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syntax [2010/08/18 11:57]
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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: $t$ 
- 
-** Quadternary operation symbols ** 
- 
-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: $f$ $g$ $h$ 
 +    *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**
-** Quadternary relation symbols **+  ***Quadternary 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.