# Glossary

Mereology - the study of part whole relationships

Tautology - formula which is true in every possible interpretation

Transitivity - if b is part of a, and a is part of e, then by natural extension, b is part of e.

Rigid - necessarily so. For instance 'human' has a rigid property because all instances of human necessarily so. ... can also be defined by signifying the same thing in every instance.

Non-Rigid - not necessarily so. For instance 'studnt' is non rigid because not all instances of a student are necessarily so. A student is a role that can be taken on by a human.

Continuants: exist in full at every instant in time

Occurents unfold over time and never exist in full at any single moment in time.

Subsumption - is-a relationships.

Patromony - is- part of relationships

Cartesian product the direct product of two sets - such that :$X\times Y = \{(x,y) | x\in X \ \text{and} \ y\in Y\}.$ <ref>Warner, S: Modern Algebra, page 6. Dover Press, 1990.</ref>

Modal Logic The basic unary (1-place) modal operators are usually written $\Box$ for Necessarily and $\Diamond$ for Possibly. In a classical modal logic, each can be expressed by the other with negation:

$\Diamond P \leftrightarrow \lnot \Box \lnot P;$
$\Box P \leftrightarrow \lnot \Diamond \lnot P.$

Thus it is possible that it will rain today if and only if it is not necessary that it will not rain today;
and it is necessary that it will rain today if and only if it is not possible that it will not rain today.

Sortal' - A sortal is something that takes numerical modifiers