{ "nbformat": 4, "nbformat_minor": 0, "metadata": { "colab": { "provenance": [], "collapsed_sections": [] }, "kernelspec": { "name": "python3", "display_name": "Python 3" }, "language_info": { "name": "python" } }, "cells": [ { "cell_type": "markdown", "source": [ "# Domácí úloha 1\n", "\n", "---" ], "metadata": { "id": "nECGmqDPwfjV" } }, { "cell_type": "markdown", "source": [ "## Instalace a import" ], "metadata": { "id": "QqlKMVNESnAy" } }, { "cell_type": "code", "execution_count": 2, "metadata": { "id": "YKaRYO1pA_Cu", "colab": { "base_uri": "https://localhost:8080/" }, "outputId": "eceb80cd-f3af-4222-f65e-5eb3127539a5" }, "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ "Looking in indexes: https://pypi.org/simple, https://us-python.pkg.dev/colab-wheels/public/simple/\n", "Collecting truth-table-generator\n", " Downloading truth_table_generator-1.1.2.tar.gz (14 kB)\n", "Requirement already satisfied: numpy in /usr/local/lib/python3.7/dist-packages (from truth-table-generator) (1.21.6)\n", "Requirement already satisfied: pandas in /usr/local/lib/python3.7/dist-packages (from truth-table-generator) (1.3.5)\n", "Collecting PTable\n", " Downloading PTable-0.9.2.tar.gz (31 kB)\n", "Requirement already satisfied: pyparsing in /usr/local/lib/python3.7/dist-packages (from truth-table-generator) (3.0.9)\n", "Requirement already satisfied: tabulate in /usr/local/lib/python3.7/dist-packages (from truth-table-generator) (0.8.10)\n", "Requirement already satisfied: jinja2 in /usr/local/lib/python3.7/dist-packages (from truth-table-generator) (2.11.3)\n", "Requirement already satisfied: MarkupSafe>=0.23 in /usr/local/lib/python3.7/dist-packages (from jinja2->truth-table-generator) (2.0.1)\n", "Requirement already satisfied: pytz>=2017.3 in /usr/local/lib/python3.7/dist-packages (from pandas->truth-table-generator) (2022.4)\n", "Requirement already satisfied: python-dateutil>=2.7.3 in /usr/local/lib/python3.7/dist-packages (from pandas->truth-table-generator) (2.8.2)\n", "Requirement already satisfied: six>=1.5 in /usr/local/lib/python3.7/dist-packages (from python-dateutil>=2.7.3->pandas->truth-table-generator) (1.15.0)\n", "Building wheels for collected packages: truth-table-generator, PTable\n", " Building wheel for truth-table-generator (setup.py) ... \u001b[?25l\u001b[?25hdone\n", " Created wheel for truth-table-generator: filename=truth_table_generator-1.1.2-py3-none-any.whl size=13960 sha256=57014e659bd1a4c942f4838009d10d6a16866a4aaf2c5dc6ee76d5465cf29de1\n", " Stored in directory: /root/.cache/pip/wheels/9a/55/b5/77f5756832494eafda92c7a94c1365ac31088a18a3a97dd480\n", " Building wheel for PTable (setup.py) ... \u001b[?25l\u001b[?25hdone\n", " Created wheel for PTable: filename=PTable-0.9.2-py3-none-any.whl size=22925 sha256=871198a06b17e207d92b3f215885a162ce296b4a5d62f5f9cdb7bf6e650f74c8\n", " Stored in directory: /root/.cache/pip/wheels/33/df/2f/674985b3f8a2de3f96357d1eadef5110f74fa91b3785e52a54\n", "Successfully built truth-table-generator PTable\n", "Installing collected packages: PTable, truth-table-generator\n", "Successfully installed PTable-0.9.2 truth-table-generator-1.1.2\n" ] } ], "source": [ "%pip install truth-table-generator" ] }, { "cell_type": "code", "source": [ "import ttg" ], "metadata": { "id": "1GC4peTNwz5H" }, "execution_count": 3, "outputs": [] }, { "cell_type": "markdown", "source": [ "## Pomocné funkce\n", "\n", "Níže jsou definovány pomocné funkce, které můžete v domácím úkolu použít. Pro použití je potřeba buňku s definicí funkcí spustit. Použití jednotlivých funkcí je vysvětleno níže." ], "metadata": { "id": "Htjfm2x2dym9" } }, { "cell_type": "code", "source": [ "def l_not(argument):\n", " \"\"\"Fuknce pro vytvoření negace logického argumentu.\n", " \"\"\"\n", " return f\"(-{argument})\"\n", "\n", "def l_and(*args):\n", " \"\"\"Funkce pro spojení dvou a více výroků pomocí logické spojky and. Pokud\n", " je na vstupu pouze jeden výrok, funkce jej vrátí uzávorkovaný.\n", " \"\"\"\n", "\n", " result = f\"({args[0]})\"\n", "\n", " for c_arg in args[1:]:\n", " result = f\"({result} and ({c_arg}))\"\n", "\n", " return result\n", "\n", "def l_or(*args):\n", " \"\"\"Funkce pro spojení dvou a více výroků pomocí logické spojky or. Pokud\n", " je na vstupu pouze jeden výrok, funkce jej vrátí uzávorkovaný.\n", " \"\"\"\n", " result = f\"({args[0]})\"\n", "\n", " for c_arg in args[1:]:\n", " result = f\"({result} or ({c_arg}))\"\n", "\n", " return result\n", "\n", "def l_imply(arg1, arg2):\n", " \"\"\"Funkce pro spojení dvou výroků pomocí logické spojky implikace.\n", " \"\"\"\n", "\n", " return f\"(({arg1}) => ({arg2}))\"\n", "\n", "def infer(conclusion, *premises):\n", " \"\"\"Funkce, která pro závěr (conclusion) a nenulový počet premis (premises)\n", " vytvoří správně uzávorkovanou formuli, kterou půjde přímo použít pro vyhodnocení\n", " pomocí ttg.\n", " \"\"\"\n", "\n", " assert len(premises) > 0, \"Lze použít pouze pro jednu a více premis\"\n", " return l_imply(l_and(*premises), conclusion)" ], "metadata": { "id": "LVbHjWAIeSa2" }, "execution_count": 23, "outputs": [] }, { "cell_type": "markdown", "source": [ "### Použití pomocných funkcí\n", "\n", "* Pomocné funkce lze využít k zápisu logických formulí\n", "* Místo `\"a and b\"` lze použít zápis `l_and(\"a\", \"b\")`, funkce zajistí i uzávorkování formule.\n", "* Funkce infer vytvoří konjunkci ze všech vložených premis a vloží je do implikace se závěrem (závěr se v případě této funkce vkládá na první pozici!)\n", "* Použití funkcí lze kombinovat se standardním zápisem\n", " * `\"a and (-b)\"` lze zapsat jako `l_and(\"a\", l_not(\"b\"))`, ale také jako `l_and(\"a\", \"-b\")`\n", "* Funkce závorkují velmi agresivně (víc než by bylo nutné), abyste se vy o závorkování nemuseli starat\n", "* Níže ukázka na cvičení 4 z minulého týdne (nejdříve varianta bez použití funkcí, pak s)" ], "metadata": { "id": "QiWUrnJFh-eJ" } }, { "cell_type": "code", "source": [ "print(ttg.Truths([\"p\", \"q\", \"r\", \"s\"], [\"p => q\", \"q => (-r)\", \"s => r\", \"((((p => q) and (q => (-r))) and (s => r)) and p) => (-s)\"]))" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "ovKxj--Gh8Fn", "outputId": "e9fa7e18-c3ed-4f7c-f163-3813bbbed54d" }, "execution_count": 5, "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ "+-----+-----+-----+-----+----------+-------------+----------+-------------------------------------------------------------+\n", "| p | q | r | s | p => q | q => (-r) | s => r | ((((p => q) and (q => (-r))) and (s => r)) and p) => (-s) |\n", "|-----+-----+-----+-----+----------+-------------+----------+-------------------------------------------------------------|\n", "| 1 | 1 | 1 | 1 | 1 | 0 | 1 | 1 |\n", "| 1 | 1 | 1 | 0 | 1 | 0 | 1 | 1 |\n", "| 1 | 1 | 0 | 1 | 1 | 1 | 0 | 1 |\n", "| 1 | 1 | 0 | 0 | 1 | 1 | 1 | 1 |\n", "| 1 | 0 | 1 | 1 | 0 | 1 | 1 | 1 |\n", "| 1 | 0 | 1 | 0 | 0 | 1 | 1 | 1 |\n", "| 1 | 0 | 0 | 1 | 0 | 1 | 0 | 1 |\n", "| 1 | 0 | 0 | 0 | 0 | 1 | 1 | 1 |\n", "| 0 | 1 | 1 | 1 | 1 | 0 | 1 | 1 |\n", "| 0 | 1 | 1 | 0 | 1 | 0 | 1 | 1 |\n", "| 0 | 1 | 0 | 1 | 1 | 1 | 0 | 1 |\n", "| 0 | 1 | 0 | 0 | 1 | 1 | 1 | 1 |\n", "| 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 |\n", "| 0 | 0 | 1 | 0 | 1 | 1 | 1 | 1 |\n", "| 0 | 0 | 0 | 1 | 1 | 1 | 0 | 1 |\n", "| 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 |\n", "+-----+-----+-----+-----+----------+-------------+----------+-------------------------------------------------------------+\n" ] } ] }, { "cell_type": "code", "source": [ "print(ttg.Truths([\"p\", \"q\", \"r\", \"s\"], [l_imply(\"p\", \"q\"), l_imply(\"q\", \"-r\"), l_imply(\"s\", \"r\"), infer(\"-s\", l_imply(\"p\", \"q\"), l_imply(\"q\", \"-r\"), l_imply(\"s\", \"r\"), \"p\")]))" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "Uqj4z3lpja8o", "outputId": "ad737a2e-0812-43be-bf5b-cf08a6b87a98" }, "execution_count": 24, "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ "+-----+-----+-----+-----+----------------+-----------------+----------------+-----------------------------------------------------------------------------------+\n", "| p | q | r | s | ((p) => (q)) | ((q) => (-r)) | ((s) => (r)) | ((((((((p) => (q))) and (((q) => (-r)))) and (((s) => (r)))) and (p))) => (-s)) |\n", "|-----+-----+-----+-----+----------------+-----------------+----------------+-----------------------------------------------------------------------------------|\n", "| 1 | 1 | 1 | 1 | 1 | 0 | 1 | 1 |\n", "| 1 | 1 | 1 | 0 | 1 | 0 | 1 | 1 |\n", "| 1 | 1 | 0 | 1 | 1 | 1 | 0 | 1 |\n", "| 1 | 1 | 0 | 0 | 1 | 1 | 1 | 1 |\n", "| 1 | 0 | 1 | 1 | 0 | 1 | 1 | 1 |\n", "| 1 | 0 | 1 | 0 | 0 | 1 | 1 | 1 |\n", "| 1 | 0 | 0 | 1 | 0 | 1 | 0 | 1 |\n", "| 1 | 0 | 0 | 0 | 0 | 1 | 1 | 1 |\n", "| 0 | 1 | 1 | 1 | 1 | 0 | 1 | 1 |\n", "| 0 | 1 | 1 | 0 | 1 | 0 | 1 | 1 |\n", "| 0 | 1 | 0 | 1 | 1 | 1 | 0 | 1 |\n", "| 0 | 1 | 0 | 0 | 1 | 1 | 1 | 1 |\n", "| 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 |\n", "| 0 | 0 | 1 | 0 | 1 | 1 | 1 | 1 |\n", "| 0 | 0 | 0 | 1 | 1 | 1 | 0 | 1 |\n", "| 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 |\n", "+-----+-----+-----+-----+----------------+-----------------+----------------+-----------------------------------------------------------------------------------+\n" ] } ] }, { "cell_type": "markdown", "source": [ "## Zadání domácí úlohy\n", "\n", "* Převeďte následující výroky do podoby logických formulí, označte premisy a závěr a pomocí ttg ověřte jejich deduktivní platnost.\n", "* Při vypracování můžete použít pomocné funkce, které máte připravené výše.\n", "\n", "### Výrok 1\n", "\n", "Doktor Manhattan a Rorschach podezřívali Ozzymandiase z přípravy spiknutí. Rorschach Ozzymandiase podezříval, takže doktor Manhattan jej nepodezříval.\n", "\n", "### Výrok 2\n", "\n", "Pokud by se z Tristana Thorna stal pirát, kapitán Alberic by jej přijal do své posádky. Kapitán Tristana do své posádky nepřijal, takže se z Tristana pirát nestal." ], "metadata": { "id": "FUOKDzdXlOif" } }, { "cell_type": "code", "source": [], "metadata": { "id": "mLDKSyPlni18" }, "execution_count": null, "outputs": [] } ] }