From 3e1b81996af41728090f5aa98e609273b533d5b3 Mon Sep 17 00:00:00 2001
From: Giovanni Ciatto <giovanni.ciatto@unibo.it>
Date: Sat, 5 Mar 2022 17:17:32 +0100
Subject: [PATCH] chore: add readme with overview

---
 README.md                            | 58 ++++++++++++++++++++++++++++
 ise-lab-knowledge-representation.sty |  2 +-
 ise-lab-knowledge-representation.tex |  6 +--
 3 files changed, 61 insertions(+), 5 deletions(-)
 create mode 100644 README.md

diff --git a/README.md b/README.md
new file mode 100644
index 0000000..976eeb8
--- /dev/null
+++ b/README.md
@@ -0,0 +1,58 @@
+## Knowledge Representation
+with Horn Clauses
+
+### Goals
+
+- Understand basic notions such as:
+    * terms
+    * clauses (facts, rules, goals)
+    * propositional vs. relational representations
+    * logic variables
+    * extensional vs. intensional representations
+    * unifiers and substitutions
+    * unification and MGU
+
+### Overview
+
+- Horn clauses
+    * Motivations
+        + nice expressiveness-tractability trade-off
+        + basis for Prolog and LP
+        + very well established: tons of literature, theorems, technologies
+    * Overall syntax (notice the difference among terms and clauses)
+    * 2P-Kt as the underlying technology for examples
+- Representing objects with terms
+    * Syntax for terms (skip variables)
+    * Examples:
+        - How to consturct Peano integers
+        - How to construct data structures with terms (e.g. lists)
+- Representing propositions, sets, or relations with predicates
+    * Syntax for horn clauses
+    * Examples
+    * Defining propositions, sets, or relations via clauses
+        + Sets as unary predicates, Relations as N-ary predicates, Propositions as 0-ary predicates
+        + How to construct sets (e.g. nat/1, lst/1)
+        + How to construct relations (e.g. succ/2, member/2, sum/3, append/3)
+- Prolog trick:
+    * same syntax for both terms and predicates 
+        + making them interchaengable
+- Propositional vs. Relational representations?
+- Logic variables: 
+    * Recall overall syntax, highlighting variables
+    * Purpose: placeholders for unknown terms (representing unknown entities)
+    * Definitions: ground term/clause/theory
+    * Extensional vs. Intensional: 
+        + logic variables support intensional representations via non-ground clauses
+        * otherwise one would require all information to be extensionally represented via ground clauses
+    * Two powerful mechanisms:
+        * Unification: computes a substitution making two terms/clauses equal
+        * Resolution: attempts to prove a goal true or not
+        * Both rely on the notion of subtitution
+- Unifier: a mapping among variables and terms (possibly attained via unification)
+    * Can be empty
+    * Can be _applied_ to a term, producing a new term
+    * Substituion: the result of unification or resolution
+        - Can be failed, or a unifier
+- Unification: algorithms to compute the most general unifier (MGU) among 2 terms 
+    * Unification table
+    * Mention the Martelli and Montanari algorithm
diff --git a/ise-lab-knowledge-representation.sty b/ise-lab-knowledge-representation.sty
index 362ca77..bde9e92 100644
--- a/ise-lab-knowledge-representation.sty
+++ b/ise-lab-knowledge-representation.sty
@@ -1,2 +1,2 @@
 % ISE numbering
-\labN{0}
+\labN{1}
diff --git a/ise-lab-knowledge-representation.tex b/ise-lab-knowledge-representation.tex
index 5e63e45..d43e567 100644
--- a/ise-lab-knowledge-representation.tex
+++ b/ise-lab-knowledge-representation.tex
@@ -14,12 +14,10 @@
 % version
 \newcommand{\versionmajor}{0}
 \newcommand{\versionminor}{1}
-\newcommand{\versionpatch}{2}
+\newcommand{\versionpatch}{3-dev}
 \newcommand{\version}{\versionmajor.\versionminor.\versionpatch}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\title[\currentLab{} -- Short Title]{
-	Long Title
-}
+\title[\currentLab{} -- Knowledge Representation]{Knowledge Representation}
 %
 \subtitle{\courseName{} / Module \moduleN{} (\courseAcronym)}
 %