Relationsumo#total_ordering_on(pm#binary_relation_type,sumo#set_or_class)a binary_relation ?REL is a total ordering on a set_or_class only if it is a partial ordering for which either (?REL ?INST1 ?INST2) or (?REL ?INST2 ?INST1) for every ?INST1 and ?INST2 in the set_or_classtype: pm#binary_predicate_typethe class of predicates relating two items - its valence is twotype: pm#asymmetric_relation_typean antisymmetric and irreflexive relationsupertype: pm#relation_to_set_or_class (*,pm#set_or_class) supertype: pm#relation_to_collection (*,pm#collection) supertype: pm#relation_from/to_thing_of_common_kind (*)this type permits to categorize relations according to their signatures and hence offers (i) a concise way to set essential exclusion relations, and (ii) a systematic and easy-to-follow categorizationsupertype: pm#relation__related_thing__relatedthing___related_with (*)type for any relation (unary, binary, ..., *-ary) and instance of pm#relation_typesupertype: pm#what_relation (*) supertype: pm#wh-/how_relation (*)this type permits to categorize relations according to the usual who/what/why/where/when/how questions ; this is a traditional but very subjective and ineffective way of categorizing relationssupertype: pm#relation__related_thing__relatedthing___related_with (*)type for any relation (unary, binary, ..., *-ary) and instance of pm#relation_typesupertype: pm#asymmetric_relation (?,?)this category only serves structuration purposes: it is instance of pm#asymmetric_relation_type which is not instance of pm#class_of_inheritable_relation_typesupertype: pm#irreflexive_relation__irreflexiverelation (?,?)this category only serves structuration purposes: it is instance of pm#irreflexive_relation_type which is not instance of pm#class_of_inheritable_relation_typesupertype: pm#binary_relation_with_particular_mathematical_property (?,?) supertype: pm#relation_with_particular_mathematical_property (*) supertype: pm#relation_with_particular_property (*)this rather fuzzy type permits to group categorization schemes less common than those covered by the previous sibling categoriessupertype: pm#relation__related_thing__relatedthing___related_with (*)type for any relation (unary, binary, ..., *-ary) and instance of pm#relation_typesupertype: pm#antisymmetric_relation__antisymmetricrelation (?,?)this category only serves structuration purposes: it is instance of pm#antisymmetric_relation_type which is not instance of pm#class_of_inheritable_relation_typesupertype: pm#binary_relation_with_particular_mathematical_property (?,?)