thodg/slides

Diff from 9a62394b317d08359ed1ef79662b4d11b36b0cad to master


diff --git a/README.md b/README.md
index 3f76c39..0d337c0 100644
--- a/README.md
+++ b/README.md
@@ -11,17 +11,17 @@ with
 
 ### Pandoc
 A few examples of Pandoc usage to generate Beamer presentations from Markdown syntax.
-[Markdown](https://github.com/thodg/slides/blob/master/pandoc/index.md)
-[PDF](https://github.com/thodg/slides/blob/master/pandoc.pdf)
+[Markdown](https://git.kmx.io/thodg/slides/_tree/master/pandoc/index.md)
+[PDF](https://git.kmx.io/thodg/slides/_blob/master/pandoc.pdf)
 
 ## 2019
 
 ### BSD
 About *BSD and UNIX history.
-[Markdown](https://github.com/thodg/slides/blob/master/bsd/index.md)
-[PDF](https://github.com/thodg/slides/blob/master/bsd.pdf)
+[Markdown](https://git.kmx.io/thodg/slides/_tree/master/bsd/index.md)
+[PDF](https://git.kmx.io/thodg/slides/_blob/master/bsd.pdf)
 
 ### RailsOnLisp
 An introduction to Common Lisp and RailsOnLisp.
-[Markdown](https://github.com/thodg/slides/blob/master/railsonlisp/index.md)
-[PDF](https://github.com/thodg/slides/blob/master/railsonlisp.pdf)
+[Markdown](https://git.kmx.io/thodg/slides/_tree/master/railsonlisp/index.md)
+[PDF](https://git.kmx.io/thodg/slides/_blob/master/railsonlisp.pdf)
diff --git a/bsd/index.md b/bsd/index.md
index 133e6d3..cb7c103 100644
--- a/bsd/index.md
+++ b/bsd/index.md
@@ -12,42 +12,42 @@ https://kmx.io/
 
 ### Diagram
 
-![UNIX](unix-history.png)
+![UNIX](https://git.kmx.io/thodg/slides/_blob/master/bsd/unix-history.png)
 
 ### Multics
 
-1960  
+1960
 
 Companies
 
   - MIT
-  
+
   - AT\&T Bell labs
-  
+
   - General Electric
 
 ### UNIX
 
-AT\&T Bell Labs 1970  
+AT\&T Bell Labs 1970
 
 Developers
 
   - Ken Thompson
-  
+
   - Dennis Ritchie
 
 ### Berkeley Unix
 
-1974  
+1974
 
 Licensed by AT\&T
 
 ### Berkeley Software Distribution
 
-1979  
+1979
 
   - `vi`
-  
+
   - `csh`
 
 Licensed by AT\&T
@@ -56,7 +56,7 @@ Licensed by AT\&T
 
     Copyright (c) <year> <copyright holder>.
     All rights reserved.
-    
+
     Redistribution and use in source and binary forms are permitted
     provided that the above copyright notice and this paragraph are
     duplicated in all such forms and that any documentation,
@@ -71,12 +71,12 @@ Licensed by AT\&T
 
 ### Net/1
 
-June 1989  
+June 1989
 
 Basis for
 
   - NetBSD
-  
+
   - FreeBSD
 
 Under BSD License
diff --git a/language/index.md b/language/index.md
index 8d2d807..b06c5f8 100644
--- a/language/index.md
+++ b/language/index.md
@@ -24,8 +24,7 @@ In model theory a schema allows you to define an ontology,
 that is a definition of what can and cannot be expressed in your
 language.
 
-It is the shape of your language, the rules which make any pattern
-part of the language or not.
+It is a set of rules which make any pattern part of the language or not.
 
 The most used schemas for formal language definition are grammars.
 
@@ -62,15 +61,10 @@ semantics.
 
 It is a direct application of the language schema.
 
-The data of the language is directed by the semantics of
-the language.
-
-Usually the schema of the language has an entropy of orders
-of magnitude higher than the available storage space for the
-language data.
+Semantics are appliable to all data.
 
 Data is a choice from the possibilities of the language schema
 driven by the semantics of the language.
 
-It is the most precise use of the language. Each datum represents
-a single valid use of the language and can be uniquely identified.
+Each datum represents a single valid use of the language and can
+be uniquely identified.
diff --git a/modal-logic/index.md b/modal-logic/index.md
index 75f2f81..ecabc5a 100644
--- a/modal-logic/index.md
+++ b/modal-logic/index.md
@@ -1,13 +1,31 @@
 # Modal logic
 
 ## 1. Notation
-¬A   "Not A"
 
-□A    "It is necessary that A"
+### 1.1 ¬A
+"Not A"
 
-◊A    "It is possible that A"
+### 1.2 □A
+"It is necessary that A"
+
+### 1.3 ◊A
+"It is possible that A"
+
+### 1.4 A → B
+"If A then B"
+
+### 1.5 A ∧ B
+"A and B"
+
+### 1.6 A ∨ B
+"A or B"
+
+### 1.7 A ⊕ B
+"A xor B"
+
+### 1.8 A ↔ B
+"If A then B and if B then A"
 
-A → B "If A then B"
 
 ## 2. Contruction
 K is a weak logic (Saul Kripke)
@@ -18,7 +36,18 @@ A is a theorem of K → □A is a theorem of K
 ### 2.2 Distribution axiom
 □(A → B) → (□A → □B)
 
-## 3. T
+### 2.3 Operator ◊
+◊A = ¬□¬A
+
+## 3. Lemmas
+
+### 3.1 Necessary conjunction
+□(A ∧ B) ↔ □A ∧ □B
+
+### 3.2 Disjonction of necessities
+◻A ∨ ◻B → □(A ∨ B)
+
+## 4. T
 T is K plus the following axiom :
 
 □A → A