Also called truthbearers, an atomic sentence is a simple declarative sentence which can either be true or false. Used in logic, atomic sentences are the building blocks for more complex statements, called molecular sentences. In logical proofs, atomic sentences are assigned letters in order to easily calculate the truth or falsity of a more complex statement.
An atomic sentence is the most basic type of sentence in logic. Similar to a simple sentence in grammar, an atomic sentence contains a subject, a verb, and often an object. For example, "Jack cooked dinner," "He is intelligent," and, "She brought the wine," are all atomic sentences.
A main goal in philosophy and logic is to determine the truth of statements and complex ideas. Atomic sentences are important because they can either be wholly true or wholly false. Either Jack cooked dinner or he did not. By using atomic sentences to build more complex sentences — or, conversely, to break down complex sentences into their basic parts — the truth of these statements can be determined through logical proofs. Logical proofs are similar to geometric proofs in function and design.
When two or more atomic sentences are strung together to form a more complex sentence, a molecular sentence is formed. For example, combining the atomic sentences, "Jack cooked dinner," and, "She brought the wine," forms the molecular sentence, "Jack cooked dinner, and she brought the wine." Additionally, molecular sentences may be formed by the negation of an atomic sentence. For example, although, "He is not intelligent," is still a simple sentence according to grammatical rules, according to logical rules, the addition of the "not" makes the statement a molecular sentence. Molecular sentences can be wholly true, partially true, or wholly false.
In symbolic logic, atomic sentences are assigned letters, often starting with "p" and then continuing alphabetically. For example, the atomic sentence, "Jack cooks dinner," may be represented by a "p" while, "She brought the wine," is represented by the letter "q." The linking words, such as "and," "if," "but," and "not," are given symbols to represent their function in the larger sentence as well.
When the sentences are broken down in this way, each sentence can be worked through just like a mathematical proof. The symbols for the linking words are logical operators and behave similarly to mathematical operators, like plus and minus. By working through a logical proof, the truth or falsehood of a molecular sentence as a whole, not just the atomic sentences which is contains, can be ascertained.