{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "yWGTIPMXotxs"
   },
   "source": [
    "# **Exercise 10. Bounded choice rules.**\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Ho57hy3em9Yi"
   },
   "source": [
    "#### **1**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "j_3LyCQFnE7K",
    "outputId": "8c702cbe-9240-41dd-a812-6349904b5255"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "b\n",
      "a\n",
      "SATISFIABLE\n"
     ]
    }
   ],
   "source": [
    "%%clingo -V0 0 \n",
    "{ a; b }.\n",
    ":- not 1 { a; b } 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "tekDyDF_nJLf"
   },
   "outputs": [],
   "source": [
    "%%clingo -V0 0 \n",
    "1 { a; b } 1."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "2EPx4Jn6oRUc"
   },
   "source": [
    "#### **2**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "rVsiBrQSofDj",
    "outputId": "0790a4c1-5359-4669-d912-24d790f74c61"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "b c\n",
      "a b c\n",
      "a c\n",
      "a b\n",
      "SATISFIABLE\n"
     ]
    }
   ],
   "source": [
    "%%clingo -V0 0 \n",
    "{ a; b; c }.\n",
    ":- not 2 { a; b; c }."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "6ElK21vgok0e"
   },
   "outputs": [],
   "source": [
    "%%clingo -V0 0 \n",
    "2 { a; b; c }."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "2EPx4Jn6oRUc"
   },
   "source": [
    "#### **3**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "rVsiBrQSofDj",
    "outputId": "0790a4c1-5359-4669-d912-24d790f74c61"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a c\n",
      "b\n",
      "SATISFIABLE\n"
     ]
    }
   ],
   "source": [
    "%%clingo -V0 0 \n",
    "{ a; b }.\n",
    ":- not 1 { a; b } 1.\n",
    "{ b; c }.\n",
    ":- not 1 { b; c } 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "6ElK21vgok0e"
   },
   "outputs": [],
   "source": [
    "%%clingo -V0 0 \n",
    "1 { a; b } 1.\n",
    "1 { b; c } 1."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "2EPx4Jn6oRUc"
   },
   "source": [
    "#### **4**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "rVsiBrQSofDj",
    "outputId": "0790a4c1-5359-4669-d912-24d790f74c61"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "c\n",
      "a c\n",
      "b\n",
      "b c\n",
      "SATISFIABLE\n"
     ]
    }
   ],
   "source": [
    "%%clingo -V0 0 \n",
    "{ a; b }.\n",
    ":- not { a; b } 1.\n",
    "{ b; c }.\n",
    ":- not 1 { b; c }."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "6ElK21vgok0e"
   },
   "outputs": [],
   "source": [
    "%%clingo -V0 0 \n",
    "{ a; b } 1.\n",
    "1 { b; c }."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Ho57hy3em9Yi"
   },
   "source": [
    "#### **5**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "j_3LyCQFnE7K",
    "outputId": "8c702cbe-9240-41dd-a812-6349904b5255"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "d b\n",
      "c a\n",
      "SATISFIABLE\n"
     ]
    }
   ],
   "source": [
    "%%clingo -V0 0\n",
    "1 { a; b } 1.\n",
    "c :- a.\n",
    "d :- b.\n",
    ":- { c; d } 0."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "tekDyDF_nJLf"
   },
   "outputs": [],
   "source": [
    "%%clingo -V0 0\n",
    "1 { a; b } 1.\n",
    "c :- a.\n",
    "d :- b.\n",
    ":- 1 { c ; d }."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "2EPx4Jn6oRUc"
   },
   "source": [
    "#### **6**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "rVsiBrQSofDj",
    "outputId": "0790a4c1-5359-4669-d912-24d790f74c61"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "b\n",
      "a c\n",
      "a d\n",
      "SATISFIABLE\n"
     ]
    }
   ],
   "source": [
    "%%clingo -V0 0 \n",
    "1 { a; b }.\n",
    "1 { c; d } 1 :- a.\n",
    ":- b, 2 { a; c; d }."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "%%clingo -V0 0 \n",
    "1 { a; b }.\n",
    "1 { c; d } 1 :- a.\n",
    ":- not 2 { a; b; c; d }."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "2EPx4Jn6oRUc"
   },
   "source": [
    "#### **7**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "rVsiBrQSofDj",
    "outputId": "0790a4c1-5359-4669-d912-24d790f74c61"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "b\n",
      "a c\n",
      "SATISFIABLE\n"
     ]
    }
   ],
   "source": [
    "%%clingo -V0 0 \n",
    "{ a; b } 1.\n",
    "1 { b; c } :- a."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "6ElK21vgok0e"
   },
   "outputs": [],
   "source": [
    "%%clingo -V0 0 \n",
    "1 { a; b } 1.\n",
    "1 { b; c } 1 :- a."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "2EPx4Jn6oRUc"
   },
   "source": [
    "#### **8**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "rVsiBrQSofDj",
    "outputId": "0790a4c1-5359-4669-d912-24d790f74c61"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "b\n",
      "SATISFIABLE\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "-:2:10-11: info: atom does not occur in any rule head:\n",
      "  c\n",
      "\n"
     ]
    }
   ],
   "source": [
    "%%clingo -V0 0 \n",
    "a :- not b.\n",
    "b :- not c."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "6ElK21vgok0e"
   },
   "outputs": [],
   "source": [
    "%%clingo -V0 0 \n",
    "1 { a } 1 :- { b } 0.\n",
    "1 { b } 1 :- { c } 0."
   ]
  }
 ],
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   "name": "Learning Easy ASP from Examples.ipynb",
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