What is entailment? (With examples)

Entailment is something that is usually in the first couple of chapters in a semantics textbook. In my opinion, the concept isn’t that difficult to get your head around. Entailment is usually discussed in pairs of propositions. Let’s look at two sentences:

  1. Jim rides a bike to school every morning.
  2. Jim can ride a bike.

Entailment is what occurs if a proposition is true. If the first proposition Jim rides a bike to school every morning is true then that proposition entails a few things:

  • Jim can ride a bike
  • Jim goes to school every morning

If the first sentence is true, then the second sentence must be true as well. That is, if Jim rides his bike to school every morning, then he must be able to ride a bike.

We can say that the first sentence entails the second sentence. Entailment could be thought of as

If X, then Y.

Let’s look at another example.

  1. Jim rides a bike to school every morning.
  2. Jim is good at riding bikes.

In this example, the first sentence does not entail the second one. If Jim rides a bike to school every morning, that doesn’t mean that he is good at riding a bike.

Perhaps he just started riding his bike to school every day. Or maybe he has ridden his bike to school every day for years, but for some reason he just can’t get the hang of it.

In this example, the first condition doesn’t necessarily entail the second condition.

We can look at one more example:

  1. Jim rides his bike to school every day.
  2. Jim has a bike.

Here, because the first sentence contains the word “his,” by definition, means that the bike belongs to him and thus the first sentences entails the second.

However, if we say:

  • Jim rides a bike to school every day

we can’t conclude that he in fact owns a bike. He may borrow a bike from a friend every morning, or maybe the bike is his sister’s. By changing one word here, the first sentence no longer entails the second.

Syntactic entailment compared to lexical entailment

Entailment can be further described by being syntactic or lexical.

Syntactic entailment is when the first statement entails the second by the syntactic structure alone. For example:

  1. Mary made the cake.
  2. The cake was was made by Mary.

However, lexical entailment requires more information. Let’s look at the following example:

  1. I have a dog.
  2. I have an animal.

In this example, the first sentence entails the second; however, the entailment does require some additional information that isn’t directly in the above sentences. The reader needs to know that a dog is an animal.

To sum up

To sum up entailment:

When p is true q is true
When p is true, q is true or false
When q is false then p is false
when q is true p is true or false

What to sound more like a native English speaker?

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