# Answers to Selected Exercises

Abstract We provide answers to selected exercises in the book Commonsense Reasoning.

Keywords Commonsense reasoning, Event calculus, Answers to exercises

## Chapter 2

2.2.The expression U[Awake, Asleep] is an abbreviation for the conjunction of the following formulas:

$\begin{array}{c}\hfill \mathit{Awake}\left({a}_{1}\right)\ne \mathit{Asleep}\left({a}_{2}\right)\hfill \\ \hfill \mathit{Awake}\left({a}_{1}\right)=\mathit{Awake}\left({a}_{2}\right)\Rightarrow {a}_{1}={a}_{2}\hfill \\ \hfill \mathit{Asleep}\left({a}_{1}\right)=\mathit{Asleep}\left({a}_{2}\right)\Rightarrow {a}_{1}={a}_{2}\hfill \end{array}$

2.3. The following formulas are positive relative to Q:

$\begin{array}{c}\hfill Q\left(A\right)\hfill \\ \hfill P\left(x\right)\Rightarrow Q\left(x\right)\hfill \end{array}$

The following formulas are not positive relative to Q:

$\begin{array}{c}\hfill \neg Q\left(A\right)\hfill \\ \hfill P\left(x\right)\Rightarrow \neg Q\left(x\right)\hfill \\ \hfill Q\left(x\right)\Rightarrow P\left(x\right)\hfill \\ \hfill Q\left(x\right)\Rightarrow P\left(x\right)\hfill \\ \hfill Q\left(A\right)\Rightarrow Q\left(B\right)\hfill \end{array}$

## Chapter 3

3.2. We use a positive ...

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