Exercise Sheet 1 for: Adaptive Logics applied to the Philosophy of Science

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Back to the main course site \(\def\impl{\supset} \def\Dab{{\sf Dab}}\) \(\newcommand{\vd}[1]{\vdash_{\bf #1}}\)

In the following tasks we use the adaptive logic that is characterized by the triple:

I use the following abbreviation: \(!A = \circ A \wedge \neg A\).

Task 1

Let \(\Gamma = \{\circ p, \circ q, \circ r, !p \vee {!}r, !q \vee {}!r, (q\wedge p) \impl s, r \impl s\}\).

  1. Is \(s\) derivable by means of the minimal abnormality strategy? Prove it.
  2. Specify \(\Phi(\Gamma)\).
  3. Specify \(U(\Gamma)\).
  4. How many different types of reliable models of \(\Gamma\) are there relative to their abnormal parts? Answer the question by naming all abnormal parts of reliable models of \(\Gamma\).

Task 2

Let \(\Gamma' = \Gamma \cup \{!p \vee {!}q\}\).

  1. Is \(s\) derivable? Give a reason for your answer.
  2. Specify \(U(\Gamma')\).
  3. How many different types of reliable models of \(\Gamma'\) are there relative to their abnormal parts? Answer the question by naming all abnormal parts of reliable models of \(\Gamma'\).

Author: Christian Straßer

Created: 2015-04-17 Fri 11:16

Emacs 24.4.1 (Org mode 8.2.10)

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