Sentence examples for validity and entailment from inspiring English sources

Validity and entailment are defined as indicated above.

Validity and entailment as defined in the Tarskian semantics of classical first-order logic can be precisely captured in this sense.

It is a well known fact that validity and entailment in the semantics for SQML can be captured in a complete system of axioms and rules of inference (a.k.a. a proof theory), which we will refer to as as SQML.

Of course Gärdenfors' semantical theory, extended with suitable epistemic variants of the classical notions of satisfaction, validity and entailment, will be capable of providing epistemic models for conditional operators.

Ideally, validity and entailment for L can be precisely captured in a system of axioms and rules of inference, in the sense that, for any given formula φ of L, (i) φ is valid if and only if it is a theorem of the system, and (ii) for any set Γ of formulas of L, Γ entails φ if and only if φ can be derived from Γ in the system.

Indeed, I would argue that this is also the case with mathematical and logical terms like "parallel line" and "entailment".

In fact it might seem that this is obvious; if we define validity or entailment in terms of truth preservation, arguments with purely non-cognitive premises will not even be candidates for validity and relations among them will not be entailments.

And there was an important extension of MVL by a graded notion of inference and entailment in Pavelka (1979).

Abelard argued that inseparability and entailment between the truth of the antecendent and consequent are required for the truth of a conditional.

The proposed constitution forbade the English practices of primogeniture and entailment, following a change made to Spanish law in 1821.

Validity analysis includes two aspects: convergent validity and discriminant validity.