{"id":4,"date":"2022-11-02T18:09:55","date_gmt":"2022-11-02T18:09:55","guid":{"rendered":"https:\/\/dornsife.usc.edu\/usclogicweb\/?page_id=4"},"modified":"2025-09-01T13:08:54","modified_gmt":"2025-09-01T20:08:54","slug":"home","status":"publish","type":"page","link":"https:\/\/dornsife.usc.edu\/usclogicweb\/","title":{"rendered":"Main"},"content":{"rendered":"\n\n\n\n      \n  \n    \n\n\n\n\n\n\n<div\n  class=\"cc--component-container cc--accordions \"\n\n  \n  \n  \n  \n  \n  \n  >\n  <div class=\"c--component c--accordions\"\n    \n      >\n\n    \n  \n      <ul>\n              <li>\n          <button type=\"button\" class=\"accordion-trigger \" id=\"heading-1-1-indbOBUo8W\" aria-controls=\"section-1-1-indbOBUo8W\" aria-expanded=\"false\" aria-disabled=\"false\">\n                          <span class=\"item-title\">Welcome<\/span>\n            \n                      <\/button>\n\n          <div id=\"section-1-1-indbOBUo8W\" role=\"region\" aria-labelledby=\"heading-1-1-indbOBUo8W\" class=\"accordion-panel\">\n\n                            \n    \n\n\n\n\n\n\n<div\n  class=\"cc--component-container cc--rich-text \"\n\n  \n  \n  \n  \n  \n  \n  >\n  <div class=\"c--component c--rich-text\"\n    \n      >\n\n    \n      \n<div class=\"f--field f--wysiwyg\">\n\n    \n  <p>USC Logic Web is an open-access platform designed to introduce users to the study of propositional and quantificational logic with identity. The project began with a donation by the Linda L. Peterson Fund for the Study and Practical Application of Logic. The\u00a0material is divided into ten units, which consist of a tutorial and a set of interactive problems designed to help consolidate comprehension and mastery of core skills introduced by the tutorial. Solutions to these problems are provided in a separate link.<\/p>\n<p>The first unit introduces the subject matter of logic and motivates the use of a formal framework for the study of validity. The remainder of the course is structured into two main blocks, one on propositional logic and another on quantificational logic. Each part presents the syntax and semantics of the relevant formal language and explains how to translate from English into that framework. A system of natural deduction is introduced for each framework.<\/p>\n<p>USC Logic Web is used as an online companion to <a href=\"https:\/\/classes.usc.edu\/term-20241\/course\/phil-220g\/\">PHIL 220g. Introduction to Logic<\/a> at USC.<\/p>\n<p>&nbsp;<\/p>\n\n\n\n<\/div>\n\n\n  <\/div><\/div>\n            \n                      <\/div>\n        <\/li>\n\n              <li>\n          <button type=\"button\" class=\"accordion-trigger \" id=\"heading-1-2-indbOBUo8W\" aria-controls=\"section-1-2-indbOBUo8W\" aria-expanded=\"false\" aria-disabled=\"false\">\n                          <span class=\"item-title\">Technology<\/span>\n            \n                      <\/button>\n\n          <div id=\"section-1-2-indbOBUo8W\" role=\"region\" aria-labelledby=\"heading-1-2-indbOBUo8W\" class=\"accordion-panel\">\n\n                            \n    \n\n\n\n\n\n\n<div\n  class=\"cc--component-container cc--rich-text \"\n\n  \n  \n  \n  \n  \n  \n  >\n  <div class=\"c--component c--rich-text\"\n    \n      >\n\n    \n      \n<div class=\"f--field f--wysiwyg\">\n\n    \n  <p>The main text has been written with the help of the <a href=\"https:\/\/bookdown.org\/\">bookdown<\/a> package created by Yihui Xie. Bookdown is open-source R package used to create ebooks from R Markdown documents.<\/p>\n<p>The interactive problems are written in markdown and powered by the <a href=\"http:\/\/carnap.io\">Carnap<\/a> platform. This is a free and open software framework designed and maintained by G. Leach-Krouse and J. Ehrlich. The <a href=\"https:\/\/carnap.io\/srv\/doc\/index.md\">documentation<\/a> explains how the problems are written and uploaded to the platform. Users receive immediate feedback upon submission, e.g., <a href=\"http:\/\/carnap.io\">Carnap<\/a> will tell them whether the answer is correct and if not, it will in some cases offer some hints.<\/p>\n<p>The visual design of the main text and the interactive problems emulates the style of Edward Tufte, which has implementations in LaTeX and HTML\/CSS.<\/p>\n<p>&nbsp;<\/p>\n\n\n\n<\/div>\n\n\n  <\/div><\/div>\n            \n                      <\/div>\n        <\/li>\n\n              <li>\n          <button type=\"button\" class=\"accordion-trigger \" id=\"heading-1-3-indbOBUo8W\" aria-controls=\"section-1-3-indbOBUo8W\" aria-expanded=\"false\" aria-disabled=\"false\">\n                          <span class=\"item-title\">Feedback<\/span>\n            \n                      <\/button>\n\n          <div id=\"section-1-3-indbOBUo8W\" role=\"region\" aria-labelledby=\"heading-1-3-indbOBUo8W\" class=\"accordion-panel\">\n\n                            \n    \n\n\n\n\n\n\n<div\n  class=\"cc--component-container cc--rich-text \"\n\n  \n  \n  \n  \n  \n  \n  >\n  <div class=\"c--component c--rich-text\"\n    \n      >\n\n    \n      \n<div class=\"f--field f--wysiwyg\">\n\n    \n  <p>Please feel free to use this <a href=\"https:\/\/docs.google.com\/forms\/d\/e\/1FAIpQLSctuhPBWO3ZoW3NLPoCQEDO09jrQ9ddKyL8kqgPl5zu5kFr2g\/viewform?usp=pp_url\">anonymous form<\/a> to submit feedback on the platform, e.g., typos, comments, or suggestions for improvement.<\/p>\n\n\n\n<\/div>\n\n\n  <\/div><\/div>\n            \n                      <\/div>\n        <\/li>\n\n          <\/ul>\n  \n  \n\n  <\/div><\/div>\n\n\n\n\n\n  \n        \n    \n    \n              \n    \n  \n\n  \n    \n\n\n\n\n\n\n<div\n  class=\"cc--component-container cc--interactive-content-pane \"\n\n  \n  \n  \n  \n  \n  \n  >\n  <div class=\"c--component c--interactive-content-pane\"\n    \n      >\n\n    \n<div class=\"inner-wrapper\">\n  <div class=\"left\">\n              \n<div class=\"f--field f--section-title\">\n\n    \n  <h2>\n          Unit 1\n      <\/h2>\n\n\n<\/div>\n      \n    <div class=\"pagination-wrapper\">\n      <ul class=\"interactive-content-pane-pagination\"><\/ul>\n    <\/div>\n  <\/div>\n\n  <div class=\"right\">\n          <div class=\"swiper\">\n        <div class=\"swiper-wrapper\">\n                      <div class=\"swiper-slide\">\n              <h3 class=\"pane-title\">\n                Reason and Argument\n              <\/h3>\n                                  \n<div class=\"f--field f--description\">\n\n    \n  <p>What is an argument? How should we draw the distinction between valid and invalid arguments? Validity and form. Formal languages and logic.<\/p>\n\n\n\n<\/div>\n                          \n  \n                              <ul>\n                                            <li>\n                                \n<div class=\"f--field f--link\">\n\n    \n    \n  \n<a \n  class=\"link\"\n  href= https:\/\/gabriel-uzquiano.github.io\/logic\/reason.html#reason\n    aria-label=\"Read more about Tutorial\"  \n>\n    Tutorial \n  <svg version=\"1.1\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" x=\"0px\" y=\"0px\" viewBox=\"0 0 35 35\" enable-background=\"new 0 0 35 35\" width=\"25\" height=\"25\" xml:space=\"preserve\"><polygon fill-rule=\"evenodd\" clip-rule=\"evenodd\" fill=\"#FC0\" points=\"19.3,27.5 29.3,17.5,19.3,7.5 16.3,10.4 21.4,15.4 6.7,15.4 6.7,19.6 21.4,19.6 16.3,24.6 \"\/><\/svg>\n<\/a>\n\n\n<\/div>\n                        <\/li>\n                                    <\/ul>\n                          <\/div>\n                      <div class=\"swiper-slide\">\n              <h3 class=\"pane-title\">\n                Practice\n              <\/h3>\n                                  \n<div class=\"f--field f--description\">\n\n    \n  <p>How to identify the conclusion of an argument. What makes an argument valid. How to tell whether an argument form is valid. What makes an argument sound.<\/p>\n\n\n\n<\/div>\n                          \n  \n                              <ul>\n                                            <li>\n                                \n<div class=\"f--field f--link\">\n\n    \n    \n  \n<a \n  class=\"link\"\n  href= https:\/\/carnap.io\/shared\/uzquiano@usc.edu\/Unit%20I%20Practice%20%28Reason%29.md\n    aria-label=\"Read more about Problems\"  \n>\n    Problems \n  <svg version=\"1.1\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" x=\"0px\" y=\"0px\" viewBox=\"0 0 35 35\" enable-background=\"new 0 0 35 35\" width=\"25\" height=\"25\" xml:space=\"preserve\"><polygon fill-rule=\"evenodd\" clip-rule=\"evenodd\" fill=\"#FC0\" points=\"19.3,27.5 29.3,17.5,19.3,7.5 16.3,10.4 21.4,15.4 6.7,15.4 6.7,19.6 21.4,19.6 16.3,24.6 \"\/><\/svg>\n<\/a>\n\n\n<\/div>\n                        <\/li>\n                                            <li>\n                                \n<div class=\"f--field f--link\">\n\n    \n    \n  \n<a \n  class=\"link\"\n  href= https:\/\/carnap.io\/shared\/uzquiano@usc.edu\/Unit%20I%20Practice%20%28Reason%29%20Solutions.md\n    aria-label=\"Read more about Solutions\"  \n>\n    Solutions \n  <svg version=\"1.1\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" x=\"0px\" y=\"0px\" viewBox=\"0 0 35 35\" enable-background=\"new 0 0 35 35\" width=\"25\" height=\"25\" xml:space=\"preserve\"><polygon fill-rule=\"evenodd\" clip-rule=\"evenodd\" fill=\"#FC0\" points=\"19.3,27.5 29.3,17.5,19.3,7.5 16.3,10.4 21.4,15.4 6.7,15.4 6.7,19.6 21.4,19.6 16.3,24.6 \"\/><\/svg>\n<\/a>\n\n\n<\/div>\n                        <\/li>\n                                    <\/ul>\n                          <\/div>\n                  <\/div>\n      <\/div>\n      <\/div>\n  \n<\/div>\n\n\n\n  <div class=\"background-images\">\n          <div class=\"swiper swiper-background-images\">\n        <div class=\"swiper-wrapper\">\n                      <div class=\"swiper-slide\">\n                          <\/div>\n\n                      <div class=\"swiper-slide\">\n                                                                  \n<div class=\"f--field f--image\">\n\n    \n    \n    \n    \n    \n    \n              \n      <img decoding=\"async\"\n                            src=\"https:\/\/dornsife.usc.edu\/usclogicweb\/wp-content\/uploads\/sites\/222\/2023\/09\/practicelow-768x432.jpg\"\n          srcset=\"https:\/\/dornsife.usc.edu\/usclogicweb\/wp-content\/uploads\/sites\/222\/2023\/09\/practicelow-768x432.jpg 768w\"          sizes=\"(min-width:1200px) 75vw, (min-width:768px) 83vw, 100vw\"\n        \n                  role=\"none\"\n        \n        role=\"presentation\"\n                                      \/>\n\n    \n    \n  \n  \n\n<\/div>\n                          <\/div>\n\n                  <\/div>\n      <\/div>\n      <\/div>\n\n\n\n  <\/div><\/div>\n\n\n  \n    \n\n\n\n\n\n\n<div\n  class=\"cc--component-container cc--intro-text align-center\"\n\n  \n  \n  \n  \n  \n  \n  >\n  <div class=\"c--component c--intro-text\"\n    \n      >\n\n    \n          \n<div class=\"f--field f--section-title\">\n\n    \n  <h2>\n          Propositional Logic\n      <\/h2>\n\n\n<\/div>\n  \n          \n<div class=\"f--field f--description\">\n\n    \n  <p>Propositional logic accounts for the validity of a wide family of natural language arguments in terms of the behavior of a specific set of sentential operators called propositional connectives.<\/p>\n\n\n\n<\/div>\n  \n\n  <\/div><\/div>\n\n\n\n\n\n  \n        \n    \n    \n              \n    \n  \n\n  \n    \n\n\n\n\n\n\n<div\n  class=\"cc--component-container cc--interactive-content-pane \"\n\n  \n  \n  \n  \n  \n  \n  >\n  <div class=\"c--component c--interactive-content-pane\"\n    \n      >\n\n    \n<div class=\"inner-wrapper\">\n  <div class=\"left\">\n              \n<div class=\"f--field f--section-title\">\n\n    \n  <h2>\n          Unit 2\n      <\/h2>\n\n\n<\/div>\n      \n    <div class=\"pagination-wrapper\">\n      <ul class=\"interactive-content-pane-pagination\"><\/ul>\n    <\/div>\n  <\/div>\n\n  <div class=\"right\">\n          <div class=\"swiper\">\n        <div class=\"swiper-wrapper\">\n                      <div class=\"swiper-slide\">\n              <h3 class=\"pane-title\">\n                Syntax of Propositional Logic\n              <\/h3>\n                                  \n<div class=\"f--field f--description\">\n\n    \n  <p>Syntax of the formal language of propositional logic. What is a well-formed formula of the formal language? How to provide a construction tree for well-formed formulas of the language. Some notational conventions.<\/p>\n\n\n\n<\/div>\n                          \n  \n                              <ul>\n                                            <li>\n                                \n<div class=\"f--field f--link\">\n\n    \n    \n  \n<a \n  class=\"link\"\n  href= https:\/\/gabriel-uzquiano.github.io\/logic\/proplogic.html#proplogic\n    aria-label=\"Read more about Tutorial\"  \n>\n    Tutorial \n  <svg version=\"1.1\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" x=\"0px\" y=\"0px\" viewBox=\"0 0 35 35\" enable-background=\"new 0 0 35 35\" width=\"25\" height=\"25\" xml:space=\"preserve\"><polygon fill-rule=\"evenodd\" clip-rule=\"evenodd\" fill=\"#FC0\" points=\"19.3,27.5 29.3,17.5,19.3,7.5 16.3,10.4 21.4,15.4 6.7,15.4 6.7,19.6 21.4,19.6 16.3,24.6 \"\/><\/svg>\n<\/a>\n\n\n<\/div>\n                        <\/li>\n                                    <\/ul>\n                          <\/div>\n                      <div class=\"swiper-slide\">\n              <h3 class=\"pane-title\">\n                Practice\n              <\/h3>\n                                  \n<div class=\"f--field f--description\">\n\n    \n  <p>How to draw a construction tree for a well-formed formula of propositional logic. The implementation of notational conventions.<\/p>\n\n\n\n<\/div>\n                          \n  \n                              <ul>\n                                            <li>\n                                \n<div class=\"f--field f--link\">\n\n    \n    \n  \n<a \n  class=\"link\"\n  href= https:\/\/carnap.io\/shared\/uzquiano@usc.edu\/Unit%20II%20Practice%20%28Syntax%29.md\n    aria-label=\"Read more about Problems\"  \n>\n    Problems \n  <svg version=\"1.1\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" x=\"0px\" y=\"0px\" viewBox=\"0 0 35 35\" enable-background=\"new 0 0 35 35\" width=\"25\" height=\"25\" xml:space=\"preserve\"><polygon fill-rule=\"evenodd\" clip-rule=\"evenodd\" fill=\"#FC0\" points=\"19.3,27.5 29.3,17.5,19.3,7.5 16.3,10.4 21.4,15.4 6.7,15.4 6.7,19.6 21.4,19.6 16.3,24.6 \"\/><\/svg>\n<\/a>\n\n\n<\/div>\n                        <\/li>\n                                            <li>\n                                \n<div class=\"f--field f--link\">\n\n    \n    \n  \n<a \n  class=\"link\"\n  href= https:\/\/carnap.io\/shared\/uzquiano@usc.edu\/Unit%20II%20Practice%20%28Syntax%29%20Solutions.md\n    aria-label=\"Read more about Solutions\"  \n>\n    Solutions \n  <svg version=\"1.1\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" x=\"0px\" y=\"0px\" viewBox=\"0 0 35 35\" enable-background=\"new 0 0 35 35\" width=\"25\" height=\"25\" xml:space=\"preserve\"><polygon fill-rule=\"evenodd\" clip-rule=\"evenodd\" fill=\"#FC0\" points=\"19.3,27.5 29.3,17.5,19.3,7.5 16.3,10.4 21.4,15.4 6.7,15.4 6.7,19.6 21.4,19.6 16.3,24.6 \"\/><\/svg>\n<\/a>\n\n\n<\/div>\n                        <\/li>\n                                    <\/ul>\n                          <\/div>\n                  <\/div>\n      <\/div>\n      <\/div>\n  \n<\/div>\n\n\n\n  <div class=\"background-images\">\n          <div class=\"swiper swiper-background-images\">\n        <div class=\"swiper-wrapper\">\n                      <div class=\"swiper-slide\">\n                          <\/div>\n\n                      <div class=\"swiper-slide\">\n                                                                  \n<div class=\"f--field f--image\">\n\n    \n    \n    \n    \n    \n    \n              \n      <img decoding=\"async\"\n                            src=\"https:\/\/dornsife.usc.edu\/usclogicweb\/wp-content\/uploads\/sites\/222\/2023\/09\/practicelow-768x432.jpg\"\n          srcset=\"https:\/\/dornsife.usc.edu\/usclogicweb\/wp-content\/uploads\/sites\/222\/2023\/09\/practicelow-768x432.jpg 768w\"          sizes=\"(min-width:1200px) 75vw, (min-width:768px) 83vw, 100vw\"\n        \n                  role=\"none\"\n        \n        role=\"presentation\"\n                                      \/>\n\n    \n    \n  \n  \n\n<\/div>\n                          <\/div>\n\n                  <\/div>\n      <\/div>\n      <\/div>\n\n\n\n  <\/div><\/div>\n\n\n\n\n\n  \n        \n    \n    \n              \n    \n  \n\n  \n    \n\n\n\n\n\n\n<div\n  class=\"cc--component-container cc--interactive-content-pane \"\n\n  \n  \n  \n  \n  \n  \n  >\n  <div class=\"c--component c--interactive-content-pane\"\n    \n      >\n\n    \n<div class=\"inner-wrapper\">\n  <div class=\"left\">\n              \n<div class=\"f--field f--section-title\">\n\n    \n  <h2>\n          Unit 3\n      <\/h2>\n\n\n<\/div>\n      \n    <div class=\"pagination-wrapper\">\n      <ul class=\"interactive-content-pane-pagination\"><\/ul>\n    <\/div>\n  <\/div>\n\n  <div class=\"right\">\n          <div class=\"swiper\">\n        <div class=\"swiper-wrapper\">\n                      <div class=\"swiper-slide\">\n              <h3 class=\"pane-title\">\n                Semantics for Propositional Logic\n              <\/h3>\n                                  \n<div class=\"f--field f--description\">\n\n    \n  <p>How to populate a truth table. The use of truth tables to determine whether a formula is a tautology or a contradiction or neither. Truth tables and validity.<\/p>\n\n\n\n<\/div>\n                          \n  \n                              <ul>\n                                            <li>\n                                \n<div class=\"f--field f--link\">\n\n    \n    \n  \n<a \n  class=\"link\"\n  href= https:\/\/gabriel-uzquiano.github.io\/logic\/semantics.html#semantics\n    aria-label=\"Read more about Tutorial\"  \n>\n    Tutorial \n  <svg version=\"1.1\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" x=\"0px\" y=\"0px\" viewBox=\"0 0 35 35\" enable-background=\"new 0 0 35 35\" width=\"25\" height=\"25\" xml:space=\"preserve\"><polygon fill-rule=\"evenodd\" clip-rule=\"evenodd\" fill=\"#FC0\" points=\"19.3,27.5 29.3,17.5,19.3,7.5 16.3,10.4 21.4,15.4 6.7,15.4 6.7,19.6 21.4,19.6 16.3,24.6 \"\/><\/svg>\n<\/a>\n\n\n<\/div>\n                        <\/li>\n                                    <\/ul>\n                          <\/div>\n                      <div class=\"swiper-slide\">\n              <h3 class=\"pane-title\">\n                Practice\n              <\/h3>\n                                  \n<div class=\"f--field f--description\">\n\n    \n  <p>How to interpret the language of propositional logic. Truth-functional connectives and their interpretation. The use of truth tables and validity.<\/p>\n\n\n\n<\/div>\n                          \n  \n                              <ul>\n                                            <li>\n                                \n<div class=\"f--field f--link\">\n\n    \n    \n  \n<a \n  class=\"link\"\n  href= https:\/\/carnap.io\/shared\/uzquiano@usc.edu\/Unit%20III%20Practice%20%28Truth%20Tables%29.md\n    aria-label=\"Read more about Problems\"  \n>\n    Problems \n  <svg version=\"1.1\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" x=\"0px\" y=\"0px\" viewBox=\"0 0 35 35\" enable-background=\"new 0 0 35 35\" width=\"25\" height=\"25\" xml:space=\"preserve\"><polygon fill-rule=\"evenodd\" clip-rule=\"evenodd\" fill=\"#FC0\" points=\"19.3,27.5 29.3,17.5,19.3,7.5 16.3,10.4 21.4,15.4 6.7,15.4 6.7,19.6 21.4,19.6 16.3,24.6 \"\/><\/svg>\n<\/a>\n\n\n<\/div>\n                        <\/li>\n                                            <li>\n                                \n<div class=\"f--field f--link\">\n\n    \n    \n  \n<a \n  class=\"link\"\n  href= https:\/\/carnap.io\/shared\/uzquiano@usc.edu\/Unit%20III%20Practice%20%28Truth%20Tables%29%20Solutions.md\n    aria-label=\"Read more about Solutions\"  \n>\n    Solutions \n  <svg version=\"1.1\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" x=\"0px\" y=\"0px\" viewBox=\"0 0 35 35\" enable-background=\"new 0 0 35 35\" width=\"25\" height=\"25\" xml:space=\"preserve\"><polygon fill-rule=\"evenodd\" clip-rule=\"evenodd\" fill=\"#FC0\" points=\"19.3,27.5 29.3,17.5,19.3,7.5 16.3,10.4 21.4,15.4 6.7,15.4 6.7,19.6 21.4,19.6 16.3,24.6 \"\/><\/svg>\n<\/a>\n\n\n<\/div>\n                        <\/li>\n                                    <\/ul>\n                          <\/div>\n                  <\/div>\n      <\/div>\n      <\/div>\n  \n<\/div>\n\n\n\n  <div class=\"background-images\">\n          <div class=\"swiper swiper-background-images\">\n        <div class=\"swiper-wrapper\">\n                      <div class=\"swiper-slide\">\n                          <\/div>\n\n                      <div class=\"swiper-slide\">\n                                                                  \n<div class=\"f--field f--image\">\n\n    \n    \n    \n    \n    \n    \n              \n      <img decoding=\"async\"\n                            src=\"https:\/\/dornsife.usc.edu\/usclogicweb\/wp-content\/uploads\/sites\/222\/2023\/09\/practicelow-768x432.jpg\"\n          srcset=\"https:\/\/dornsife.usc.edu\/usclogicweb\/wp-content\/uploads\/sites\/222\/2023\/09\/practicelow-768x432.jpg 768w\"          sizes=\"(min-width:1200px) 75vw, (min-width:768px) 83vw, 100vw\"\n        \n                  role=\"none\"\n        \n        role=\"presentation\"\n                                      \/>\n\n    \n    \n  \n  \n\n<\/div>\n                          <\/div>\n\n                  <\/div>\n      <\/div>\n      <\/div>\n\n\n\n  <\/div><\/div>\n\n\n\n\n\n  \n        \n    \n    \n              \n    \n  \n\n  \n    \n\n\n\n\n\n\n<div\n  class=\"cc--component-container cc--interactive-content-pane \"\n\n  \n  \n  \n  \n  \n  \n  >\n  <div class=\"c--component c--interactive-content-pane\"\n    \n      >\n\n    \n<div class=\"inner-wrapper\">\n  <div class=\"left\">\n              \n<div class=\"f--field f--section-title\">\n\n    \n  <h2>\n          Unit 4\n      <\/h2>\n\n\n<\/div>\n      \n    <div class=\"pagination-wrapper\">\n      <ul class=\"interactive-content-pane-pagination\"><\/ul>\n    <\/div>\n  <\/div>\n\n  <div class=\"right\">\n          <div class=\"swiper\">\n        <div class=\"swiper-wrapper\">\n                      <div class=\"swiper-slide\">\n              <h3 class=\"pane-title\">\n                Translation into Propositional Logic\n              <\/h3>\n                                  \n<div class=\"f--field f--description\">\n\n    \n  <p>How to translate from English into the language of propositional logic. Problems with translation. The formalization of real life arguments in English. How to use truth tables to determine whether they are propositionally valid.<\/p>\n\n\n\n<\/div>\n                          \n  \n                              <ul>\n                                            <li>\n                                \n<div class=\"f--field f--link\">\n\n    \n    \n  \n<a \n  class=\"link\"\n  href= https:\/\/gabriel-uzquiano.github.io\/logic\/translationproplogic.html#translationproplogic\n    aria-label=\"Read more about Tutorial\"  \n>\n    Tutorial \n  <svg version=\"1.1\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" x=\"0px\" y=\"0px\" viewBox=\"0 0 35 35\" enable-background=\"new 0 0 35 35\" width=\"25\" height=\"25\" xml:space=\"preserve\"><polygon fill-rule=\"evenodd\" clip-rule=\"evenodd\" fill=\"#FC0\" points=\"19.3,27.5 29.3,17.5,19.3,7.5 16.3,10.4 21.4,15.4 6.7,15.4 6.7,19.6 21.4,19.6 16.3,24.6 \"\/><\/svg>\n<\/a>\n\n\n<\/div>\n                        <\/li>\n                                    <\/ul>\n                          <\/div>\n                      <div class=\"swiper-slide\">\n              <h3 class=\"pane-title\">\n                Practice\n              <\/h3>\n                                  \n<div class=\"f--field f--description\">\n\n    \n  <p>Translation into the language of propositional logic. Problems with translation. Formalization of complex arguments in English.<\/p>\n\n\n\n<\/div>\n                          \n  \n                              <ul>\n                                            <li>\n                                \n<div class=\"f--field f--link\">\n\n    \n    \n  \n<a \n  class=\"link\"\n  href= https:\/\/carnap.io\/shared\/uzquiano@usc.edu\/Unit%20IV%20Practice%20%28Translation%29.md\n    aria-label=\"Read more about Problems\"  \n>\n    Problems \n  <svg version=\"1.1\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" x=\"0px\" y=\"0px\" viewBox=\"0 0 35 35\" enable-background=\"new 0 0 35 35\" width=\"25\" height=\"25\" xml:space=\"preserve\"><polygon fill-rule=\"evenodd\" clip-rule=\"evenodd\" fill=\"#FC0\" points=\"19.3,27.5 29.3,17.5,19.3,7.5 16.3,10.4 21.4,15.4 6.7,15.4 6.7,19.6 21.4,19.6 16.3,24.6 \"\/><\/svg>\n<\/a>\n\n\n<\/div>\n                        <\/li>\n                                            <li>\n                                \n<div class=\"f--field f--link\">\n\n    \n    \n  \n<a \n  class=\"link\"\n  href= https:\/\/carnap.io\/shared\/uzquiano@usc.edu\/Unit%20IV%20Practice%20%28Translation%29%20Solutions.md\n    aria-label=\"Read more about Solutions\"  \n>\n    Solutions \n  <svg version=\"1.1\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" x=\"0px\" y=\"0px\" viewBox=\"0 0 35 35\" enable-background=\"new 0 0 35 35\" width=\"25\" height=\"25\" xml:space=\"preserve\"><polygon fill-rule=\"evenodd\" clip-rule=\"evenodd\" fill=\"#FC0\" points=\"19.3,27.5 29.3,17.5,19.3,7.5 16.3,10.4 21.4,15.4 6.7,15.4 6.7,19.6 21.4,19.6 16.3,24.6 \"\/><\/svg>\n<\/a>\n\n\n<\/div>\n                        <\/li>\n                                    <\/ul>\n                          <\/div>\n                  <\/div>\n      <\/div>\n      <\/div>\n  \n<\/div>\n\n\n\n  <div class=\"background-images\">\n          <div class=\"swiper swiper-background-images\">\n        <div class=\"swiper-wrapper\">\n                      <div class=\"swiper-slide\">\n                          <\/div>\n\n                      <div class=\"swiper-slide\">\n                                                                  \n<div class=\"f--field f--image\">\n\n    \n    \n    \n    \n    \n    \n              \n      <img decoding=\"async\"\n                            src=\"https:\/\/dornsife.usc.edu\/usclogicweb\/wp-content\/uploads\/sites\/222\/2023\/09\/practicelow-768x432.jpg\"\n          srcset=\"https:\/\/dornsife.usc.edu\/usclogicweb\/wp-content\/uploads\/sites\/222\/2023\/09\/practicelow-768x432.jpg 768w\"          sizes=\"(min-width:1200px) 75vw, (min-width:768px) 83vw, 100vw\"\n        \n                  role=\"none\"\n        \n        role=\"presentation\"\n                                      \/>\n\n    \n    \n  \n  \n\n<\/div>\n                          <\/div>\n\n                  <\/div>\n      <\/div>\n      <\/div>\n\n\n\n  <\/div><\/div>\n\n\n\n\n\n  \n        \n    \n    \n              \n    \n  \n\n  \n    \n\n\n\n\n\n\n<div\n  class=\"cc--component-container cc--interactive-content-pane \"\n\n  \n  \n  \n  \n  \n  \n  >\n  <div class=\"c--component c--interactive-content-pane\"\n    \n      >\n\n    \n<div class=\"inner-wrapper\">\n  <div class=\"left\">\n              \n<div class=\"f--field f--section-title\">\n\n    \n  <h2>\n          Unit 5\n      <\/h2>\n\n\n<\/div>\n      \n    <div class=\"pagination-wrapper\">\n      <ul class=\"interactive-content-pane-pagination\"><\/ul>\n    <\/div>\n  <\/div>\n\n  <div class=\"right\">\n          <div class=\"swiper\">\n        <div class=\"swiper-wrapper\">\n                      <div class=\"swiper-slide\">\n              <h3 class=\"pane-title\">\n                Natural Deduction for Propositional Logic\n              <\/h3>\n                                  \n<div class=\"f--field f--description\">\n\n    \n  <p>A system of natural deduction for propositional logic. Natural deduction rules for conjunction and the conditional. Rules for disjunction and negation. How to construct a natural deduction proof. Common mistakes and strategies.<\/p>\n\n\n\n<\/div>\n                          \n  \n                              <ul>\n                                            <li>\n                                \n<div class=\"f--field f--link\">\n\n    \n    \n  \n<a \n  class=\"link\"\n  href= https:\/\/gabriel-uzquiano.github.io\/logic\/natdedprop.html#natdedprop\n    aria-label=\"Read more about Tutorial\"  \n>\n    Tutorial \n  <svg version=\"1.1\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" x=\"0px\" y=\"0px\" viewBox=\"0 0 35 35\" enable-background=\"new 0 0 35 35\" width=\"25\" height=\"25\" xml:space=\"preserve\"><polygon fill-rule=\"evenodd\" clip-rule=\"evenodd\" fill=\"#FC0\" points=\"19.3,27.5 29.3,17.5,19.3,7.5 16.3,10.4 21.4,15.4 6.7,15.4 6.7,19.6 21.4,19.6 16.3,24.6 \"\/><\/svg>\n<\/a>\n\n\n<\/div>\n                        <\/li>\n                                    <\/ul>\n                          <\/div>\n                      <div class=\"swiper-slide\">\n              <h3 class=\"pane-title\">\n                Practice\n              <\/h3>\n                                  \n<div class=\"f--field f--description\">\n\n    \n  <p>Natural deduction rules for conjunction, conditional, disjunction, and negation. Strategies for complex proofs.<\/p>\n\n\n\n<\/div>\n                          \n  \n                              <ul>\n                                            <li>\n                                \n<div class=\"f--field f--link\">\n\n    \n    \n  \n<a \n  class=\"link\"\n  href= https:\/\/carnap.io\/shared\/uzquiano@usc.edu\/Unit%20V%20Practice%20%28Proof%29.md\n    aria-label=\"Read more about Problems\"  \n>\n    Problems \n  <svg version=\"1.1\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" x=\"0px\" y=\"0px\" viewBox=\"0 0 35 35\" enable-background=\"new 0 0 35 35\" width=\"25\" height=\"25\" xml:space=\"preserve\"><polygon fill-rule=\"evenodd\" clip-rule=\"evenodd\" fill=\"#FC0\" points=\"19.3,27.5 29.3,17.5,19.3,7.5 16.3,10.4 21.4,15.4 6.7,15.4 6.7,19.6 21.4,19.6 16.3,24.6 \"\/><\/svg>\n<\/a>\n\n\n<\/div>\n                        <\/li>\n                                            <li>\n                                \n<div class=\"f--field f--link\">\n\n    \n    \n  \n<a \n  class=\"link\"\n  href= https:\/\/carnap.io\/shared\/uzquiano@usc.edu\/Unit%20V%20Practice%20%28Proof%29%20Solutions.md\n    aria-label=\"Read more about Solutions\"  \n>\n    Solutions \n  <svg version=\"1.1\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" x=\"0px\" y=\"0px\" viewBox=\"0 0 35 35\" enable-background=\"new 0 0 35 35\" width=\"25\" height=\"25\" xml:space=\"preserve\"><polygon fill-rule=\"evenodd\" clip-rule=\"evenodd\" fill=\"#FC0\" points=\"19.3,27.5 29.3,17.5,19.3,7.5 16.3,10.4 21.4,15.4 6.7,15.4 6.7,19.6 21.4,19.6 16.3,24.6 \"\/><\/svg>\n<\/a>\n\n\n<\/div>\n                        <\/li>\n                                    <\/ul>\n                          <\/div>\n                  <\/div>\n      <\/div>\n      <\/div>\n  \n<\/div>\n\n\n\n  <div class=\"background-images\">\n          <div class=\"swiper swiper-background-images\">\n        <div class=\"swiper-wrapper\">\n                      <div class=\"swiper-slide\">\n                          <\/div>\n\n                      <div class=\"swiper-slide\">\n                                                                  \n<div class=\"f--field f--image\">\n\n    \n    \n    \n    \n    \n    \n              \n      <img decoding=\"async\"\n                            src=\"https:\/\/dornsife.usc.edu\/usclogicweb\/wp-content\/uploads\/sites\/222\/2023\/09\/practicelow-768x432.jpg\"\n          srcset=\"https:\/\/dornsife.usc.edu\/usclogicweb\/wp-content\/uploads\/sites\/222\/2023\/09\/practicelow-768x432.jpg 768w\"          sizes=\"(min-width:1200px) 75vw, (min-width:768px) 83vw, 100vw\"\n        \n                  role=\"none\"\n        \n        role=\"presentation\"\n                                      \/>\n\n    \n    \n  \n  \n\n<\/div>\n                          <\/div>\n\n                  <\/div>\n      <\/div>\n      <\/div>\n\n\n\n  <\/div><\/div>\n\n\n  \n    \n\n\n\n\n\n\n<div\n  class=\"cc--component-container cc--intro-text align-center\"\n\n  \n  \n  \n  \n  \n  \n  >\n  <div class=\"c--component c--intro-text\"\n    \n      >\n\n    \n          \n<div class=\"f--field f--section-title\">\n\n    \n  <h2>\n          Quantificational Logic\n      <\/h2>\n\n\n<\/div>\n  \n          \n<div class=\"f--field f--description\">\n\n    \n  <p>Quantificational logic accounts for the validity of an even wider family of natural language arguments in terms of predication and the behavior of quantificational expressions.<\/p>\n\n\n\n<\/div>\n  \n\n  <\/div><\/div>\n\n\n\n\n\n  \n        \n    \n    \n              \n    \n  \n\n  \n    \n\n\n\n\n\n\n<div\n  class=\"cc--component-container cc--interactive-content-pane \"\n\n  \n  \n  \n  \n  \n  \n  >\n  <div class=\"c--component c--interactive-content-pane\"\n    \n      >\n\n    \n<div class=\"inner-wrapper\">\n  <div class=\"left\">\n              \n<div class=\"f--field f--section-title\">\n\n    \n  <h2>\n          Unit 6\n      <\/h2>\n\n\n<\/div>\n      \n    <div class=\"pagination-wrapper\">\n      <ul class=\"interactive-content-pane-pagination\"><\/ul>\n    <\/div>\n  <\/div>\n\n  <div class=\"right\">\n          <div class=\"swiper\">\n        <div class=\"swiper-wrapper\">\n                      <div class=\"swiper-slide\">\n              <h3 class=\"pane-title\">\n                Syntax of Quantificational Logic\n              <\/h3>\n                                  \n<div class=\"f--field f--description\">\n\n    \n  <p>Vocabulary and syntax of quantificational logic. How to provide a construction tree for well-formed formulas of the language. Some notational conventions. The distinction between free and bound variables. The distinction between open and closed formulas.<\/p>\n\n\n\n<\/div>\n                          \n  \n                              <ul>\n                                            <li>\n                                \n<div class=\"f--field f--link\">\n\n    \n    \n  \n<a \n  class=\"link\"\n  href= https:\/\/gabriel-uzquiano.github.io\/logic\/formal-language.html#formal-language\n    aria-label=\"Read more about Tutorial\"  \n>\n    Tutorial \n  <svg version=\"1.1\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" x=\"0px\" y=\"0px\" viewBox=\"0 0 35 35\" enable-background=\"new 0 0 35 35\" width=\"25\" height=\"25\" xml:space=\"preserve\"><polygon fill-rule=\"evenodd\" clip-rule=\"evenodd\" fill=\"#FC0\" points=\"19.3,27.5 29.3,17.5,19.3,7.5 16.3,10.4 21.4,15.4 6.7,15.4 6.7,19.6 21.4,19.6 16.3,24.6 \"\/><\/svg>\n<\/a>\n\n\n<\/div>\n                        <\/li>\n                                    <\/ul>\n                          <\/div>\n                      <div class=\"swiper-slide\">\n              <h3 class=\"pane-title\">\n                Practice\n              <\/h3>\n                          \n  \n                              <ul>\n                                            <li>\n                                \n<div class=\"f--field f--link\">\n\n    \n    \n  \n<a \n  class=\"link\"\n  href= https:\/\/carnap.io\/shared\/uzquiano@usc.edu\/Unit%20VI%20Practice%20%28Syntax%29.md\n    aria-label=\"Read more about Problems\"  \n>\n    Problems \n  <svg version=\"1.1\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" x=\"0px\" y=\"0px\" viewBox=\"0 0 35 35\" enable-background=\"new 0 0 35 35\" width=\"25\" height=\"25\" xml:space=\"preserve\"><polygon fill-rule=\"evenodd\" clip-rule=\"evenodd\" fill=\"#FC0\" points=\"19.3,27.5 29.3,17.5,19.3,7.5 16.3,10.4 21.4,15.4 6.7,15.4 6.7,19.6 21.4,19.6 16.3,24.6 \"\/><\/svg>\n<\/a>\n\n\n<\/div>\n                        <\/li>\n                                            <li>\n                                \n<div class=\"f--field f--link\">\n\n    \n    \n  \n<a \n  class=\"link\"\n  href= https:\/\/carnap.io\/shared\/uzquiano@usc.edu\/Unit%20VI%20Practice%20%28Syntax%29%20Solutions.md\n    aria-label=\"Read more about Solutions\"  \n>\n    Solutions \n  <svg version=\"1.1\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" x=\"0px\" y=\"0px\" viewBox=\"0 0 35 35\" enable-background=\"new 0 0 35 35\" width=\"25\" height=\"25\" xml:space=\"preserve\"><polygon fill-rule=\"evenodd\" clip-rule=\"evenodd\" fill=\"#FC0\" points=\"19.3,27.5 29.3,17.5,19.3,7.5 16.3,10.4 21.4,15.4 6.7,15.4 6.7,19.6 21.4,19.6 16.3,24.6 \"\/><\/svg>\n<\/a>\n\n\n<\/div>\n                        <\/li>\n                                    <\/ul>\n                          <\/div>\n                  <\/div>\n      <\/div>\n      <\/div>\n  \n<\/div>\n\n\n\n  <div class=\"background-images\">\n          <div class=\"swiper swiper-background-images\">\n        <div class=\"swiper-wrapper\">\n                      <div class=\"swiper-slide\">\n                          <\/div>\n\n                      <div class=\"swiper-slide\">\n                                                                  \n<div class=\"f--field f--image\">\n\n    \n    \n    \n    \n    \n    \n              \n      <img decoding=\"async\"\n                            src=\"https:\/\/dornsife.usc.edu\/usclogicweb\/wp-content\/uploads\/sites\/222\/2023\/09\/practicelow-768x432.jpg\"\n          srcset=\"https:\/\/dornsife.usc.edu\/usclogicweb\/wp-content\/uploads\/sites\/222\/2023\/09\/practicelow-768x432.jpg 768w\"          sizes=\"(min-width:1200px) 75vw, (min-width:768px) 83vw, 100vw\"\n        \n                  role=\"none\"\n        \n        role=\"presentation\"\n                                      \/>\n\n    \n    \n  \n  \n\n<\/div>\n                          <\/div>\n\n                  <\/div>\n      <\/div>\n      <\/div>\n\n\n\n  <\/div><\/div>\n\n\n\n\n\n  \n        \n    \n    \n              \n    \n  \n\n  \n    \n\n\n\n\n\n\n<div\n  class=\"cc--component-container cc--interactive-content-pane \"\n\n  \n  \n  \n  \n  \n  \n  >\n  <div class=\"c--component c--interactive-content-pane\"\n    \n      >\n\n    \n<div class=\"inner-wrapper\">\n  <div class=\"left\">\n              \n<div class=\"f--field f--section-title\">\n\n    \n  <h2>\n          Unit 7\n      <\/h2>\n\n\n<\/div>\n      \n    <div class=\"pagination-wrapper\">\n      <ul class=\"interactive-content-pane-pagination\"><\/ul>\n    <\/div>\n  <\/div>\n\n  <div class=\"right\">\n          <div class=\"swiper\">\n        <div class=\"swiper-wrapper\">\n                      <div class=\"swiper-slide\">\n              <h3 class=\"pane-title\">\n                Semantics for Quantificational Logic\n              <\/h3>\n                                  \n<div class=\"f--field f--description\">\n\n    \n  <p>Models for quantificational logic. The evaluation of closed formulas in a model. What is for a closed formula to be true in a model. How to use models to test for equivalence and validity.<\/p>\n\n\n\n<\/div>\n                          \n  \n                              <ul>\n                                            <li>\n                                \n<div class=\"f--field f--link\">\n\n    \n    \n  \n<a \n  class=\"link\"\n  href= https:\/\/gabriel-uzquiano.github.io\/logic\/semantics-1.html#semantics-1\n    aria-label=\"Read more about Tutorial\"  \n>\n    Tutorial \n  <svg version=\"1.1\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" x=\"0px\" y=\"0px\" viewBox=\"0 0 35 35\" enable-background=\"new 0 0 35 35\" width=\"25\" height=\"25\" xml:space=\"preserve\"><polygon fill-rule=\"evenodd\" clip-rule=\"evenodd\" fill=\"#FC0\" points=\"19.3,27.5 29.3,17.5,19.3,7.5 16.3,10.4 21.4,15.4 6.7,15.4 6.7,19.6 21.4,19.6 16.3,24.6 \"\/><\/svg>\n<\/a>\n\n\n<\/div>\n                        <\/li>\n                                    <\/ul>\n                          <\/div>\n                      <div class=\"swiper-slide\">\n              <h3 class=\"pane-title\">\n                Practice\n              <\/h3>\n                                  \n<div class=\"f--field f--description\">\n\n    \n  <p>How to model a set of formulas.\u00a0 The use of models to test for consistency, equivalence, and validity.<\/p>\n\n\n\n<\/div>\n                          \n  \n                              <ul>\n                                            <li>\n                                \n<div class=\"f--field f--link\">\n\n    \n    \n  \n<a \n  class=\"link\"\n  href= https:\/\/carnap.io\/shared\/uzquiano@usc.edu\/Unit%20VII%20Practice%20%28Models%29.md\n    aria-label=\"Read more about Practice\"  \n>\n    Practice \n  <svg version=\"1.1\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" x=\"0px\" y=\"0px\" viewBox=\"0 0 35 35\" enable-background=\"new 0 0 35 35\" width=\"25\" height=\"25\" xml:space=\"preserve\"><polygon fill-rule=\"evenodd\" clip-rule=\"evenodd\" fill=\"#FC0\" points=\"19.3,27.5 29.3,17.5,19.3,7.5 16.3,10.4 21.4,15.4 6.7,15.4 6.7,19.6 21.4,19.6 16.3,24.6 \"\/><\/svg>\n<\/a>\n\n\n<\/div>\n                        <\/li>\n                                            <li>\n                                \n<div class=\"f--field f--link\">\n\n    \n    \n  \n<a \n  class=\"link\"\n  href= https:\/\/carnap.io\/shared\/uzquiano@usc.edu\/Unit%20VII%20Practice%20%28Models%29%20Solutions.md\n    aria-label=\"Read more about Solutions\"  \n>\n    Solutions \n  <svg version=\"1.1\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" x=\"0px\" y=\"0px\" viewBox=\"0 0 35 35\" enable-background=\"new 0 0 35 35\" width=\"25\" height=\"25\" xml:space=\"preserve\"><polygon fill-rule=\"evenodd\" clip-rule=\"evenodd\" fill=\"#FC0\" points=\"19.3,27.5 29.3,17.5,19.3,7.5 16.3,10.4 21.4,15.4 6.7,15.4 6.7,19.6 21.4,19.6 16.3,24.6 \"\/><\/svg>\n<\/a>\n\n\n<\/div>\n                        <\/li>\n                                    <\/ul>\n                          <\/div>\n                  <\/div>\n      <\/div>\n      <\/div>\n  \n<\/div>\n\n\n\n  <div class=\"background-images\">\n          <div class=\"swiper swiper-background-images\">\n        <div class=\"swiper-wrapper\">\n                      <div class=\"swiper-slide\">\n                          <\/div>\n\n                      <div class=\"swiper-slide\">\n                                                                  \n<div class=\"f--field f--image\">\n\n    \n    \n    \n    \n    \n    \n              \n      <img decoding=\"async\"\n                            src=\"https:\/\/dornsife.usc.edu\/usclogicweb\/wp-content\/uploads\/sites\/222\/2023\/09\/practicelow-768x432.jpg\"\n          srcset=\"https:\/\/dornsife.usc.edu\/usclogicweb\/wp-content\/uploads\/sites\/222\/2023\/09\/practicelow-768x432.jpg 768w\"          sizes=\"(min-width:1200px) 75vw, (min-width:768px) 83vw, 100vw\"\n        \n                  role=\"none\"\n        \n        role=\"presentation\"\n                                      \/>\n\n    \n    \n  \n  \n\n<\/div>\n                          <\/div>\n\n                  <\/div>\n      <\/div>\n      <\/div>\n\n\n\n  <\/div><\/div>\n\n\n\n\n\n  \n        \n    \n    \n              \n    \n  \n\n  \n    \n\n\n\n\n\n\n<div\n  class=\"cc--component-container cc--interactive-content-pane \"\n\n  \n  \n  \n  \n  \n  \n  >\n  <div class=\"c--component c--interactive-content-pane\"\n    \n      >\n\n    \n<div class=\"inner-wrapper\">\n  <div class=\"left\">\n              \n<div class=\"f--field f--section-title\">\n\n    \n  <h2>\n          Unit 8\n      <\/h2>\n\n\n<\/div>\n      \n    <div class=\"pagination-wrapper\">\n      <ul class=\"interactive-content-pane-pagination\"><\/ul>\n    <\/div>\n  <\/div>\n\n  <div class=\"right\">\n          <div class=\"swiper\">\n        <div class=\"swiper-wrapper\">\n                      <div class=\"swiper-slide\">\n              <h3 class=\"pane-title\">\n                Translation into Quantificational Logic\n              <\/h3>\n                                  \n<div class=\"f--field f--description\">\n\n    \n  <p>How to translate from English into the language of quantificational logic. Quantification. Issues with translation. Structural ambiguity.<\/p>\n\n\n\n<\/div>\n                          \n  \n                              <ul>\n                                            <li>\n                                \n<div class=\"f--field f--link\">\n\n    \n    \n  \n<a \n  class=\"link\"\n  href= https:\/\/gabriel-uzquiano.github.io\/logic\/translation.html#translation\n    aria-label=\"Read more about Tutorial\"  \n>\n    Tutorial \n  <svg version=\"1.1\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" x=\"0px\" y=\"0px\" viewBox=\"0 0 35 35\" enable-background=\"new 0 0 35 35\" width=\"25\" height=\"25\" xml:space=\"preserve\"><polygon fill-rule=\"evenodd\" clip-rule=\"evenodd\" fill=\"#FC0\" points=\"19.3,27.5 29.3,17.5,19.3,7.5 16.3,10.4 21.4,15.4 6.7,15.4 6.7,19.6 21.4,19.6 16.3,24.6 \"\/><\/svg>\n<\/a>\n\n\n<\/div>\n                        <\/li>\n                                    <\/ul>\n                          <\/div>\n                      <div class=\"swiper-slide\">\n              <h3 class=\"pane-title\">\n                Practice\n              <\/h3>\n                                  \n<div class=\"f--field f--description\">\n\n    \n  <p>Translation into the language of quantificational logic. Issues with translation. Formalization of complex arguments in English.<\/p>\n\n\n\n<\/div>\n                          \n  \n                              <ul>\n                                            <li>\n                                \n<div class=\"f--field f--link\">\n\n    \n    \n  \n<a \n  class=\"link\"\n  href= https:\/\/carnap.io\/shared\/uzquiano@usc.edu\/Unit%20VIII%20%28Translation%29.md\n    aria-label=\"Read more about Problems\"  \n>\n    Problems \n  <svg version=\"1.1\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" x=\"0px\" y=\"0px\" viewBox=\"0 0 35 35\" enable-background=\"new 0 0 35 35\" width=\"25\" height=\"25\" xml:space=\"preserve\"><polygon fill-rule=\"evenodd\" clip-rule=\"evenodd\" fill=\"#FC0\" points=\"19.3,27.5 29.3,17.5,19.3,7.5 16.3,10.4 21.4,15.4 6.7,15.4 6.7,19.6 21.4,19.6 16.3,24.6 \"\/><\/svg>\n<\/a>\n\n\n<\/div>\n                        <\/li>\n                                            <li>\n                                \n<div class=\"f--field f--link\">\n\n    \n    \n  \n<a \n  class=\"link\"\n  href= https:\/\/carnap.io\/shared\/uzquiano@usc.edu\/Unit%20VIII%20%28Translation%29%20Solutions.md\n    aria-label=\"Read more about Solutions\"  \n>\n    Solutions \n  <svg version=\"1.1\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" x=\"0px\" y=\"0px\" viewBox=\"0 0 35 35\" enable-background=\"new 0 0 35 35\" width=\"25\" height=\"25\" xml:space=\"preserve\"><polygon fill-rule=\"evenodd\" clip-rule=\"evenodd\" fill=\"#FC0\" points=\"19.3,27.5 29.3,17.5,19.3,7.5 16.3,10.4 21.4,15.4 6.7,15.4 6.7,19.6 21.4,19.6 16.3,24.6 \"\/><\/svg>\n<\/a>\n\n\n<\/div>\n                        <\/li>\n                                    <\/ul>\n                          <\/div>\n                  <\/div>\n      <\/div>\n      <\/div>\n  \n<\/div>\n\n\n\n  <div class=\"background-images\">\n          <div class=\"swiper swiper-background-images\">\n        <div class=\"swiper-wrapper\">\n                      <div class=\"swiper-slide\">\n                          <\/div>\n\n                      <div class=\"swiper-slide\">\n                                                                  \n<div class=\"f--field f--image\">\n\n    \n    \n    \n    \n    \n    \n              \n      <img decoding=\"async\"\n                            src=\"https:\/\/dornsife.usc.edu\/usclogicweb\/wp-content\/uploads\/sites\/222\/2023\/09\/practicelow-768x432.jpg\"\n          srcset=\"https:\/\/dornsife.usc.edu\/usclogicweb\/wp-content\/uploads\/sites\/222\/2023\/09\/practicelow-768x432.jpg 768w\"          sizes=\"(min-width:1200px) 75vw, (min-width:768px) 83vw, 100vw\"\n        \n                  role=\"none\"\n        \n        role=\"presentation\"\n                                      \/>\n\n    \n    \n  \n  \n\n<\/div>\n                          <\/div>\n\n                  <\/div>\n      <\/div>\n      <\/div>\n\n\n\n  <\/div><\/div>\n\n\n\n\n\n  \n        \n    \n    \n              \n    \n  \n\n  \n    \n\n\n\n\n\n\n<div\n  class=\"cc--component-container cc--interactive-content-pane \"\n\n  \n  \n  \n  \n  \n  \n  >\n  <div class=\"c--component c--interactive-content-pane\"\n    \n      >\n\n    \n<div class=\"inner-wrapper\">\n  <div class=\"left\">\n              \n<div class=\"f--field f--section-title\">\n\n    \n  <h2>\n          Unit 9\n      <\/h2>\n\n\n<\/div>\n      \n    <div class=\"pagination-wrapper\">\n      <ul class=\"interactive-content-pane-pagination\"><\/ul>\n    <\/div>\n  <\/div>\n\n  <div class=\"right\">\n          <div class=\"swiper\">\n        <div class=\"swiper-wrapper\">\n                      <div class=\"swiper-slide\">\n              <h3 class=\"pane-title\">\n                Natural Deduction for Quantificational Logic\n              <\/h3>\n                                  \n<div class=\"f--field f--description\">\n\n    \n  <p>Natural deduction rules for the universal and existential quantifiers. How to construct a natural deduction proof in quantificational logic. Common mistakes and strategies.<\/p>\n\n\n\n<\/div>\n                          \n  \n                              <ul>\n                                            <li>\n                                \n<div class=\"f--field f--link\">\n\n    \n    \n  \n<a \n  class=\"link\"\n  href= https:\/\/gabriel-uzquiano.github.io\/logic\/natural-deduction.html#natural-deduction\n    aria-label=\"Read more about Tutorial\"  \n>\n    Tutorial \n  <svg version=\"1.1\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" x=\"0px\" y=\"0px\" viewBox=\"0 0 35 35\" enable-background=\"new 0 0 35 35\" width=\"25\" height=\"25\" xml:space=\"preserve\"><polygon fill-rule=\"evenodd\" clip-rule=\"evenodd\" fill=\"#FC0\" points=\"19.3,27.5 29.3,17.5,19.3,7.5 16.3,10.4 21.4,15.4 6.7,15.4 6.7,19.6 21.4,19.6 16.3,24.6 \"\/><\/svg>\n<\/a>\n\n\n<\/div>\n                        <\/li>\n                                    <\/ul>\n                          <\/div>\n                      <div class=\"swiper-slide\">\n              <h3 class=\"pane-title\">\n                Practice\n              <\/h3>\n                                  \n<div class=\"f--field f--description\">\n\n    \n  <p>Natural deduction rules for the universal and existential quantifiers. Strategies for complex proofs.<\/p>\n\n\n\n<\/div>\n                          \n  \n                              <ul>\n                                            <li>\n                                \n<div class=\"f--field f--link\">\n\n    \n    \n  \n<a \n  class=\"link\"\n  href= https:\/\/carnap.io\/shared\/uzquiano@usc.edu\/Unit%20IX%20%28Proof%29.md\n    aria-label=\"Read more about Problems\"  \n>\n    Problems \n  <svg version=\"1.1\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" x=\"0px\" y=\"0px\" viewBox=\"0 0 35 35\" enable-background=\"new 0 0 35 35\" width=\"25\" height=\"25\" xml:space=\"preserve\"><polygon fill-rule=\"evenodd\" clip-rule=\"evenodd\" fill=\"#FC0\" points=\"19.3,27.5 29.3,17.5,19.3,7.5 16.3,10.4 21.4,15.4 6.7,15.4 6.7,19.6 21.4,19.6 16.3,24.6 \"\/><\/svg>\n<\/a>\n\n\n<\/div>\n                        <\/li>\n                                            <li>\n                                \n<div class=\"f--field f--link\">\n\n    \n    \n  \n<a \n  class=\"link\"\n  href= https:\/\/carnap.io\/shared\/uzquiano@usc.edu\/Unit%20IX%20%28Proof%29%20Solutions.md\n    aria-label=\"Read more about Solutions\"  \n>\n    Solutions \n  <svg version=\"1.1\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" x=\"0px\" y=\"0px\" viewBox=\"0 0 35 35\" enable-background=\"new 0 0 35 35\" width=\"25\" height=\"25\" xml:space=\"preserve\"><polygon fill-rule=\"evenodd\" clip-rule=\"evenodd\" fill=\"#FC0\" points=\"19.3,27.5 29.3,17.5,19.3,7.5 16.3,10.4 21.4,15.4 6.7,15.4 6.7,19.6 21.4,19.6 16.3,24.6 \"\/><\/svg>\n<\/a>\n\n\n<\/div>\n                        <\/li>\n                                    <\/ul>\n                          <\/div>\n                  <\/div>\n      <\/div>\n      <\/div>\n  \n<\/div>\n\n\n\n  <div class=\"background-images\">\n          <div class=\"swiper swiper-background-images\">\n        <div class=\"swiper-wrapper\">\n                      <div class=\"swiper-slide\">\n                          <\/div>\n\n                      <div class=\"swiper-slide\">\n                          <\/div>\n\n                  <\/div>\n      <\/div>\n      <\/div>\n\n\n\n  <\/div><\/div>\n\n\n\n\n\n  \n        \n    \n    \n              \n    \n  \n\n  \n    \n\n\n\n\n\n\n<div\n  class=\"cc--component-container cc--interactive-content-pane \"\n\n  \n  \n  \n  \n  \n  \n  >\n  <div class=\"c--component c--interactive-content-pane\"\n    \n      >\n\n    \n<div class=\"inner-wrapper\">\n  <div class=\"left\">\n              \n<div class=\"f--field f--section-title\">\n\n    \n  <h2>\n          Unit 10\n      <\/h2>\n\n\n<\/div>\n      \n    <div class=\"pagination-wrapper\">\n      <ul class=\"interactive-content-pane-pagination\"><\/ul>\n    <\/div>\n  <\/div>\n\n  <div class=\"right\">\n          <div class=\"swiper\">\n        <div class=\"swiper-wrapper\">\n                      <div class=\"swiper-slide\">\n              <h3 class=\"pane-title\">\n                Quantificational Logic with Identity\n              <\/h3>\n                                  \n<div class=\"f--field f--description\">\n\n    \n  <p>How to supplement quantificational logic with identity. Quantification and Number. Definite Descriptions.<\/p>\n\n\n\n<\/div>\n                          \n  \n                              <ul>\n                                            <li>\n                                \n<div class=\"f--field f--link\">\n\n    \n    \n  \n<a \n  class=\"link\"\n  href= https:\/\/gabriel-uzquiano.github.io\/logic\/identity.html#identity\n    aria-label=\"Read more about Identity\"  \n>\n    Identity \n  <svg version=\"1.1\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" x=\"0px\" y=\"0px\" viewBox=\"0 0 35 35\" enable-background=\"new 0 0 35 35\" width=\"25\" height=\"25\" xml:space=\"preserve\"><polygon fill-rule=\"evenodd\" clip-rule=\"evenodd\" fill=\"#FC0\" points=\"19.3,27.5 29.3,17.5,19.3,7.5 16.3,10.4 21.4,15.4 6.7,15.4 6.7,19.6 21.4,19.6 16.3,24.6 \"\/><\/svg>\n<\/a>\n\n\n<\/div>\n                        <\/li>\n                                    <\/ul>\n                          <\/div>\n                      <div class=\"swiper-slide\">\n              <h3 class=\"pane-title\">\n                Practice\n              <\/h3>\n                                  \n<div class=\"f--field f--description\">\n\n    \n  <p>Quantification and Number. Definite Descriptions.<\/p>\n\n\n\n<\/div>\n                          \n  \n                              <ul>\n                                            <li>\n                                \n<div class=\"f--field f--link\">\n\n    \n    \n  \n<a \n  class=\"link\"\n  href= https:\/\/carnap.io\/shared\/uzquiano@usc.edu\/Unit%20X%20%28Identity%29.md\n    aria-label=\"Read more about Problems\"  \n>\n    Problems \n  <svg version=\"1.1\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" x=\"0px\" y=\"0px\" viewBox=\"0 0 35 35\" enable-background=\"new 0 0 35 35\" width=\"25\" height=\"25\" xml:space=\"preserve\"><polygon fill-rule=\"evenodd\" clip-rule=\"evenodd\" fill=\"#FC0\" points=\"19.3,27.5 29.3,17.5,19.3,7.5 16.3,10.4 21.4,15.4 6.7,15.4 6.7,19.6 21.4,19.6 16.3,24.6 \"\/><\/svg>\n<\/a>\n\n\n<\/div>\n                        <\/li>\n                                            <li>\n                                \n<div class=\"f--field f--link\">\n\n    \n    \n  \n<a \n  class=\"link\"\n  href= https:\/\/carnap.io\/shared\/uzquiano@usc.edu\/Unit%20X%20%28Identity%29%20Solutions.md\n    aria-label=\"Read more about Solutions\"  \n>\n    Solutions \n  <svg version=\"1.1\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" x=\"0px\" y=\"0px\" viewBox=\"0 0 35 35\" enable-background=\"new 0 0 35 35\" width=\"25\" height=\"25\" xml:space=\"preserve\"><polygon fill-rule=\"evenodd\" clip-rule=\"evenodd\" fill=\"#FC0\" points=\"19.3,27.5 29.3,17.5,19.3,7.5 16.3,10.4 21.4,15.4 6.7,15.4 6.7,19.6 21.4,19.6 16.3,24.6 \"\/><\/svg>\n<\/a>\n\n\n<\/div>\n                        <\/li>\n                                    <\/ul>\n                          <\/div>\n                  <\/div>\n      <\/div>\n      <\/div>\n  \n<\/div>\n\n\n\n  <div class=\"background-images\">\n          <div class=\"swiper swiper-background-images\">\n        <div class=\"swiper-wrapper\">\n                      <div class=\"swiper-slide\">\n                          <\/div>\n\n                      <div class=\"swiper-slide\">\n                                                                  \n<div class=\"f--field f--image\">\n\n    \n    \n    \n    \n    \n    \n              \n      <img decoding=\"async\"\n                            src=\"https:\/\/dornsife.usc.edu\/usclogicweb\/wp-content\/uploads\/sites\/222\/2023\/09\/practicelow-768x432.jpg\"\n          srcset=\"https:\/\/dornsife.usc.edu\/usclogicweb\/wp-content\/uploads\/sites\/222\/2023\/09\/practicelow-768x432.jpg 768w\"          sizes=\"(min-width:1200px) 75vw, (min-width:768px) 83vw, 100vw\"\n        \n                  role=\"none\"\n        \n        role=\"presentation\"\n                                      \/>\n\n    \n    \n  \n  \n\n<\/div>\n                          <\/div>\n\n                  <\/div>\n      <\/div>\n      <\/div>\n\n\n\n  <\/div><\/div>\n\n\n  \n  \n    \n\n\n\n\n\n\n<div\n  class=\"cc--component-container cc--contact-details \"\n\n  \n  \n  \n  \n  \n  \n  >\n  <div class=\"c--component c--contact-details\"\n    \n      >\n\n    \n  <div class=\"inner-wrapper\">\n\n          <div class=\"header-container\">\n\n                      \n<div class=\"f--field f--section-title\">\n\n    \n  <h2>\n          Contact Details\n      <\/h2>\n\n\n<\/div>\n        \n                      \n<div class=\"f--field f--link\">\n\n    \n    \n  \n<a \n  class=\"link\"\n  href= https:\/\/dornsife.usc.edu\/phil\/\n    aria-label=\"Read more about USC School of Philosophy\"  \n>\n    USC School of Philosophy \n  <svg version=\"1.1\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" x=\"0px\" y=\"0px\" viewBox=\"0 0 35 35\" enable-background=\"new 0 0 35 35\" width=\"25\" height=\"25\" xml:space=\"preserve\"><polygon fill-rule=\"evenodd\" clip-rule=\"evenodd\" fill=\"#000\" points=\"19.3,27.5 29.3,17.5,19.3,7.5 16.3,10.4 21.4,15.4 6.7,15.4 6.7,19.6 21.4,19.6 16.3,24.6 \"\/><\/svg>\n<\/a>\n\n\n<\/div>\n        \n      <\/div>\n    \n    \n      <div class=\"contacts-container\">\n\n        \n                      <div class=\"contact-card\">\n\n                              <h3>Gabriel Uzquiano<\/h3>\n              \n              \n              \n                              <div class=\"f--email\">\n                  <a href=\"mailto:uzquiano@usc.edu\">uzquiano@usc.edu<\/a>\n                <\/div>\n              \n            <\/div>\n                    \n      <\/div>\n\n        \n     \n    \n  <\/div>\n\n\n  <\/div><\/div>\n\n\n\n\n  \n    \n\n\n\n\n\n\n<div\n  class=\"cc--component-container cc--rich-text \"\n\n  \n  \n  \n  \n  \n  \n  >\n  <div class=\"c--component c--rich-text\"\n    \n      >\n\n    \n      \n<div class=\"f--field f--wysiwyg\">\n\n    \n  <p><a href=\"https:\/\/dornsife.usc.edu\/usclogicweb\/\">USC Logic Web<\/a> \u00a9 2024 by <a href=\"https:\/\/creativecommons.org\">Gabriel Uzquiano<\/a> is licensed under <a href=\"https:\/\/creativecommons.org\/licenses\/by-nc\/4.0\/\">Creative Commons Attribution-NonCommercial 4.0 International<\/a><\/p>\n\n\n\n<\/div>\n\n\n  <\/div><\/div>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":9,"featured_media":286,"parent":0,"menu_order":0,"comment_status":"open","ping_status":"closed","template":"","meta":{"_acf_changed":false,"footnotes":""},"class_list":["post-4","page","type-page","status-publish","has-post-thumbnail","hentry"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.1.1 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Main - USC Logic Web<\/title>\n<meta name=\"description\" content=\"USC Logic Web.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/dornsife.usc.edu\/usclogicweb\/\" \/>\n<meta property=\"og:locale\" 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