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Modus Ponens is a form of logical argument where one can deduce a consequent from a conditional (if-then) statement and its antecedent. Example: If it rains, then the ground will be wet. It is raining. Therefore, the ground is wet.

Modus Tollens is a form of argument where one can deduce the negation of an antecedent from a conditional statement and the negation of its consequent. Example: If it rains, then the ground will be wet. The ground is not wet. Therefore, it is not raining.

Hypothetical Syllogism is a logical argument consisting of two conditional statements and a conclusion that combines the antecedent of one statement with the consequent of the other. Example: If it is raining, then the ground will be wet. If the ground is wet, then the plants will grow. Therefore, if it is raining, then the plants will grow.

Disjunctive Syllogism is a form of logical deduction that concludes one disjunct must be false if the other is true when faced with a disjunction. Example: Either it is raining, or it is not raining. It is not raining. Therefore, it must be raining.

Constructive Dilemma is a form of argument with a pair of conditional statements and a disjunction as its antecedent. Example: If it rains, the ground gets wet. If it does not rain, the plants will not grow. It is either raining or it is not raining. Therefore, either the ground gets wet, or the plants will not grow.

Destructive Dilemma is a form of argument similar to the constructive dilemma, but negates both parts of the disjunctive premise. Example: If it rains, then we will stay indoors. If it does not rain, we will go for a walk. It is either not raining or we are not indoors. Therefore, we will go for a walk or it is raining.

Categorical Syllogism involves an argument with two premises and a conclusion, each statement beginning with 'All', 'No', or 'Some'. Example: All humans are mortal. Socrates is a human. Therefore, Socrates is mortal.

This is a fallacy where a positive conclusion is derived from at least one negative premise. Example: No fish are dogs. Some pets are dogs. Therefore, some pets are fish. This is not a valid conclusion.

Existential Fallacy occurs when a conclusion about existence is deduced from premises that do not necessarily claim existence. Example: All unicorns have horns. Charlie is a unicorn. Therefore, Charlie exists. The premises do not assert the existence of Charlie.