Definition:Scope of Connective/Definition 2

Definition

Let $\LL_0$ be the language of propositional logic.

Let $\circ$ be a connective of $\LL_0$.

Let $\mathbf W$ be a well-formed formula of $\LL_0$.

The scope of an occurrence of $\circ$ in $\mathbf W$ is defined as:

the set of statements that it connects, whether simple or compound.

This article is complete as far as it goes, but it could do with expansion. In particular: Expand the notation to define $\circ$ in its full nature as $\map \circ S$, where $S$ is the tuple of its operands. We have not defined the "scope" of the general operand, because we have not gone far down that route yet. You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by adding this information. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{Expand}} from the code. If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page.

This page or section has statements made on it that ought to be extracted and proved in a Theorem page. You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by creating any appropriate Theorem pages that may be needed. To discuss this page in more detail, feel free to use the talk page.

The arity of $\circ$ determines the cardinality of this set.

In the case of a unary connective, there will be only one such statement.

Also see

• Definition:Main Connective