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How can be translated to predicates the following two sentences:

Every person has someone who defends him/her against attacks of others.

Some people are only defended by pacific people.

It's not clear for me:

1 - how to deal with the "others" in the first sentence

2 - the second sentence is true for people who are not defended by anyone?

user232560
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  • The "others" means that the attacker cannot be equal to the attacked. We need something like $x \ne y$. – Mauro ALLEGRANZA Aug 26 '22 at 13:09
  • So it's possible that some people A is attacked and defended by the same person B distinct from A ? – user232560 Aug 26 '22 at 13:11
  • I think not: I assume that there are three distinct individuals invoved. – Mauro ALLEGRANZA Aug 26 '22 at 13:13
  • It's possible that one person defends itself against the attack of others? – user232560 Aug 26 '22 at 13:16
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    This type of problems is terrible, because they are marred by the ambiguities of natural language... the best approach is to choose a specific reading of the natural language sentence and symbolize it accordingly. – Mauro ALLEGRANZA Aug 26 '22 at 13:21
  • What about the second proposition? – user232560 Aug 26 '22 at 13:23
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    I agree about the ambiguity: Suppose that Alice is a defender of Bob for the purposes of statement 1. It's unclear whether that means, if Alice were to attack Bob, would Alice then be required to defend Bob against her own attack? And likewise, if Bob were to attack himself, would Alice be required to defend Bob against his self-attack? (In other words, does "tothers" mean "other than the target / person being defended", "other than the defender", or "other than either the target or the defender"?) – Daniel Schepler Aug 26 '22 at 17:36

1 Answers1

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Addendum added to respond to the OP's (i.e. original poster's) revision of the problem.

$P(x,y)$ denotes that Person-y defends Person-x whenever Person-x is attacked by any Person-z such that (Person-z $\neq$ Person-x) and (Person-z $\neq$ Person-y).

Then, for all Person-x, there exists a Person-y such that $P(x,y).$

There exists Person-x such that Person-y is not pacific implies that it is not the case that $P(x,y)$.

Comments:

The 2nd response could be alternatively be phrased as

There exists Person-x such that $P(x,y)$ implies that Person-y is pacific.

Also, I have (moderately) blurred the distinction between being defended and being defended against an attack by others. Technically, they are not equivalent. That is, if you are being defended against an attack by others, then you are being defended. However, just because you are being defended, that does not necessarily imply that the defender is defending you against an attack by others.

Addendum
Responding to the OP's revision of the problem.

Those two propositions with this one: "Pacific people don't attack anyone", form part of a problem where is asked to prove that: there is a person A that doesn't attack other person B.

$Q(x)$ denotes that Person-x is pacific.

$A(x,y)$ denotes that Person-x attacks Person-y.

The $\neg$ sign is to used to negate an assertion.

To the OP:

There is an obstacle to my completing the answer. Please see this article on MathSE protocol.

Before you revised your posting, you were merely asking how to convert a statement into symbolic logic. Now, you have taken your posting further, and are requesting that a MathSE reviewer actually solve a logic problem.

In accordance with the protocol article, I am not allowed to do that until you improve the quality of your posting.

user2661923
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  • Those two propositions with this one: "Pacific people don't attack anyone", form part of a problem where is asked to prove that: there is a person A that doesn't attack other person B – user232560 Aug 26 '22 at 13:55
  • @user232560 See the Addendum that I have just added to the end of my answer. – user2661923 Aug 26 '22 at 16:12