Part Clause about avoiding redundant FOL statements (CEO) The task is to add a paragraph in the introduction of CRMbase showing that asymmetric implies irreflexive. There is a typo in the existing text Reflexive should be Irreflexive. The new paragraph is highlighted in yellow Best Chr-E
asymmetric Asymmetric is defined in the standard way found in mathematics or logic: A property is asymmetric if the domain and the range are the same class and for all instances of x, y of this class, the following is the case: If x is related by P to y, then y is not related by P to x. An example of an asymmetric property is E18 Physical Thing. P46 is composed of (forms part of): E18 Physical Thing. reflexive Reflexive is defined in the standard way found in mathematics or logic: A property P is reflexive if the domain and range are the same class and for all instances x, of this class the following is the case: x is related by P to itself. The intention of a property as described in the scope note will decide whether a property is reflexive or not. An example of a reflexive property is E53 Place. P89 falls within (contains): E53 Place. irreflexive Irreflexivity is defined in the standard way found in mathematics or logic: A property P is irreflexive if the domain and range are the same class and for all instances x of this class, the following is the case: x is not related by P to itself. An example of an irreflexive property is E33 Linguistic Object. P73 has translation (is translation of): E33 Linguistic Object. P is asymmetric implies that P is irreflexive: Assume that P is asymmetric then for all x,y: P(x,y) implies not P(y,x). So P(x,x) will imply not P(x,x) which is a contradiction and P(x,x) cannot be the case.
_______________________________________________ Crm-sig mailing list [email protected] http://cidoc-crm.org/crm-sig-mailing-list
