Is Rabc a Valid Formula in Predicate Logic?

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Discussion Overview

The discussion revolves around the validity and interpretation of the formula Rabc in predicate logic, specifically examining whether it makes sense to express relationships among three entities (Adam, Betty, and Celsi) using a three-place predicate. The scope includes theoretical considerations of predicate logic and the semantics of relational expressions.

Discussion Character

  • Exploratory
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions whether the formula Rabc, where R represents "Run towards," makes sense and seeks clarification on its meaning.
  • Another participant suggests that Rabc could be valid if b and c are in the same location, but otherwise, it does not hold true.
  • A further contribution elaborates that if b is north of a and c is northeast of a, then a could be running towards both without b and c being in the same location.
  • One participant introduces the concept of a three-place predicate using "between," arguing that it necessitates three subjects and cannot be divided into simpler predicates without losing meaning.
  • Another participant proposes that Rabc could be interpreted as "Adam is running towards Betty and Celsi," but questions whether it can also imply "Adam is in between Betty and Celsi."

Areas of Agreement / Disagreement

Participants express differing views on the interpretation and validity of the formula Rabc, with no consensus reached on whether it can be universally applied or understood in all contexts.

Contextual Notes

Participants highlight the importance of location and relational context in determining the validity of the formula, indicating that assumptions about the spatial arrangement of the entities involved are crucial to the discussion.

pivoxa15
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In predicate logic

Let R = Run towards

a=Adam
b=Betty
c=Celsi

Would a formula like Rabc make sense?

What would it read?

Would Rabc = Rab & Rac
 
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if b and c are in the same location then it makes sense, but otherwise it doesnt.
an example of three place predicate is "between", x is between y and z, here you can't divide it into Bxy&Bxz cause it doesn't make sense.
 
loop quantum gravity said:
if b and c are in the same location then it makes sense, but otherwise it doesnt.

b could be north of a and c is north east of a. Then a could be running towards both of them without b and c both in the same location.
loop quantum gravity said:
...an example of three place predicate is "between", x is between y and z,

So if B is between

then you could have Bxyz (i.e. a formula with 3 subjects) which translates to x is between y and z. In this case it is necessary to have three subjects after B, anything else won't make sense.
 
Last edited:
Is it true that in general if Rabc

than it can be read (a R b and c)

i.e Adam 'is running towards' Betty and Celsi.

Adam 'is in between' Betty and Celso.
 

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