In logic, the argument form or test form of an argument results from replacing the different words, or sentences, that make up the argument with letters, along the lines of algebra; the letters represent logical variables. The sentence forms which classify argument forms of common arguments important are studied in logic. Logic, from Classical Greek λόγος (logos), originally meaning the word, or what is spoken, (but coming to mean thought or reason) is the study of criteria for the evaluation of arguments, although the exact definition of logic is a matter of controversy among philosophers. ... In logic, an argument is an attempt to demonstrate the truth of an assertion called a conclusion, based on the truth of a set of assertions called premises. ... Algebra is a branch of mathematics concerning the study of structure, relation and quantity. ... In computer science and mathematics, a variable (sometimes called a pronumeral) is a symbol denoting a quantity or symbolic representation. ... Logic, from Classical Greek λόγος (logos), originally meaning the word, or what is spoken, (but coming to mean thought or reason) is the study of criteria for the evaluation of arguments, although the exact definition of logic is a matter of controversy among philosophers. ...

Here is an example of an argument:

A All humans are mortal. Socrates is human. Therefore, Socrates is mortal.

We can rewrite argument A by putting each sentence on its own line:

B

All humans are mortal.

Socrates is human.

Therefore, Socrates is mortal.

To demonstrate the important notion of the form of an argument, substitute letters for similar items throughout B:

C

All S are P.

a is S.

Therefore, a is P.

All we have done in C is to put 'S' for 'human' and 'humans', 'P' for 'mortal', and a for 'Socrates'; what results, C, is the form of the original argument in A. So argument form C is the form of argument A. Moreover, each individual sentence of C is the sentence form of its respective sentence in A.

Attention is given to argument and sentence form, because form is what makes an argument valid or cogent. Some examples of valid arguments forms are modus ponens, modus tollens, and the disjunctive syllogism. Two invalid argument forms are affirming the consequent and denying the antecedent. In logic, the form of an argument is valid precisely if it cannot lead from true premises to a false conclusion. ... An argument is cogent if and only if the truth of the arguments premises would render the truth of the conclusion probable (i. ... In Logic, Modus ponens (Latin: mode that affirms) is a valid, simple argument form (often abbreviated to MP): If P, then Q. P. Therefore, Q. or in logical operator notation: P → Q P ⊢ Q where ⊢ represents the logical assertion. ... In logic, Modus tollens (Latin for mode that denies) is the formal name for indirect proof or proof by contrapositive (contrapositive inference), often abbreviated to MT. It can also be referred to as denying the consequent, and is a valid form of argument (unlike similarly-named but invalid arguments such... A disjunctive syllogism, also known as modus tollendo ponens (literally: mode which, by denying, affirms) is a valid, simple argument form: P or Q Not P Therefore, Q In logical operator notation: ¬ where represents the logical assertion. ... Affirming the consequent is a logical fallacy in the form of a hypothetical proposition. ... Denying the antecedent (also known as vacuous implication) is a type of logical fallacy. ...

See also

• Analytic proposition
• Synthetic proposition