A categorical proposition is a statement that makes a general claim about a category of things. In this case, the statement "All dogs are mammals" is a categorical proposition because it makes a general claim about all dogs.

The subject term of a categorical proposition is the term that refers to the category of things that the proposition is making a claim about. In this case, the proposition "No cats are dogs" is making a claim about cats, so the subject term is "cats".

The predicate term of a categorical proposition is the term that refers to the property or characteristic that the proposition is attributing to the subject term. In this case, the proposition "All men are mortal" is attributing the property of mortality to men, so the predicate term is "mortal".

An affirmative proposition is a statement that affirms or asserts something about a category of things. In this case, the proposition "All dogs are mammals" is an affirmative proposition because it affirms that all dogs are mammals.

A negative proposition is a statement that denies or negates something about a category of things. In this case, the proposition "No cats are dogs" is a negative proposition because it denies that any cats are dogs.

A universal proposition is a statement that makes a claim about all members of a category of things. In this case, the proposition "All dogs are mammals" is a universal proposition because it makes a claim about all dogs.

A particular proposition is a statement that makes a claim about some members of a category of things. In this case, the proposition "Some birds can fly" is a particular proposition because it makes a claim about some birds.

The converse of a proposition is a new proposition that is formed by switching the subject and predicate terms. In this case, the converse of the proposition "All dogs are mammals" is "All mammals are dogs".

The inverse of a proposition is a new proposition that is formed by negating the subject term and the predicate term. In this case, the inverse of the proposition "No cats are dogs" is "No dogs are cats".

The contrapositive of a proposition is a new proposition that is formed by negating the antecedent and the consequent of the original proposition. In this case, the contrapositive of the proposition "If it rains, then the grass gets wet" is "If the grass does not get wet, then it does not rain".

A true categorical proposition is a statement that is true for all members of the category of things that it is making a claim about. In this case, the proposition "All dogs are mammals" is a true categorical proposition because it is true for all dogs.

A false categorical proposition is a statement that is not true for all members of the category of things that it is making a claim about. In this case, the proposition "No fish have legs" is a false categorical proposition because it is not true for all fish.

The distribution of the subject term in a categorical proposition indicates whether the proposition is making a claim about all or some members of the category of things that the subject term refers to. In this case, the proposition "All dogs are mammals" is making a claim about all dogs, so the distribution of the subject term is universal.

The distribution of the predicate term in a categorical proposition indicates whether the proposition is making a claim about all or some members of the category of things that the predicate term refers to. In this case, the proposition "Some birds can fly" is making a claim about some birds, so the distribution of the predicate term is particular.

A singular subject term refers to a single individual. In this case, the proposition "Socrates is a philosopher" has a singular subject term because it is making a claim about a single individual, Socrates.