Kant

Kant is one of the most popular philosophical frameworks ran in LD debate. In contrast to theories like utilitarianism, which determine whether actions are just based on the consequences of an action, Kant advocates for a deontological theory, where the goodness of an action is intrinsic to the action itself. Kant can be a very strategic framework since many judges at least understand the basics, and it largely differs from utilitarian frameworks, so as a result, you can exclude much of your opponent's offense. Below is a brief description on how many Kant frameworks are justified in LD debate.

Syllogism

Many Kant frameworks contain the idea that human beings are intrinsically valuable. There are intrinsic properties, that all humans share, that make them valuable as agents. Often, rationality is used to bind human agents together.

These frameworks start with the premise that all human agents are rational beings. A rational agent is one that is capable of setting and pursuing their own ends, essentially, being able to think of an action and act upon it. There are various justifications for this argument which you can see in the sample cases, but for instance, whenever we choose an action, we deliberately set out to take all of the steps necessary for fulfilling that action.

Next, given that all agents are rational, an action that is justified for one agent must be justified for all agents. Logically, it could not be moral for one agent to take an action, but immoral for another agent to take that very same action. Kant then lays out a "test", so to speak, to determine whether an action would be justified for all agents to take.

Kant proposes we universalize an action to determine whether it would be moral for all agents to take. For instance, suppose Agent A wanted to murder Agent B. By universalizing the action of murdering, that is, imagining the world in which every single agent took that action, Agent B would murder Agent A. Therefore, Agent A would be unable to carry out the original action of murdering, because they would be dead. Clearly, this leads to a contradiction, which is illogical, and thus immoral under a Kantian framework. This is called a Contradiction in Conception because it is impossible to conceptualize a world in which both actions are being in taken.

Another type of contradiction is called a Contradiction in Wills. Here, it would be possible to conceptualize a world to universalize a given action, but it would not be an ideal world. For instance, if Agent A walks past Agent B, who is drowning in a pool, technically, Agent A is under no obligation to save Agent B by a contradiction of conception, as one could perfectly conceptualize a world in which drowning people were never saved. However, if Agent A was in the position of Agent B, they would presumably want to be saved, so therefore, by seeing themself in the place of the other agent, the world would not be ideal. Therefore, Agent A could be under some indirect obligation to save Agent B. As an aside, in the debate sense, this might only be relevant if there is no act-omission distinction.

In any case, the conclusion of a Kantian framework is usually a standard of "consistency with the categorical imperative", where the categorical imperative is this imperative previously mentioned to make sure that contradictions do not take place upon universalizing an action. You can refer to the sample cases for examples of Kantian offense employed in debate.