# Differences

This shows you the differences between two versions of the page.

syntax [2010/08/18 11:58]
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syntax [2010/08/18 12:13] (current)
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-[[Syntax]] | [[Terms]] | [[Equations]] | [[Quasiequations]] | [[Theories]]+[[Syntax]] | [[Terms]] | [[Equations]] | [[Horn formulas]] | [[Universal formulas]] | [[First-order formulas]] | [[Theories]]
-===== Variables =====+
+==== Variables ====
$x$ $y$ $z$ $u$ $v$ $w$ $x_0$ $x_1$ $x_2$ ... $x$ $y$ $z$ $u$ $v$ $w$ $x_0$ $x_1$ $x_2$ ...
-===== 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: $\sum_n$ $\prod_n$+==== Operation symbols ====
-Mixfix: {_} [_] (_)+  ***Constant symbols**
+    *$a$ $b$ $c$ $d$ $e$ $\bot$ $\top$ $\emptyset$ $\infty$ $0$-$9$ $\alpha-\omega$
-** $\omega$-ary operation symbols **+  ***Unary operation symbols**
+    *Prefix: $f$ $g$ $h$ $-$ $\neg$ $\sim$
+    *Postfix: $'$ ${}^{-1}$ ${}^{\cup}$
-$\sum_\omega$ $\prod_\omega+ ***Binary operation symbols** + *Prefix:$fgh$+ *Infix:$+-*\cdot\times\div/\backslash\circ\oplus\otimes\odot\wedge\vee\to$-**$\kappa$-ary operation symbols **+ ***Ternary operation symbols** + *Prefix:$t$-$\sum_\kappa\prod_\kappa+  ***Quadternary operation symbols**
+    *Prefix: $q$
-** $\infty$-ary operation symbols **+  *$n$**-ary operation symbols**
+    *Prefix: $\sum_n$ $\prod_n$
+    *Mixfix: { } [ ] ( )
-$\sum$ $\prod$ $\bigcap$ $\bigcup$ $\bigwedge$ $\bigvee$ +  *$\omega$**-ary operation symbols**
-= Relation symbols =+    *$\sum_\omega$ $\prod_\omega$
-** 0-ary relation symbols **+  *$\kappa$**-ary operation symbols**
+    *$\sum_\kappa$ $\prod_\kappa$
-Propositions ⊥ ⊤ T F+  *$\infty$**-ary operation symbols**
+    *$\sum$ $\prod$ $\bigcap$ $\bigcup$ $\bigwedge$ $\bigvee$
-** Unary relation symbols **
-Prefix: P Q+==== Relation symbols ====
-** Binary relation symbols **+  ***0-ary relation symbols**
+    *Propositions ⊥ ⊤ T F
-Prefix: R+  ***Unary relation symbols**
+    *Prefix: P Q
-Infix: = ≠ ≤ < ≥ > ⪯ ≺ ⪰ ≻ ≡ ≅ ≈ ∈ ∉ +  ***Binary relation symbols**
+    *Prefix: R
+    *Infix: = ≠ ≤ < ≥ > ⪯ ≺ ⪰ ≻ ≡ ≅ ≈ ∈ ∉
-** Ternary relation symbols **+  ***Ternary relation symbols**
-** n-ary relation symbols **+  ***n-ary relation symbols**
-** ω-ary relation symbols **+  ***ω-ary relation symbols**
-** κ-ary relation symbols **+  ***κ-ary relation symbols**
-** ∞-ary relation symbols **+  ***∞-ary relation symbols**
-= Connectives =
-** 0-ary connectives **+==== Connectives ====
-** Unary connectives **+  ***0-ary connectives**
-⋄ □+  ***Unary connectives**
+    *⋄ □
-** Binary connectives **+  ***Binary connectives**
+    *Infix: and ∧ or ∨ ⇒ ⇔
+    *Mixfix: if_then_ &nbsp; while_do_
-Infix: and ∧ or ∨ ⇒ ⇔ +  ***Ternary connectives**
+    *if_then_else_
-Mixfix: if_then_ &nbsp; while_do_+  ***Quadternary connectives**
-** Ternary connectives **+  ***n-ary connectives**
-if_then_else_+  ***ω-ary connectives**
-** Quadternary connectives **+  ***κ-ary connectives**
-** n-ary connectives **+  ***∞-ary connectives**
-** ω-ary connectives **
-** κ-ary connectives **+==== Quantifiers ====
-** ∞-ary connectives **+    *∀ ∃
-===== Quantifiers =====
-∀ ∃+==== Delimiters ====
-===== Delimiters =====+    *( ) [ ] { } 〈 〉
-( ) [ ] { } 〈 〉
-===== Signatures / Languages =====+==== Signatures / Languages ====
A signature or language is a sequence of operation symbols, relation symbols and connectives. A signature or language is a sequence of operation symbols, relation symbols and connectives.