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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
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    p (There is only one proposition, so...) – Quentin Ruyant Nov 14 '14 at 10:44
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    Can you demonstrate some effort here? What do you imagine it would be? – virmaior Nov 14 '14 at 13:41
  • The point of the question is whether one can translate the statute into PL without prior interpretation. If "The doctor or the dentist can write prescriptions" should be translated, on the standard account, as (P ∧ Q), then it would appear that the translator is to some degree must interpret the sentence. Furthermore, one would need to "interpret" how to bracket the ors connectives, even if appears commonsense. Of course, one could treat this as a single proposition, but that would bring into ? the value of propositional logic since all that we have here are simple or clauses. – user155194 Nov 14 '14 at 14:22
  • So, my question is whether we really should treat these complex legal statutes as single propositions? If so, Propositional Logic can tell us very little about this complex demonstrative sentence if it is our unit of analysis. Another option would be to translate the atomic demonstrative sentences as "Capital murder is the premeditated murder of any individual in the commission of abduction by an individual over the age of 18 in the state of Virginia." If so, we would have 2*6*2*2 atomic demonstratives. Then, we would still need to resolve the bracketing, even though it appears commonsense. – user155194 Nov 14 '14 at 14:34

1 Answers1

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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
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  • Mario - Thank you - this is quite helpful. QQ - How would one fully notate the compound expression in first-order predicate logic? Would it be ∀xPxaev where x = pre-meditated murder of an individual; a = in the commission of an abduction; e = by an individual over 18 y/o; v = in the state of Virginia? And, is the best translation to use the "act" the primary predicate term? – user155194 Nov 14 '14 at 20:55