How can I determine if an input sentence is consistent with a certain subject? How can I determine if an input sentence is consistent with a certain subject?

For example, suppose I am given the following dataset.

| Subject       | User input           | Output |
|---------------|----------------------|--------|
| Dog ownership | I own a dog          | Yes    |
| Dog ownership | My dog is called Joe | Yes    |
| Dog ownership | I don't have a dog   | No     |


In the examples above, the subject "dog ownership" is consistent with the input sentences "I own a dog" and "My dog is called Joe" (because, if your dog is called Joe, then you also own a dog).
If you have lots of training data, ANN's (deep learning) could quite possibly get you there.  But I have a hunch you might also get some mileage out of using something like a rule induction approach.  Maybe something like CN2. I'd suggest at least reading up on those and see if you can see a way to apply that to your system.