Parts and Boundaries 4 - functions that map between values of B and I

Plural

• ∀x,y. plural(x,y) -> ~bounded(x) and complex(x) and bounded(y) and x=_$y
• ∀x. ~bounded(x) and complex(x) -> ∃y. plural(x,y)

Note that =_$ is an equivalence relation for conceptual parts of speech:

• ∀x,y. x=_$y <-> (matter(x) <-> matter(y) and event(x) <-> event(y) and place(x) <-> place(y) and event(x) <-> event(y))

e.g. (a) 'cattle/cows': plural(x,y), cow(y); (b) 'the light flashed (until dawn)': plural(e,f), lightflash(f).

Element

• ∀x,y. element(x,y) -> bounded(x) and ~complex(x) and ~bounded(y) and complex(y) and x=_$y

e.g. 'a grain of rice': element(x,y), rice(y). Note that 'element' is an extracting function - element(x,y) does not imply the existence of y, unlike its inverse plural(x,y).

This might also be used for substances (e.g. 'a drop of water'), but I think it'd be better to have another function that reanalyses substances as aggregates first.

Composition

• ∀x,y. composition(x,y) -> bounded(x) and ~complex(x) and ~bounded(y) and ~complex(y) and x=_$y

e.g. 'a coffee': composition(x,y), coffee(y); 'a house of wood': house(x), composition(x,y), wood(y). Further extensions are possible for 'a house of bricks', 'a pile of bricks/sand', 'a stack of bricks', 'a herd of cows'.

Grinder

• ∀x,y. grinder(x,y) -> ~bounded(x) and ~complex(x) and bounded(y) and ~complex(y)

e.g. 'beef': grinder(x,y), cow(y); 'Bill is writing a novel': grinder(x,y), write(y,bill,z), novel(z).