# 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 :**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle X\times Y = \{(x,y) | x\in X \ \text{and} \ y\in Y\}. }**
^{[1]}

**Modal Logic**
The basic unary (1-place) modal operators are usually written **Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \Box}**
for *Necessarily* and **Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \Diamond}**
for *Possibly*. In a classical modal logic, each can be expressed by the other with negation:

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \Diamond P \leftrightarrow \lnot \Box \lnot P;}****Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \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

- ↑ Warner, S:
*Modern Algebra*, page 6. Dover Press, 1990.