Daniel Fischer wrote:
class BEING human => HUMAN human where Sub-classing is logical implication BEING(human) => HUMAN(human) All types t that make BEING(t) = true also make HUMAN(t)=true
No, it's the other way round. Every HUMAN is also a BEING, hence
HUMAN(t) => BEING(t)
Could I say that HUMAN is a subset of BEING? Sebastian Fischer wrote:
You can define subclasses even if no instances exist. And as Daniel said, the code
class BEING human => HUMAN human where
defines a subclass HUMAN of BEING which means that every instance of HUMAN must also be a BEING. You can read it as: "a BEING is also a HUMAN by the following definitions".
Thanks for pointing out my error But I am still not sure of the interpretation of logical implication wrt to sub-classes. Lets simplify the representation and just regard the classes in the example as propositions (instead of predicates). I am not sure if this simplification still makes the example valid. Below is a reasonable interpretation of propositional logical implication. a) If I wear a raincoat then I stay dry (sufficient condition) wareRaincoat => stayDry b) I will stay dry only if I ware a raincoat(necessary condition) stayDry => wareRaincoat In the light of the above examples how should I interpret the class-to-subclass relation as logical implication? Is it a) If BEING then HUMAN (sufficient condition): BEING => HUMAN b) HUMAN is true only if BEING (necessary condition): HUMAN => BEING c) Neither? Thanks, Pat This message has been scanned for content and viruses by the DIT Information Services E-Mail Scanning Service, and is believed to be clean. http://www.dit.ie