### Variables

$x$ $y$ $z$ $u$ $v$ $w$ $x_0$ $x_1$ $x_2$ …

### Operation symbols

• Constant symbols
• $a$ $b$ $c$ $d$ $e$ $\bot$ $\top$ $\emptyset$ $\infty$ $0$-$9$ $\alpha-\omega$
• Unary operation symbols
• Prefix: $f$ $g$ $h$ $-$ $\neg$ $\sim$
• Postfix: $'$ ${}^{-1}$ ${}^{\cup}$
• Binary operation symbols
• Prefix: $f$ $g$ $h$
• Infix: $+$ $-$ $*$ $\cdot$ $\times$ $\div$ $/$ $\backslash$ $\circ$ $\oplus$ $\otimes$ $\odot$ $\wedge$ $\vee$ $\to$
• Ternary operation symbols
• Prefix: $t$
• Prefix: $q$
• $n$-ary operation symbols
• Prefix: $\sum_n$ $\prod_n$
• Mixfix: { } [ ] ( )
• $\omega$-ary operation symbols
• $\sum_\omega$ $\prod_\omega$
• $\kappa$-ary operation symbols
• $\sum_\kappa$ $\prod_\kappa$
• $\infty$-ary operation symbols
• $\sum$ $\prod$ $\bigcap$ $\bigcup$ $\bigwedge$ $\bigvee$

### Relation symbols

• 0-ary relation symbols
• Propositions ⊥ ⊤ T F
• Unary relation symbols
• Prefix: P Q
• Binary relation symbols
• Prefix: R
• Infix: = ≠ ≤ < ≥ > ⪯ ≺ ⪰ ≻ ≡ ≅ ≈ ∈ ∉
• Ternary relation symbols
• n-ary relation symbols
• ω-ary relation symbols
• κ-ary relation symbols
• ∞-ary relation symbols

### Connectives

• 0-ary connectives
• Unary connectives
• ⋄ □
• Binary connectives
• Infix: and ∧ or ∨ ⇒ ⇔
• Mixfix: if_then_ &nbsp; while_do_
• Ternary connectives
• if_then_else_
• n-ary connectives
• ω-ary connectives
• κ-ary connectives
• ∞-ary connectives

• ∀ ∃

### Delimiters

• ( ) [ ] { } 〈 〉

### Signatures / Languages

A signature or language is a sequence of operation symbols, relation symbols and connectives.

Prefix symbols always apply first. Infix symbols and postfix symbols can

In a typed (or multisorted) language the input/output slots of operation symbols and relation symbols are associated to a specific type.

In an order-sorted language the types form a partially ordered set that determines the subtyping relation.

##### QR Code  