Formaalsel

Formaalsel is a hypothetical term used in theoretical discussions of formal semantics and logic to describe a formalized self-referential mechanism embedded in a language or model. The name blends formal with a self-reference notion, signaling a framework where statements about the framework itself can be expressed and evaluated within a stratified meta-language.

Conceptually, formaalsel provides a controlled way to express meta-statements and to interpret them using an auxiliary semantics that tracks which statements belong to the object language and which belong to the meta-language. The formalism typically includes a defined syntax for meta-statements and a truth-conditional semantics that assigns truth-values relative to a fixed interpretation of the base language.

Usage and motivation: Proponents use formaalsel to study self-reference, reflexivity in natural and formal languages, and to model self-explanation processes in artificial systems. It is proposed as a tool for analyzing paradoxes, such as the liar paradox, by clearly separating levels of discourse and imposing constraints on how statements can refer to themselves.

Examples: A formaalsel statement might be "This statement is true within formaalsel" or "Statement S is provable in formaalsel." Depending on the chosen semantics, these statements can illuminate consistency or reveal limits of the formal system.

Limitations: As a conceptual framework, formaalsel faces questions about consistency, expressive power, and computational complexity, and it remains a topic of theoretical exploration rather than an established mainstream tool.

See also: formal semantics, meta-language, self-reference, liar paradox, reflexivity, modal logic.