The Material Conditional

In the exercises, we’ve defined the Boolean truth-function IF.

1. Implement this function using relays. (2 points)

   Note: To include the diagram of your relay, you can:

   • draw a diagram with pen and paper and include it in your LaTeX document using \includegraphics. See https://docs.overleaf.com/writing-and-editing/inserting-images ;

   • use more advanced LaTeX-tools, like https://ctan.org/pkg/tikz-relay?lang=en .

2. Verify your work by translating the circuit and specification to formulas (1 point) and show that they are equivalent (1 point)

   Hint: Remember what XOR does with relation to equivalence!

Planning

Solve the following planning problem using Satplan:

There’s a banana dangling from the ceiling. IA  loves bananas! But the banana is out of reach. Luckily, there’s a stick that would allow IA  to reach the banana.

1. Describe the propositional language, including fluents (1 point) and actions (1 point). Try to be as simple as possible.

   Hint: A single kind of fluent and two actions are enough! (red added later for clarification)

2. Give the KB with all necessary principles governing possibilities and interaction of actions and fluents (1 point), as well as persistence conditions (1 point).

   Hint: You can be rather simplistic about the effects of actions. For example, knocking the banana results in having it next time-stamp.

3. Describe the planning problem as a SAT-problem. (1 point)

4. Find a model (manually, but not necessarily algorithmically—use your human intelligence) and read off a plan. (1 point)