04-planning_uncertainty_hmm_lsg.ipynb

{
 "cells": [
  {
   "attachments": {
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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Planung\n",
    "\n",
    "## 1. Ein einfaches Planungs-Problem\n",
    "Das Anziehen von Socken und Schuhen ist ein Planungsproblem. Schuhe können nur angezogen werden, wenn die jeweilige Socke schon angezogen ist. In dieser Aufgabe soll das Anziehen von Socken und Schuhen modelliert werden.\n",
    "* Zeichnen Sie den partiell geordneten Plan, und alle total geordneten Pläne auf. (Lösung in \"U4/loesung\" zu finden)\n",
    "* Lösen Sie das Problem mit dem ff Planner. \n",
    "* Laden Sie dafür die Datei “Uebung4.zip” aus Stud.IP herunter und entpacken Sie diese. \n",
    "* Alternativ starten Sie ein neues Terminal hier im Jupyter Dashboard und navigieren in den Ordner \"U4\".\n",
    "* Den Planer können Sie wie folgt aufrufen: ./ff -o shoes/d.pddl -f shoes/p.pddl. Interpretieren Sie die Ausgabe.\n",
    "\n",
    "## 2. Das Office-Planungsproblem\n",
    "In dieser Aufgabe soll der typische Arbeitstag der Mitarbeiter am Lehrstuhl MMIS (Kaffee holen, umherlaufen, Dinge ausdrucken) als Planungsproblem modelliert werden. Mitarbeiter können nur Kaffee machen, wenn die Kaffeemaschine mit Kaffee und Wasser befüllt ist. Kaffee kann am Kaffee-Glas geholt werden, Wasser am Wasserhahn. Mitarbeiter können immer nur ein Ding gleichzeitig in der Hand halten. Am Drucker kann nur gedruckt werden, wenn der Drucker mit Papier befüllt ist. Papier gibt es am Papier-Schrank. Das Ziel der Mitarbeiter ist es, alle Printjobs gedruckt zu haben, alle einen Kaffee in der Hand zu halten, und am Ausgang zu stehen.\n",
    "\n",
    "![grafik.png](attachment:grafik.png)\n",
    "\n",
    "Die verfügbare Aktionen der Mitarbeiter sind:\n",
    "\n",
    "* goto: Ein Mitarbeiter bewegt sich zwischen zwei Positionen. Die beiden Positionen dürfen nicht gleich sein.\n",
    "* fetch: Ein Mitarbeiter nimmt Papier, Kaffee oder Wasser, wenn er sich an der jeweigen Location befindet.\n",
    "* replenish: Ein Mitarbeiter füllt den Drucker oder die Kaffeemaschine auf. Das geht dann, wenn der die entsprechende Ressource in der Hand hält.\n",
    "* get-coffee: Ein Mitarbeiter nimmt sich einen Kaffee, wenn er an der Maschine steht, und diese befüllt ist.\n",
    "* print: Ein Mitarbeiter druckt einen Printjob, wenn er am Drucker steht, und der Drucker Papier enthält.\n",
    "\n",
    "Definieren Sie die entsprechenden Aktionen in der Datei abc-d.pddl. Rufen Sie den Planer wie folgt auf: ./ff -o abc/abc-d.pddl -f abc/abc-p.pddl. Interpretieren Sie die Ausgabe.\n",
    "* Lösung in \"U4/loesung\" zu finden"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Satz von Bayes\n",
    "\n",
    "Bob möchte gerne wissen, ob es regnet. Dazu schaut er aus dem Fenster, ob die Straße nass ist. Wenn es tatsächlich regnet, ist die Straße mit einer Wahrscheinlichkeit von 95 % nass (in 5 % der Fälle regnet es noch nicht lange genug, damit die Straße für Bob nass aussieht). Wenn es nicht regnet, ist die Straße mit einer Wahrscheinlichkeit von 25 % nass (weil der Nachbar von Bob den Rasensprenger laufen lässt, der auch die Straße trifft). Darüber hinaus weiß Bob, dass es an 40 % aller Tage regnet. Benutzen Sie für die folgenden Aufgaben die folgende Notation:\n",
    "\n",
    "* $r$: Es regnet.\n",
    "* $\\bar{r}$: Es regnet nicht.\n",
    "* $n$: Die Straße ist nass.\n",
    "\n",
    "Berechnen Sie die folgenden Wahrscheinlichkeiten:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$p(r) = 0.4$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$p(\\bar{r}) = 0.6$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$p(n|r) = 0.95$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$p(n|\\bar{r}) = 0.25$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$p(r|n) =\\frac{p(n|r)p(r)}{p(n)}$\n",
    "\n",
    "$=\\frac{p(n|r)p(r)}{p(n|r)p(r)+p(n|\\bar{r})p(\\bar{r})}$\n",
    "\n",
    "$=\\frac{0.95*0.4}{0.95*0.4+0.25*0.6}=0.72$"
   ]
  }
 ],
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