Editing Propositional calculus (section)

==Sentences==
{{Main article|Proposition}}
Propositional logic, as currently studied in universities, is a specification of a standard of [[logical consequence]] in which only the meanings of [[Logical connective|propositional connectives]] are considered in evaluating the conditions for the truth of a sentence, or whether a sentence logically follows from some other sentence or group of sentences.<ref name=":2" />

=== Declarative sentences ===
Propositional logic deals with '''statements''', which are defined as declarative sentences having truth value.<ref name="ms8"/><ref name=":1" /> Examples of statements might include:

* ''[[Wikipedia]] is a free online encyclopedia that anyone can edit.''
* ''[[London]] is the capital of [[England]].''
* ''All [[Wikipedia community|Wikipedia editors]] speak at least three [[language]]s.''
Declarative sentences are contrasted with [[question]]s, such as "What is Wikipedia?", and [[Imperative mood|imperative]] statements, such as "Please add [[citation]]s to support the claims in this article.".<ref name="ms9"/><ref name="ms10"/> Such non-declarative sentences have no [[truth value]],<ref name="ms11"/> and are only dealt with in [[Non-classical logic|nonclassical logics]], called [[Erotetics|erotetic]] and [[imperative logic]]s.

=== Compounding sentences with connectives ===
{{See also|Atomic formula|Atomic sentence}}
In propositional logic, a statement can contain one or more other statements as parts.<ref name=":1" /> ''Compound sentences'' are formed from simpler sentences and express relationships among the constituent sentences.<ref name=":4"/> This is done by combining them with [[logical connective]]s:<ref name=":4" /><ref name=":21"/> the main types of compound sentences are [[negation]]s, [[Logical conjunction|conjunctions]], [[Logical disjunction|disjunctions]], [[Material conditional|implications]], and [[Logical biconditional|biconditionals]],<ref name=":4" /> which are formed by using the corresponding connectives to connect propositions.<ref name="ms12"/><ref name="ms13"/> In [[English language|English]], these connectives are expressed by the words "and" ([[logical conjunction|conjunction]]), "or" ([[logical disjunction|disjunction]]), "not" ([[negation]]), "if" ([[material conditional]]), and "if and only if" ([[Logical biconditional|biconditional]]).<ref name=":1" /><ref name=":5" /> Examples of such compound sentences might include:

* ''Wikipedia is a free online encyclopedia that anyone can edit, '''and''' [[1,000,000|millions]] [[Help:Editing|already have]].'' (conjunction)
* '''''It is not true that''' all Wikipedia editors speak at least three languages.'' (negation)
* '''''Either''' London is the capital of England, '''or''' London is the capital of the [[United Kingdom]], '''or both.''''' (disjunction){{refn|group=lower-alpha|The "or both" makes it clear<ref name=":21" /> that it's a ''logical disjunction'', not an [[exclusive or]], which is more common in English.}}

If sentences lack any logical connectives, they are called ''simple sentences'',<ref name=":1" /> or ''atomic sentences'';<ref name=":21" /> if they contain one or more logical connectives, they are called ''compound sentences'',<ref name=":4" /> or ''molecular sentences''.<ref name=":21" />

''Sentential connectives'' are a broader category that includes logical connectives.<ref name=":2" /><ref name=":21" /> Sentential connectives are any linguistic particles that bind sentences to create a new compound sentence,<ref name=":2" /><ref name=":21" /> or that inflect a single sentence to create a new sentence.<ref name=":2" /> A ''logical connective'', or ''propositional connective'', is a kind of sentential connective with the characteristic feature that, when the original sentences it operates on are (or express) [[proposition]]s, the new sentence that results from its application also is (or expresses) a [[proposition]].<ref name=":2" /> Philosophers disagree about what exactly a proposition is,<ref name=":22" /><ref name=":2" /> as well as about which sentential connectives in natural languages should be counted as logical connectives.<ref name=":21" /><ref name=":2" /> Sentential connectives are also called ''sentence-functors'',<ref name="BostockIntermediate" /> and logical connectives are also called ''truth-functors''.<ref name="BostockIntermediate" />