The CLCE statements in this example have been adapted from http://www.clp.ox.ac.uk/people/staff/pulman/grocers.html.
Following are the CLCE declarations for the nouns and adjectives. The CLCE "from" option has been extended to allow Boolean combinations of previously declared relations. The adjective "dishonest" is defined as "not honest"; the noun "bachelor" could be defined as "man and not married". The only restriction is that all relations in any Boolean combination must have the same number of arguments, such as all monadic or all dyadic.
Declare honest, industrious, healthy as adjective,
dishonest as adjective from (not honest),
unhealthy as adjective from (not healthy),
grocer, cyclist, person as noun.
The following CLCE statements define the type hierarchy:
Every grocer is a person. Every cyclist is a person.The following axioms are based on the puzzle by Lewis Carroll. The only changes are to replace Carroll's plurals, such as "All grocers are", with the corresponding singular form "Every grocer is" and to accommodate grocers and cyclists of both sexes by replacing "man" with "person".
Every honest industrious person is healthy. No grocer is healthy. Every industrious grocer is honest. Every cyclist is industrious. Every unhealthy cyclist is dishonest.The answer to the following question can be deduced from the declarations, axioms, and type hierarchy:
Is it true that no grocer is a cyclist?