In logic and analytic philosophy, an atomic sentence is a type of declarative sentence which is either true or false (may also be referred to as a proposition, statement or truthbearer) and which cannot be broken down into other simpler sentences. For example, "The dog ran" is an atomic sentence in natural language, whereas "The dog ran and the cat hid" is a molecular sentence in natural language.
From a logical analysis point of view, the truth or falsity of sentences in general is determined by only two things: the logical form of the sentence and the truth or falsity of its simple sentences. This is to say, for example, that the truth of the sentence "John is Greek and John is happy" is a function of the meaning of "and", and the truth values of the atomic sentences "John is Greek" and "John is happy". However, the truth or falsity of an atomic sentence is not a matter that is within the scope of logic itself, but rather whatever art or science the content of the atomic sentence happens to be talking about.[1]
Logic has developed artificial languages, for example sentential calculus and predicate calculus, partly with the purpose of revealing the underlying logic of natural-language statements, the surface grammar of which may conceal the underlying logical structure. In these artificial languages an atomic sentence is a string of symbols which can represent an elementary sentence in a natural language, and it can be defined as follows. In a formal language, a well-formed formula (or wff) is a string of symbols constituted in accordance with the rules of syntax of the language. A term is a variable, an individual constant or an n-place function letter followed by n terms. An atomic formula is a wff consisting of either a sentential letter or an n-place predicate letter followed by n terms. A sentence is a wff in which any variables are bound. An atomic sentence is an atomic formula containing no variables. It follows that an atomic sentence contains no logical connectives, variables, or quantifiers. A sentence consisting of one or more sentences and a logical connective is a compound (or molecular) sentence.
^The Philosophy of Logic by Willard Van Orman Quine (1970).
In logic and analytic philosophy, an atomicsentence is a type of declarative sentence which is either true or false (may also be referred to as a proposition...
In proof theory, polarity assignment for atomic formulas is an essential component of focusing. Atomicsentence Hodges, Wilfrid (1997). A Shorter Model...
constituents are atomicsentences. A contemporary semantic definition of truth would define truth for the atomicsentences as follows: An atomicsentence F(x1,....
depends on being by holding that the truth of molecular sentences depends on the truth of atomicsentences, whose truth in turn depends on being. All non-maximalist...
with first-order logic which analyzes the internal structure of the atomicsentences. Boolean algebra (logic) Boolean datatype Boolean domain Boolean function...
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every atomicsentence of the language L {\displaystyle L} , and let A t ( x ) {\displaystyle At(x)} be the number of distinct atomicsentences in x {\displaystyle...
a (usually infinite) conjunction containing every possible ground atomicsentence, either negated or unnegated; such a conjunction describes a possible...
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written that A ⊧ φ [a] If φ has no free variables, that is, if φ is an atomicsentence, and it is satisfied by A, then one writes A ⊧ φ In this case, one...
classical valuation defined on every atomicsentence of the language L and let At(x) be the number of distinct atomicsentences in a formula x. There are then...
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with one or more variables: 'Fa' or 'Fab,' etc. Non-atomicsentences are built from atomicsentences by using truth functions, quantifiers, and some other...
Given a method for establishing the satisfaction (or not) of every atomicsentence of the form A(..., xk, ...), the usual rules for truth-functional connectives...
applied to a sequence of terms without any logical connectives. atomicsentence A sentence that contains no logical connectives or quantifiers, expressing...
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claim of the antecedent is false. If a name fails to refer, then an atomicsentence containing it, that is not an identity statement, can be assigned a...
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