From 99a18e5adf4a164d1b6748d637ecb831600c2714 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Thomas=20M=C3=BCller?= Date: Wed, 28 Jun 2017 00:32:26 +0200 Subject: [PATCH] Add Gdl-SaV-B exam from WS1617 --- GdI-SaV-B Logik/WS1617 Logik.tex | 116 ++++++++++++++++++ GdI-SaV-B Logik/fig1.png | Bin 0 -> 26599 bytes .../WS1516 Klausurvorlage.tex | 59 --------- 3 files changed, 116 insertions(+), 59 deletions(-) create mode 100644 GdI-SaV-B Logik/WS1617 Logik.tex create mode 100644 GdI-SaV-B Logik/fig1.png delete mode 100644 ISDL-ISS3-M IT-Wertschoepfung/WS1516 Klausurvorlage.tex diff --git a/GdI-SaV-B Logik/WS1617 Logik.tex b/GdI-SaV-B Logik/WS1617 Logik.tex new file mode 100644 index 0000000..9f616aa --- /dev/null +++ b/GdI-SaV-B Logik/WS1617 Logik.tex @@ -0,0 +1,116 @@ +\input{../settings/settings} +\usepackage{amssymb}% +\usepackage{MnSymbol}% +%\usepackage{wasysym}% + +\begin{document} + + \klausur{Gdl-SaV-B (Logik)} + {Prof. M. Mendler, Ph. D.} + {Wintersemester 16/17} + {90} + {Wörterbuch (Englisch-Deutsch/Deutsch-Englisch)} + + \newpage + + \begin{center} + \begin{tabular}{|c|c|c|c|c|c|c|c|} + \hline + \textbf{(Sub-)Question} & 1 & 2a & 2b & 3a & 3b & 4a & 4b \\ + \hline + \textbf{Available Marks} & 12 & 12 & 20 & 10 & 12 & 8 & 16 \\ + \hline + $\Sigma$ & & & & & & & \\ + \hline + \end{tabular} + \end{center} + + \newpage + + \textbf{Syntax} + \begin{enumerate} + \item Consider the formulas $\phi$ and $\psi$ defined as follows: + + $$ \phi =_{def} (P \supset \square R ) \wedge \neg P $$ + $$ \psi =_{def} S \wedge \neg \diamondsuit Q $$ + + Use the Martelli-Montanari Algorithm (the algorithm is given in Apeendix I) to check whether there is a \textit{most general unifier} $\theta$ for $\phi$ and $\psi$, i.e., a solution for the unification problem $ E = \{\phi = \psi\}$. In case there is such a unifier, state it. + + Make clear how you obtain your results by providing \textbf{every single transformation step} of the algorithm, specifyfing the corresponding number of the rule which you apply. + + \textbf{Hilbert and Tableau Calculus} + \item + \begin{enumerate} + \item With the model axiom $\Gamma = \{A\}$, find a suitable Hilbert deduction in the modal KD such that $$ KD;\Gamma;\vdash_{H} \lozenge(A \vee C).$$ + In other words: prove that $\lozenge(A \vee C)$ holds if $A$ holds, using the modal Hilbert Calculus with the axiom schmees from KD.\\ + For this, you need (beside your model axiom) the following: + \begin{itemize} + \item the rule of \textit{Modus Ponens,} + \item the rule of \textit{Necessitation,} + \item the propositional axiom scheme: $P \supset (P \vee Q),$ + \item the modal axiom scheme (D): $\square P \supset \lozenge P$. + \end{itemize} + \textbf{Hint:} You may need to instantiate the variables $P$ and $Q$ of the axiom schemes appropriately to perform the proof. + \item Consider the formula $\phi$ given as + $$ ((\lozenge \square P) \wedge \lozenge Q \supset \square (P \wedge \lozenge Q). $$ + Using the S5 tableau calculus (see Appendix II) show that $\phi$ is valid in all S5-frames. + \end{enumerate} + + \item A traffic light can have four different states: \textit{red, red/yellow, green} and \textit{yellow}. In a working traffic light, these states change in the indicated order. + Consider the set $Var =_{def} \{RED, YELLOW, GREEN\}$ of propositional variables with the following meanings: + \begin{center} + \begin{tabular}{|l|l|} + \hline + \textbf{Variable} & \textbf{Meaning} \\ + \hline + \hline + $RED$ & \textit{The red light is on.} \\ + \hline + $YELLOW$ & \textit{The yellow light is on.} \\ + \hline + $GREEN$ & \textit{The green light is on.} \\ + \hline + \end{tabular} + \end{center} + + In the \textit{red/yellow}, both $RED$ and $YELLOW$ hold. + + \begin{enumerate} + \item Some broken traffic light has a malfunction and satisties the \textit{Propositional Temporal Logic (PLTL)} formula $\psi$ defined thus: + $$ \psi =_{def} \diamondsuit RED \wedge \square (RED \supset X RED) $$ + + Draw a time-line representing a model $(\mathcal{T},V)$ with at least one world $t$ where $\psi$ holds. + + \textbf{Explain in detail} the properties of your model, which enforce that $\mathcal{T},V,t \models \psi$ and how they enforce it. + \item Find a formula of PLTL that expresses the following statement: + \begin{quote} + \textit{Whenever the light is red, it becomes green eventually after being red/yellow for some time (i.e., red/yellow at least for one time instance).} + + Note that between states \textit{red} and \textit{green}, \textbf{only} \textit{red/yellow} is permitted. + \end{quote} + \end{enumerate} + + \textbf{Semantics and Correspondence Theory} + + \item + \begin{enumerate} + \item Consider a mono-modal frame $\mathcal{F}_{1} = (W_{1} \rightarrow_{1})$ with $W_{1} =_{def} \{w_{1},w_{2},w_{3},w_{4}\}$and $\rightarrow_{1}$ as indicated in the following figure. + + \image{0.5}{fig1.PNG}{}{} + + Copy the transition system of $\mathcal{F}_{1}$ to your exam answer paper and add further transitions to obtain an extended frame $\mathcal{F}_{2} = (W_{1},\rightarrow)$ such that the \textbf{frame axiom (5)} holds, i.e., such that $\mathcal{F}_{2} \models \lozenge P \supset \square \lozenge P.$ Add only a minimal amount of transitions that is necessary to make the statement become true. Do not remove any transition and do not change $W_{1}$! + + \item + Prove formally that in \textbf{all} frames $\mathcal{F}$ (not only in $\mathcal{F}_{1}$ or $\mathcal{F}_{2}$) it holds: + $$ \mathcal{F} \models \square (P \supset Q) \supset (\square P \supset \square Q). $$ + Do this by arguing on the formal semantics of normal modal logics. In other words prove + $$ \mathcal{F},V,w \models \square (P \supset Q) \supset (\square P \supset \square Q) $$ + + for an arbitrary frame $\mathcal{F} = (W,\rightarrow)$, valuation $V$ and world $w \in W$. + + Do \textbf{not} use Hilbert Calculus or a Tableau Calculus! + + + \end{enumerate} + \end{enumerate} +\end{document} \ No newline at end of file diff --git a/GdI-SaV-B Logik/fig1.png b/GdI-SaV-B Logik/fig1.png new file mode 100644 index 0000000000000000000000000000000000000000..8401138d887c716a10af7c67f87c7a23295494cc GIT binary patch literal 26599 zcmV)$K#sqOP)2zK!@$MCzQe-7#lOG9!NA4E!^XnD#KXVH!@$YI!N$YC#KFA8#lgzKzQ@AA z$-=_N!@|kHz{S75#lgVG!okVGzQn-5$iKhFyuQW2z{kMB#lpkLz{1DB!NtA3#J#`4 zz`w%2zr?`7$iczMzrn-7z{J48#=*qM!NSJA!NtG9#=yhMzr)GC!N$A4#Js=6zr)7A z!O6bC$-cnFv$(ywy1lo#ytlZ$y0^Q!xV^l+!n(Y{xx2u)yuQA`#KF6~yuH4@zQDr3 z!o9t}z`?}5yuHN3!@$49zrV!5zr(=4#=gGAzQ4!5zsA47$H2hE!oteM#LKy}!P|zrn!6$HmFNzsS42#KOhPvb4FpxxTlz zzPr1?yt~1+w!OK#!oa)1y}Q7{zQDu1#>BtKyuHM>x4gf+!N9%6yuZJ`yTiP@!os}7 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\begin{enumerate} - \item \underline{Skizzieren Sie} das Strategic Alignment Model (SAM). \underline{Erläutern Sie} dessen Grundidee sowie die Funktionen des ''strategic fit`` und der ''functional integration``. (10 Pkt.) - \item \underline{Erläutern Sie} die dominanten Alignment-Perspektiven ''strategy execution``, ''technology transformation``, ''service level`` und ''competitive potential`` nach Henderson und Venkatraman (1993). \underline{Geben Sie} für eine der Perspektiven ein Beispiel. (10 Pkt.) -\item \underline{Erläutern Sie} die drei Pfade des operativen Alignments. Gehen Sie dabei auch auf die drei Dimensionen des operativen Alignments ein (Wagner und Weitzel 2012). (10 Pkt.) - \end{enumerate} -\end{enumerate} -\item \textbf{WAHLTEIL (3 aus 5 Aufgaben)} -\begin{enumerate} - \setcounter{enumi}{1} - \item Aufgabe --- IT-Business-Value (20 Pkt.) - \begin{enumerate} - \item \underline{Diskutieren Sie} die Gründe für eine mögliche Kommoditisierung der IT, wie sie von Carr (2003) postuliert wurde. \underline{Erläutern Sie} die von ihm für das IT-Management entwickelten Handlungsempfehlungen. (10 Pkt.) - \item \underline{Erläutern Sie} das IT-Produktivitätsparadoxon (Brynjolfsson 1996). \underline{Gehen Sie dabei} auf die Erklärungsansätze des Paradoxons ein. (10 Pkt) - \end{enumerate} - - \item Aufgabe --- IT-Strategie (20 Pkt) - \begin{enumerate} - \item \underline{Nennen und erläutern Sie} die drei Strategietypen nach Miles und Snow (1978).\\ Dabei sollen Sie auch auf die Probleme jedes Strategietyps eingehen. \underline{Nennen} Sie jeweils ein Beispiel. (10 Pkt.) - \item \underline{Beschreiben Sie} die drei Ihnen bekannten Wettbewerbslandschaften (Tanriverdi et al. 2010). \underline{Diskutieren Sie} die Anwendbarkeit des Five-Forces-Modells (Porter 2008) in einer tanzenden und zerklüfteten (''dancing rugged``) Wettbewerbslandschaft. (10 Pkt.) - \end{enumerate} - -\item Aufgabe --- IT-Ressourcen und IT-Assets (20 Pkt.) -\begin{enumerate} - \item \underline{Erläutern Sie}, was nach Melville et al. (2004) unter IT-Ressourcen sowie unter komplementären organisationalen Ressourcen zu verstehen ist.\\ \underline{Zeigen Sie Unterschiede und Gemeinsamkeiten} zu dem Konzept der IT-Assets nach Ross et al. (1996) auf. (10 Pkt.) - \item \underline{Erläutern Sie}, was man unter dem ''Assessment Grid for IT Assets`` nach Ross et al. (1996) versteht und \underline{beschreiben Sie} die Handlungsempfehlungen, die aus den unterschiedlichen Assets-Bewertungen resultieren. (10 Pkt) -\end{enumerate} - -\item Aufgabe --- IT-Architektur -\begin{enumerate} - \item \underline{Nennen und erläutern Sie} die Reifegradstufen der IT-Architektur nach Ross (2003) \underline{sowie} die drei IT-Outsourcing-Arrangements nach Ross und Beath (2006; ''strategic partnership``, ''co-sourcing alliance`` und ''transaction exchange``). \underline{Nehmen Sie dabei Bezug} auf den Einfluss der IT-Outsourcing-Arrangements auf die Reifegradstufen der IT-Architektur (10 Pkt.) - \item \underline{Erläutern Sie} die technologiebezogenen und geschäftsbezogenen Nutzenaspekte, die eine gute IT-Architektur auszeichnen. (10 Pkt.) -\end{enumerate} -\newpage -\item Aufgabe --- IT-Governance (20 Pkt.) -\begin{enumerate} - \item \underline{Erläutern Sie} die fünf durch das \textit{IT Governance Institute (ITGI)} definierten Kernaufgabenbereiche der IT-Governance. \underline{Gehen Sie dabei} für jeden der fünf Bereiche auf eine Methode ein, mithilfe deren der jeweilige Bereich gesteuert werden kann. (10 Pkt.) - \item \textit{Sie sind CIO in einem großen Unternehmen. Bisher wurden in diesem Entscheidungen bzgl. IT-Investitionen und deren Priorisierung durch eine Business-Monarchie getroffen. Eine Folge daraus ist, dass das IT-Budget zum Großteil in geschäftsgetriebene Projekte investiert wird; währendessen werden Aktivitäten insbesondere in den Bereichen Infrastruktur und Sicherheit häufig zurückgestellt. Nachdem dies zu einigen Problemen geführt hat, überlegen Sie nun, einen Vorschlag zur Änderung der Entscheidungsfindung bzgl. IT-Investitionen/-Priorisierung zu machen. Sie schwanken dabei zwischen IT-Monarchie und Duopol.}\\\\ - \underline{Beschreiben Sie} die beiden Entscheidungsstile und \underline{disktuieren} Sie jeweilige mögliche Vor- und Nachteile --- auch in Bezug auf die Business-Monarchie. (10 Pkt.) -\end{enumerate} - - \end{enumerate} -\end{itemize} -\centering \textbf{Fine.} -\end{document}