Briefly research the topic. Choose your topic and begin reading about it. Find out what the major controversies or areas of interest are in the field and decide on a stand that you will take. If you already know the position you want to argue in your paper, be sure to research materials that support your position and materials that oppose your position so that you can counter the opposing arguments.
Collect information. As you gather and briefly review sources, mark and put aside those that look particularly helpful. For logical arguments, pay particular attention to statistics, studies and facts.
Write an outline. Choose your thesis and main points (known as claims or premises in argumentative writing), and write a rough outline of your paper. This is necessary in order to know what arguments or claims you need to support and what information you need to gather.
Do in-depth research on three to five main arguments. After your cursory research, decide on several of the strongest arguments in favor of your point of view. The number will vary depending on the length of your paper and the complexity of the issue. Do in-depth research on each point, making note cards or lists of facts supporting each argument. Keep track of sources as you find supporting material so that it is easy to construct endnotes and bibliographical information when writing your paper.
Develop inductive support. Logical reasoning usually depends on inductive or deductive arguments. If you use inductive reasoning, you present a specific case or group of facts, then make a generalization based on the specific case. For example, you can make the specific assertion that the taxpayer-funded stadium in Cincinnati has turned into a money pit for taxpayers. Then you draw the generalized conclusion that: therefore, it is a bad idea for cities to agree to taxpayer-funded stadiums. You then construct the argument by using facts and numbers outlining the unexpected and ongoing costs of the Cincinnati Bengals' stadium, the continued and increasing costs to the taxpayers and the few benefits they receive. A solid logical argument would include statistics from other stadium projects as well. Have three or four supporting pieces of data, quotes or conclusions for each main point.
Develop deductive arguments. Deductive arguments begin with a generalization, then draw specific conclusions that apply to a specific case. For example, you may make the claim that students who attend class regularly get better grades. Then you make a specific assertion based on that claim -- if you want to do well in English class, you should attend class each day. To make a logical argument stand, you would then need to back up the original assertion with statistics, facts and personal testimony that support your claim. For example, find university studies that compare the grades of students who attend class frequently and those who do not. Then get personal testimony from teachers who compare grades of those who attend class regularly and those who don't; then finish with personal anecdotes from yourself or other students. The strongest logical arguments are supported with objective, verifiable evidence.
Write a solid introduction and conclusion. After finding at least three solid arguments and creating a sound, logical case in favor of your position, write a strong introduction and conclusion. In the introduction, begin with a shocking statistic, a pithy quote or a short story. Draw the reader into the problem, then state your thesis and briefly preview your main arguments. After you have completed all the other sections of your paper, write the conclusion. Briefly summarize the main points of your argument, restate your thesis and end with a strong clincher. Relating back to your quote or story at the beginning of the paper is a great way to close a logical argument paper.