within technology

There are many many ways in which biometrics are used within everyday life such as your social security number, passports, medical records, dental records, drivers license, student ID, credit cards... you get the picture; These are all created and can be used for identification of a person.

The main reason for Biometrics in the modern day is for verification and security, verification defines if the person in question is actually who they say they are, this can be done via a password, PIN, signature etc. Whereas Identification is actually finding out who the person is I.E the forms you fill in whilst applying for passports and such.
It is infact rather easy to have your identification if it was just as simple as filling out a form, so therefore there are more accurate ways in which you can be identified and verified, such as a picture ID, but there are also more complicated ways which would be used in higher security situations, such as a bank vault... This ranges from fingerprints - in use with a scanner, Iris/Retina scanners which involve the use of infra-red lasers to read the patterns of the blood vessels within your eyes as they are unique to each of the people that use them because everyones blood vessel patterns are different to others.

Main methods of identification and verification are:
Fingerprints
Facial Recognition
Hand Geometry - finger length/width
Iris Scan - Front of eye
Retina Scan - Back of eye
Vascular Patterns
DNA - Blood, hair etc.
Voice Recognition
Keystroke Patterns

I should also mention that it is vital for all data that is being used for these processes is stored securely and to be encryted to maintain the high security level.

Stoke City 2 - 0 Fulham

Its been a while since I posted due to home issues and also because of work/starting university but I am now hoping to get back and post a few more a week now :)

It has been a while since I posted some information about my team Stoke City FC so I thought I would begin with the result at the weekend, it was a 2-0 win for Stoke over the decent side of Fulham. It was yet another home win which means if I am not mistaken that we have only lost one home game in the whole year at the Britannia Stadium (non-competetive); I was unable to attend the match because I was too busy serving coffee and scooping ice cream for people further down the road at work...

Despite losing away to the likes of Swansea and Sunderland our form this season has been brilliant with us drawing 1-1 with Man United (thats a win result for us!), beating liverpool and holding out for a draw with chelsea (also a win for us). We have also managed to win a few more less noticable games but nevertheless our season couldn't have got off to a much better start. The saturday game was an important victory because it means that we head into our european game on thursday with a winning mentality which is vital when playing against teams such as Dinamo Kiev and Maccabi Tel Aviv, it also means that we maintain our good league form and I am hoping that would could possibly be within the top 8 by the new year. Our last 3 seasons have been a matter of survival and Tony Pulis has been adamant that we reach the 40 point milestone in order to survive. However I now believe that we need to aim higher than that and by being in the top 8, it will help greatly to maintaining our place in the top half of the division.

We had Jonathon Walters score a goal for us against Fulham which is good news as you always need your forwards to be scoring when called upon, it is also brilliant that super Jon is keeping up his quality and ever increasing his popularity with our fans. Another goal which I think is vital is Rory Delap, he scored the second and I am delighted that he has finally been rewarded for his hard work and effort. Many people underestimate Rory and unfairly label him as a donkey used just for his throw, slow, poor ball distribution etc. However when played in his correct position he proved on saturday that he can pass the ball, help the flow of the game, put in important tackles when needed, is back to help when needed and also forward when attacking as an extra option. At his age of 35 for a central midfielder, Delap is old, but as the statistics show he was one of the players on the pitch that covvered the most ground in the entirity of the game. Another player I adore is Wilkinson but that is a whole other story altogether :P

Accumulator

Last week I placed two bets of six on several football teams to win, however the only team that actually pulled through out of the 12 I bet on was Stoke... I will bet on Stoke to win the majority of the time but I would like people to help me choose teams that you think will win. Even if you don't know who they are playing, if you comment below I will select that team to win in my next bet. It is mainly luck anyway :P

Thanks for reading