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The Lingo of Logic (and how to tell if you’ll be happy tomorrow!)

The study of logic concerns the study of sentences (or propositions in the lingo of logic) and whether they are true or false. Using traditional logic we can use the information we have about a situation to infer knowledge about a statement built on our previous knowledge. 

For example, consider the following reasoning:

  • I know that if I see a black swan I am happy.
  • Tomorrow I will see a black swan.
  • Therefore – tomorrow I will be happy.

This is an example of logical inference called modus ponens. I have used the logical implication connecting the state of ‘seeing a black swan’ and the state of ‘being happy’ to deduce that tomorrow I will be happy.

Logic allows us to evaluate the arguments of others, make arguments of our own, and arrive at a conclusion backed by rigorous reasoning. Furthermore, logic forms the backbone of computer science. (Alan Turing invented the Turing Machine while conducting research in logic.)

Traditional logic is couched in the notion of there being two truth values. In the black swan example, the variables may only hold truth values of ‘true’ or ‘false’.  (I can be happy or not happy, tomorrow I will see a black swan or I will not see a black swan.) This basic assumption, that we use truth as a binary property, is not always the best way to model human behaviour.

When considering how we would like to assert ourselves in conversation, we are often presented with uncertainty. If we require knowledge about the state of the world to make a decision, how do we use this to decide what to say? If I wanted to tell you if I will be happy tomorrow, but my knowledge about the appearance of a black swan tomorrow is incomplete, then I cannot provide an inference on my happiness tomorrow.

How we deal with partial or uncertain information requires a new mathematical framework, which goes further than the traditional realms of propositional logic. This theory can allow many AI systems (such as natural language generation systems) to provide assertions that are much more complex, and more appropriate to the task at hand.

Read the abstract and download Henrietta’s paper here.