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Language and Logic

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Logic is such a common word used these days to properly deduce things from one or more premises. There are certain rules to it and more but I will go through a few and how they can be applied for language and distinctions in it, or lack of them. For easyness I will be using a table like

X A
1 0
B 1
0

where A and B represent the two options possed and X will be replaced by the function. If it shows 1 in the box it means that option is applied in that situation and 0 means it isnt.

Or

This is a common word and logical function, It usually represent where A can be the option or B can be, but also both can be valid at once.

Or A
1 0
B 1 1 1
0 1 0

This is the commonly spoken "Or" but may be emphezised by saying "A or B or both" in everyday speech to make it clear compared to the other or. This is in technical terms called "Inclusive Or" but will in this blog be refered to simply as "Or" as the other got another name in short terms.

  • Or: Him or me or both

Xor

Xor is the other kind of or, it represents a kind of or where the option of both being valid/true is excluded, hence Called "Exlusive Or" or simply "Xor"

Xor A
1 0
B 1 0 1
0 1 0

There are languages, including my own, which makes this distinction of when the option of both being valid makes the words change. Many langauges do make this differens but uses expressions for it including english.

  • Or: Him or me or both
  • Xor: Either him or me

And

And is among the most used and general words in english again, in logic it means that A and B must both be true at the same time

And A
1 0
B 1 1 0
0 0 0

This holds true in normal language aswell as the two being tied togather always share the thing in question that is being talked about.

  • Or: Him or me or both
  • Xor: Either him or me
  • And: Him and me

Xand

This one is more used in Logic than in languages as far as I know, but it is like and with the differens that both can also be held false aswell, either both are true or both are false in the form of "Either he and I did it or neither did" which could be formex as "He xand I did it"

Xand A
1 0
B 1 1 0
0 0 1
  • Or: Him or me or both
  • Xor: Either him or me
  • And: Him and me
  • Xand: Him and me or neither

Adj-and

This one is considerbly less about logic in traditional form but more a linguistical differens in meaning. Think on the sentence "The red and green man walked".

It can mean one of two things, either a man that is red and green coloured at the same time walked, or a Red coloured man and a green coloured man both at once walked. How is that differens known? Usually in english by context but languages can make the differens by a different conjunction. For simplicity I call it Adj-and.

  • Or: Him or me or both
  • Xor: Either him or me
  • And: Him and me
  • Xand: Him and me or neither
  • Adj-and: Green man and red man

Not/No

Not and no is a form of negation which would in logical sense be that if A is true, then negated it becomes false, or if its false it becomes true and same goes in language in many cases. Notice this should not be confused with a system of where more than one particle or things are used for one single negation and hence is not a double negation.

  • Or: Him or me or both
  • Xor: Either him or me
  • And: Him and me
  • Xand: Him and me or neither
  • Adj-and: Green man and red man
  • Neg: Not me

No Logic

No, this is not where there is No logic what so ever, it is simply meant as negation logic where one logical function is negated.

Nor

Nor is the negation of or giving the chart of

Nor A
1 0
B 1 0 0
0 0 1

And hence nor would mean its only when both A and B are both false

  • Or: Him or me or both
  • Xor: Either him or me
  • And: Him and me
  • Xand: Him and me or neither
  • Adj-and: Green man and red man
  • Neg: Not me
  • Nor: Neither him nor me

Nand

Not And, negative and gives the shape of

Nand A
1 0
B 1 0 1
0 1 1

Nand is true whenever A and B arent both held true More to come, all for now, suggestions thoughts are welcome

  • Or: Him or me or both
  • Xor: Either him or me
  • And: Him and me
  • Xand: Him and me or neither
  • Adj-and: Green man and red man
  • Neg: Not me
  • Nand: Not him and not me

Not Xor/Xand

These are left out because negating them will result in each other

Implies/Follows

This is not the most obvious one but still important in many cases. it goes in the sense of "A implies B" in the sense that B is supposed ot be depended on A. The chart is

=> A
1 0
B 1 1 0
0 1 1

It is logical that if A is true and B is true then the result is true because A implies B, and if B is true but A is not then its false because it is obvious then that A is not implying B. But the others are less so. The reason is simply that if both are false it seems reasonble that if A implies B that both should be false at the same time, while if A is true but B is false it can be because B is depended on multiple things and the other criterias aren't fullfilled while still being implied.

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