Differences

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

syntax [2010/08/18 12:00]
jipsen
syntax [2010/08/18 12:13] (current)
jipsen
Line 1: Line 1:
-[[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**+==== Operation symbols ====
-$a$ $b$ $c$ $d$ $e$ $\bot$ $\top$ $\emptyset$ $\infty$ $0$-$9$ $\alpha-\omega$+  ***Constant symbols** 
 +    *$a$ $b$ $c$ $d$ $e$ $\bot$ $\top$ $\emptyset$ $\infty$ $0$-$9$ $\alpha-\omega$
-**Unary operation symbols**+  ***Unary operation symbols** 
 +    *Prefix: $f$ $g$ $h$ $-$ $\neg$ $\sim$ 
 +    *Postfix: $'$ ${}^{-1}$ ${}^{\cup}$
-Prefix: $f$ $g$ $h$ $-$ $\neg$ $\sim$+  ***Binary operation symbols** 
 +    *Prefix: $f$ $g$ $h
 +    *Infix: $+$ $-$ $*$ $\cdot$ $\times$ $\div$ $/$ $\backslash$ $\circ$ $\oplus$ $\otimes$ $\odot$ $\wedge$ $\vee$ $\to$
-Postfix: $'$ ${}^{-1}$ ${}^{\cup}$+  ***Ternary operation symbols** 
 +    *Prefix: $t$
-**Binary operation symbols**+  ***Quadternary operation symbols** 
 +    *Prefix: $q$
-Prefix: $f$ $g$ $h$+  *$n$**-ary operation symbols** 
 +    *Prefix: $\sum_n$ $\prod_n$ 
 +    *Mixfix: { } [ ] ( )
-Infix: $+$ $-$ $*$ $\cdot$ $\times$ $\div$ $/$ $\backslash$ $\circ$ $\oplus$ $\otimes$ $\odot$ $\wedge$ $\vee$ $\to$+  *$\omega$**-ary operation symbols** 
 +    *$\sum_\omega$ $\prod_\omega$
-**Ternary operation symbols**+  *$\kappa$**-ary operation symbols** 
 +    *$\sum_\kappa$ $\prod_\kappa$
-Prefix: $t$+  *$\infty$**-ary operation symbols** 
 +    *$\sum$ $\prod$ $\bigcap$ $\bigcup$ $\bigwedge$ $\bigvee$
-**Quadternary operation symbols** 
-Prefix: $q$+==== Relation symbols ====
-$n$**-ary operation symbols**+  ***0-ary relation symbols** 
 +    *Propositions ⊥ ⊤ T F
-Prefix: $\sum_n$ $\prod_n$+  ***Unary relation symbols** 
 +    *Prefix: P Q
-Mixfix: {_} [_] (_)+  ***Binary relation symbols** 
 +    *Prefix:
 +    *Infix: = ≠ ≤ < ≥ > ⪯ ≺ ⪰ ≻ ≡ ≅ ≈ ∈ ∉
-$\omega$**-ary operation symbols**+  ***Ternary relation symbols**
-$\sum_\omega$ $\prod_\omega+  ***Quadternary relation symbols**
-$\kappa$**-ary operation symbols**+  ***n-ary relation symbols**
-$\sum_\kappa$ $\prod_\kappa+  ***ω-ary relation symbols**
-$\infty$**-ary operation symbols**+  **-ary relation symbols**
-$\sum$ $\prod$ $\bigcap$ $\bigcup$ $\bigwedge$ $\bigvee$ +  ***∞-ary relation symbols**
-= Relation symbols =+
-**0-ary relation symbols** 
- 
-Propositions ⊥ ⊤ T F 
- 
-**Unary relation symbols** 
- 
-Prefix: P Q 
- 
-**Binary relation symbols** 
- 
-Prefix: R 
- 
-Infix: = ≠ ≤ < ≥ > ⪯ ≺ ⪰ ≻ ≡ ≅ ≈ ∈ ∉  
- 
-**Ternary relation symbols** 
- 
-**Quadternary relation symbols** 
- 
-**n-ary relation symbols** 
- 
-**ω-ary relation symbols** 
- 
-**κ-ary relation symbols** 
- 
-**∞-ary relation symbols** 
==== Connectives ==== ==== Connectives ====
-**0-ary connectives** +  ***0-ary connectives**
- +
-**Unary 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.