-1

If one wanted to use standard propositional logic, what would be the most efficient way to translate a sentence from a natural language like:

"Capital murder is the premeditated or non-premeditated murder of any individual in the commission of abduction, robbery, rape, attempted rape, forcible sodomy or attempted forcible sodomy by an individual over the age of 18 or an individual under the age of 18 who is judged to have acted in the capacity of an adult in the state of Virginia or in the extra-territorial jurisdiction of the courts of the state of Virginia."

user155194
  • 568
  • 2
  • 8

1 Answers1

1

We can make only some comment about your question, that do not form a real answer ...

Consider for simplicity only the "sub-clause" :

Capital murder is the premeditated or non-premeditated murder of any individual in the commission of abduction, robbery, rape, attempted rape, forcible sodomy or attempted forcible sodomy

First of all, it is a definition and the logical structure of definitions is not analyzed by propositional logic.

With proposistional logic, we can "formalize" it as :

  • Capital murder is the premeditated murder of any individual in the commission of abduction

or

  • Capital murder is the non-premeditated murder of any individual in the commission of abduction

or

  • Capital murder is the premeditated murder of any individual in the commission of robbery

or

  • Capital murder is the non-premeditated murder of any individual in the commission of robbery

or ...

As you said in your comment, it is of the form :

p1∨p2∨...∨pn, with n=12.

What we can say about it ? Basically, we have that pi ⊢ p1∨p2∨...∨pn, that is, establishing that we have a "case" in the list, we can conclude that "capital murder" applies to it.

If we move to predicate logic we are defining a predicate :

Capital(x) iff Premeditated murder of any individual in the commission of Abduction(x) or Non-Premeditated murder of any individual in the commission of Abduction(x) or ...

What we have to note is the "role" of the negation : the "predicate" NPA(x) is not the negation of PA(x).

When we say that P(x) ∨ not-P(x) we are saying that, for every "object" x in the universe of discourse, P holds of it or not, which is true.

But in our case, we cannot assume that, for any "action" x, it is the case that it is a "Premeditated murder of any individual in the commission of Abduction" or it is a "Non-Premeditated murder of any individual in the commission of Abduction", because it is not true that every "action" which is not a case of "Premeditated murder ..." is a case of "Non-Premeditated murder..."

Mauro ALLEGRANZA
  • 47,995
  • 3
  • 46
  • 104