atomic formula

A propositional variable can stand on its own as an atomic formula.

The next step is to define the atomic formulas.

In model theory, structures assign an interpretation to the atomic formulas.

Nothing else is an atomic formula of dependence logic.

Interpretation of the atomic formulas of L is more complicated.

There are three types of atomic formulas in dependence logic:

An atomic sentence is an atomic formula containing no variables.

Finally, each atomic formula implies the existence of a corresponding class relation:

In bivalent logics, given an interpretation, this atomic formula will then be true or false.

Let a sentential variable be a 0-place atomic formula, whose extension is a classical truth value, by definition.

In mathematical logic, a literal is an atomic formula (atom) or its negation.

In proof theory, polarity assignment for atomic formulas is an essential component of focusing.

The following two atomic formulas succinctly describe the typing rules: and (notation to be improved).

All atomic formulas are thus of the form , where is a relation symbol and is a variable.

The atomic formulas of ST are of two forms, (identity) and .

Formulas are built out of atomic formulas using logical connectives and quantifiers.

Propositional variables are the atomic formulas of propositional logic.

Compound formulas are formed by combining the atomic formulas using the logical connectives.

Scott began with an axiom he declined to name: the atomic formula x y implies that y is a set.

A bisimulation of models is additionally required to preserve forcing of atomic formulas:

In the intended interpretation, the variables these stand for classes, and the atomic formula means "class X is an element of class Y".

In first-order logic, an atomic formula consists of a predicate symbol applied to an appropriate number of terms.

Then the translation can be succinctly described as: prefix to every atomic formula, disjunction, and existential quantifier.

If is an atomic formula of , define a formula of recursively as follows.

We then define the set of atomic formulas A[S,type] with the following rules: