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Unlike the material conditional, the strict conditional is not vacuously true when its antecedent is false. To see why, observe that both <math>P</math> and <math>\Box(P \rightarrow Q)</math> will be false at <math>w</math> if there is some accessible world <math>v</math> where <math>P</math> is true and <math>Q</math> is not. The strict conditional is also context-dependent, at least when given a relational semantics (or something similar). In the relational framework, accessibility relations are parameters of evaluation which encode the range of possibilities which are treated as "live" in the context. Since the truth of a strict conditional can depend on the accessibility relation used to evaluate it, this feature of the strict conditional can be used to capture context-dependence.

Unlike the material conditional, the strict conditional is not vacuously true when its antecedent is false. To see why, observe that both <math>P</math> and <math>\Box(P \rightarrow Q)</math> will be false at <math>w</math> if there is some accessible world <math>v</math> where <math>P</math> is true and <math>Q</math> is not. The strict conditional is also context-dependent, at least when given a relational semantics (or something similar). In the relational framework, accessibility relations are parameters of evaluation which encode the range of possibilities which are treated as "live" in the context. Since the truth of a strict conditional can depend on the accessibility relation used to evaluate it, this feature of the strict conditional can be used to capture context-dependence.

与实质条件不同，严格条件在其前件为假时严格为真。要知道为什么，请观察，如果有一些可能世界<math>v</math>，其中<math>P</math>为真，<math>Q</math>为假，那么<math>P</math>和 <math>\Box(P \rightarrow Q)</math>在<math>w</math>处都为假。严格条件也是依赖于上下文的，至少在给定关系语义（或类似的东西）时是如此。在关系框架中，可及性关系是评价的参数，它编码了在上下文中被视为 "活 "的可能性范围。由于严格条件的真实性可能取决于用来评价它的可及性关系，所以严格条件的这一特征可以用来捕捉上下文的依赖性。

与实质条件不同，严格条件在其前件为假时严格为真。要知道为什么，请观察，如果有一些可能世界<math>v</math>，其中<math>P</math>为真，<math>Q</math>为假，那么<math>P</math>和 <math>\Box(P \rightarrow Q)</math>在<math>w</math>处都为假。严格条件也是依赖于上下文的，至少在给定关系语义（或类似的东西）时是如此。在关系框架中，可及性关系是评价的参数，它编码了在上下文中被视为 "活跃"的可能性范围。由于严格条件的真实性可能取决于用来评价它的可及性关系，所以严格条件的这一特征可以用来捕捉上下文的依赖性。

The strict conditional analysis encounters many known problems, notably monotonicity. In the classical relational framework, when using a standard notion of entailment, the strict conditional is monotonic, i.e. it validates ''Antecedent Strengthening''. To see why, observe that if <math>P \rightarrow Q</math> holds at every world accessible from <math>w</math>, the monotonicity of the material conditional guarantees that <math>P \land R \rightarrow Q</math> will be too. Thus, we will have that <math> \Box(P \rightarrow Q) \models \Box(P \land R \rightarrow Q) </math>.

The strict conditional analysis encounters many known problems, notably monotonicity. In the classical relational framework, when using a standard notion of entailment, the strict conditional is monotonic, i.e. it validates ''Antecedent Strengthening''. To see why, observe that if <math>P \rightarrow Q</math> holds at every world accessible from <math>w</math>, the monotonicity of the material conditional guarantees that <math>P \land R \rightarrow Q</math> will be too. Thus, we will have that <math> \Box(P \rightarrow Q) \models \Box(P \land R \rightarrow Q) </math>.