Axiomatizing the italicized parts (lines 2427): (01)
Domain predicates: (02)
(prizeAmt n): n is the amount of the prize, a nonnegative integer
(work w): w is a work
(aw n w): amount of money n is awarded to work w
(person p): p is a person
(ap n p): amount of money n is awarded to person p
(do p w): person p participated in the doing of work w (03)
Arithmetic and set theoretic predicates, functions, and constants from
background theories (defined in the obvious ways): (04)
the nonnegative integers, e.g., 0, 2 and 3
n=(diff n1 n2): n is the difference between n1 and n2 (n1n2)
n=(quotient n1 n2): n is the quotient of n1 divided by n2, with
whatever rounding convention the Nobel committee
uses and with an arbitrary value stipulated when
n2=0; we'll be careful not to invoke that.
(leq n1 n2): integer n1 is less than or equal to integer n2 (05)
(set s): s is a set
(subset s1 s): s1 is a subset of s
n=(card s): integer n is the cardinality of set s
s=(union s1 s2): set s is the union of sets s1 and s2
(member x s): entity x is a member of set s
s1=(deleteElt s x): set s1 is the result of deleting element x from
set s
(null s): s is the null set (06)
(equal x1 x2): entity x1 is the same as entity x2 (07)
Axioms: (08)
A work has a set (or team) of performers. (09)
(forall (w)
(if (work w)
(exist (t)
(and (set t)(performers t w)
(forall (p)
(if (member p t)(and (person p)(do p w))))))) (010)
Note: I could have said "iff" for the last "if" but Nobel Prizes are
notorious for leaving out people who contributed to the discovery. (011)
A prize amount has a set of at most 2 works it is divided equally
among. (012)
(forall (n)
(if (prizeAmt n)
(exist (s)
(and (leq (card s) 2)
(forall (w)
(if (member w s)
(and (work w)(aw (quotient n (card s)) w)))))))) (013)
Note: It is possible that s is empty, as when no prize is awarded.
The term "(quotient n 0)" won't be invoked in this case. (014)
The prize for a work is divided equally (but see below) among a team
of people who did the work. (015)
(forall (n w)
(if (and (aw n w)(performers t w))
(forall (p)
(if (member p t)(ap (quotient n (card t)) p))))) (016)
No more than 3 people can share the award. (017)
(forall (n1 n2 w1 w2 t1 t2)
(if (and (aw n1 w1)(aw n2 w2)(performers t1 w1)(performers t2 w2))
(leq (card (union t1 t2)) 3))) (018)
I think that captures all the conditions. (019)
Note however that the penultimate axiom says the amount given to the
work is divided equally among the performers. But the rules say
"jointly", not "equally". (So Watson could have gotten 10 times as
much as Crick.) This is slightly more complicated. (020)
One way to do it is to extend the definitionof "aw" from works to the
teams that perform the works. (021)
(forall (t w n)
(if (and (performers t w)(aw n w))
(aw n t))) (022)
Each team member's award is a part of the total award. (023)
(forall (n t p n1)
(if (and (aw n t)(member p t)(ap n1 p))
(aw (diff n n1)(deleteElt t p)))) (024)
The null team is awarded zero dollars. (025)
(forall (n t)
(if (null t)(aw 0 t))) (026)
These are the only ways an amount can be awarded ("aw") to a set. (027)
(forall (n1 t1)
(if (and (aw n1 t1)(set t1))
(exist (n t w)
(and (work w)(aw n w)(performers t w)(subset t1 t))))) (028)
 (029)
To embed all this in announcements, we extend certain predicates with
category and time arguments, with obvious changes to the above axioms: (030)
(prizeAmt n c t): n is the total amount of money for the prize in
category c in month t.
(aw n w c t): amount of money n is given for work w in category c in
month t.
(ap n p c t): amount of money n is given to person p in category c in
month t. (031)
The new domain predicates: (032)
(category c): c is a category of Nobel Prize, i.e., a member of the
set of constants
{Chemistry, Physics, Medicine, Literature, Peace, Economics} (033)
(announce c p w n t): a prize in category c is announced for
recipient p for work w in amount n in month t.
p is a person, and w is a work, or they are designated values, say
the null set, in case there is no prize in that category in that
year. (034)
From the background theory of time (e.g., OwLTime): (035)
(October t y): t is the month of October of some year y (036)
Axioms: (037)
What an announcement means. (038)
(forall (c p w n1 t)
(if (announce c p w n1 t)
(and (category c)
(exist (y)(October t y))
(iff (null p)(null w))
(or (null p)
(exist (n s)
(and (aw n w c t)(ap n1 p c t)
(performers s w)(member p s))))))) (039)
Announcements are made every October in each category. (040)
(forall (c y t)
(if (and (October t y)(category c))
(exist (p w n n1)
(and (prizeAmt n c t)(announce c p w n1 t))))) (041)
 (042)
John, (043)
Thanks for your quick response. See further in line below. (044)
Ragards (045)
Sjir (046)
PS I am happy to provide the artefacts in SBVR, OWL, UML, CogNIAM and SQL. I
hope many others will specify the artefact in at least one formalism. My
assumption is that comparing these results will provide new insights. (047)
From: ontologforumbounces@xxxxxxxxxxxxxxxx on behalf of John F. Sowa
Sent: Tue 12/14/2010 6:08 PM
To: ontologforum@xxxxxxxxxxxxxxxx
Subject: Re: [ontologforum] Experiment in ontology engineering for part of the
Nobel Prize (048)
Sjir, (049)
The approach I have recommended is to start with controlled NLs
and use tools for translating them to other notations. [[Sjir: this is part of
the approach or methodology; may I propose to first start with the
artefacts and thereafter concentrate on the process how the artefact was
arrived at.]] (050)
For your suggested example, I would start by translating
the English to controlled English (CLCE) and then translate
the CLCE to other notations, such as CLIF and CGIF. (051)
But your text is rather long, and it wasn't clear how much
of the it you wanted us to translate. [[Sjir: The following lines contain
structurally relevant information to be reflected in the ontology: 11, 12,
17 through 30 and 33. (052)
What part did you expect
people to translate? Was it just this italicized part? [[Sjir: the italicized
part is copied from the Nobel Prize statutes.]] (053)
> A prize amount may be equally divided between two works, each
> of which is considered to merit a prize. If a work that is being
> rewarded has been produced by two or three persons, the prize
> shall be awarded to them jointly. In no case may a prize amount
> be divided between more than three persons. (054)
Did you expect us to translate any other part of the text
to our preferred notation or just this one segment? [[Sjir: see above.]] (055)
John (056)
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