The mathematical notation to describe logical entailment of a scentence "α entails another sentence β" is

The correct answer is α \(⊨\) B

Key Points

• The symbol $⊨$ is used in mathematical logic to denote logical entailment.
• Logical entailment means that if a set of sentences (premises) is true, then another sentence (conclusion) must also be true.
• In the notation $\alpha ⊨ \beta$ , $\alpha$ represents a set of premises, and $\beta$ represents the conclusion.
• This notation indicates that whenever $\alpha$ is true, $\beta$ must also be true.
• Logical entailment is a fundamental concept in fields such as formal logic, computer science, and artificial intelligence.

Additional Information

• Logical entailment is different from material implication. While material implication ( $\alpha \rightarrow \beta$ ) is a statement that is true except when $\alpha$ is true and $\beta$ is false, entailment ensures that the truth of $\alpha$ guarantees the truth of $\beta$ .
• In formal proofs, logical entailment is used to derive conclusions from a set of axioms or hypotheses.
• The concept of logical entailment is closely related to the notion of validity in formal systems.
• Logical entailment is used in automated theorem proving and logical reasoning systems.