Atom (Logic)

Atoms are the building blocks of logic, and are used to form more complicated well-formed formulae . As the name suggests, they cannot be broken down further. An atom can either refer to a proposition (in propositional logic) or an atomic predicate (in predicate logic).

Conventionally, they are denoted with uppercase variables starting from $P$, i.e. $P,Q,R,S\dots$

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Definition §

Atom

An atom is a formula that does not contain any sub-formulas inside it.

• In propositional logic, this refers to single-letter proposition: $P,Q,R,\dots$ are all atoms
• In predicate logic, this refers to predicates that do not contain any sub-predicates, but can contain any number of terms: $P(x),Q(x,y,c),R(f(z),a,w)$ are all atoms

Examples §

Examples: Propositional Logic §

• $P=2\text{ is even}$
• $Q=\text{It will rain tommorrow}$
• $R=3+9>32$

Examples : Predicate Logic §

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