[Attempto] Question about fol output of APE ('should' and 'must')

[Norbert E. Fuchs]

> On 21 Jan 2015, at 23:52 , Joshua Cason <joshua.aaron.cason at gmail.com> wrote:
> 
> Dear All,
> 
> I just wanted to confirm that sentences with 'should' and 'must' are not supposed to be translatable to fol in APE. I was having trouble with some sentences I was trying, and I finally realized it was the use of those words that caused the trouble.
> 
> Best,
> Josh Cason

Joshua

ACE provides modality with modal auxiliaries for possibility (can/cannot/can not/can't), necessity (must/have to/does not have to), recommendation (should/should not/shouldn't), and admissibility (may/may not) all of which are translated by APE into a similar DRS.

Here are some examples:

A man can sleep.

[A]
object(A,man,countable,na,eq,1)-1/2
   CAN
   [B]
   predicate(B,sleep,A)-1/4


A man must sleep.

[A]
object(A,man,countable,na,eq,1)-1/2
   MUST
   [B]
   predicate(B,sleep,A)-1/4


A man should sleep.

[A]
object(A,man,countable,na,eq,1)-1/2
   SHOULD
   [B]
   predicate(B,sleep,A)-1/4


A man may sleep.

[A]
object(A,man,countable,na,eq,1)-1/2
   MAY
   [B]
   predicate(B,sleep,A)-1/4


Only the modalities 'possibility' and 'necessity' have a translation into FOL using the possible world semantics (http://en.wikipedia.org/wiki/Possible_world, http://en.wikipedia.org/wiki/Modal_logic#Semantics) via the standard transformation (http://en.wikipedia.org/wiki/Standard_translation). 

The standard translation adds to each DRS condition an argument – in our translation the initial argument – that stands for a possible world. Possible worlds are related by an accessibility relation that in the case of my reasoner RACE is the equivalence relation (reflexive, symmetric and transitive) to allow for as many deductions as possible.

Here are the 'possibility' and 'necessity' examples from above in FOL

A man can sleep. (= There is at least on accessible world in which a man sleeps.)

exists(A,&(object(B,A,man,countable,na,eq,1)-1/2,exists(C,&(accessibility_relation(B,C)-accessibility_relation/0,exists(D,predicate(C,D,sleep,A)-1/4)))))

Please note that for consistency the condition accessibility_relation/2 gets a sentence/token indicator accessibility_relation/0.


A man must sleep. (= In all accessible worlds a man sleeps.)

exists(A,&(object(B,A,man,countable,na,eq,1)-1/2,forall(C,=>(accessibility_relation(B,C)-accessibility_relation/0,exists(D,predicate(C,D,sleep,A)-1/4)))))


I hope that this answers your question. If not, let me and the mailing list know.

Best.

Norbert E. Fuchs
Department of Informatics & Institute of Computational Linguistics
University of Zurich