# Truth-Functional Logic (TFL) Truth-Functional [[Logic]], also known as propositional [[Logic]] or sentential [[Logic]], is a fundamental system in formal [[Logic]]. It deals with propositions (statements that can be true or false) and the logical relationships between them. ## Key Characteristics 1. Focuses on the logical structure of compound statements. 2. Uses [[Atomic Sentences]] as basic building blocks. 3. Employs logical [[Connectives]] to form complex statements. 4. Truth value of compound statements depends solely on the truth values of their components. 5. Deals exclusively with [[Assertoric Sentences]], not [[Non-Assertoric Sentences]]. ## Basic Components 1. [[Atomic Sentences]]: Represented by uppercase letters (A, B, C, etc.) 2. Logical [[Connectives]]: - [[Negation]] (not): ¬ - [[Conjunction]] (and): ∧ - [[Disjunction]] (or): ∨ - [[Conditional]] (if...then): → - [[Biconditional]] (if and only if): ↔ ## Symbolization TFL uses a [[Symbolization Key]] to translate between natural language and formal logical expressions. Example: - A: "Jobke is awake" - B: "Jobke is snoring" - "Jobke is awake or she is snoring" becomes "A ∨ B" in TFL ## Truth Tables [[Truth Tables]] are used to define the meaning of logical [[Connectives]] and evaluate the truth value of compound statements. ## Advantages 1. Simplicity: Focuses on the logical form of arguments. 2. Clarity: Removes ambiguities present in natural language. 3. Computability: Easily implemented in computer systems. ## Limitations 1. Cannot represent internal structure of [[Atomic Sentences]]. 2. Limited in expressing quantified statements (all, some, etc.). 3. Some natural language arguments cannot be adequately represented in TFL. 4. Cannot directly handle [[Non-Assertoric Sentences]] like questions or commands. ## Applications 1. Evaluating [[Validity]] of arguments. 2. Basis for more complex logical systems. 3. Foundational for computer science and digital electronics. ## Relation to Other Concepts - [[Formal Language]]: TFL is a specific [[Formal Language]] used in [[Logic]]. - [[Validity]]: TFL is used to assess the [[Validity]] of arguments. - [[First-Order Logic]]: FOL extends TFL to include [[Quantifiers]] and predicates. - [[Atomic Sentences]]: Basic building blocks of TFL. TFL provides a powerful framework for analyzing the logical structure of arguments and statements, forming the foundation for more advanced logical systems and applications in various fields.