From 6e9795a3ad67bd65134266dfdc6349578609af79 Mon Sep 17 00:00:00 2001
From: "Dobbertin, Niclas" <niclas.dobbertin@mailbox.org>
Date: Mon, 14 Oct 2024 13:38:14 +0200
Subject: update

---
 paper2/thesis.tex | 48 +++++++++++++++++++++++++++++++++++-------------
 1 file changed, 35 insertions(+), 13 deletions(-)

(limited to 'paper2/thesis.tex')

diff --git a/paper2/thesis.tex b/paper2/thesis.tex
index ab59dd3..36e1bd8 100644
--- a/paper2/thesis.tex
+++ b/paper2/thesis.tex
@@ -60,13 +60,14 @@ Living in a complex environment like the real world, a plethora of different tas
 much more efficient if knowledge from tasks can be reused in other tasks
 
 
+
 % \citep{anderson}
 % \citep{Taatgen_2013}
 % \citep{Brasoveanu_2021}
 % \citep{Frensch_1991}
 % \citep{Elio_1986}
 
-Cognitive Architectures, modeling learning, production systems, ACT-R
+Cognitive Architectures, modeling learning, production systems, ACT-R, frensch task
 
 \subsection*{Productions}
 
@@ -179,7 +180,7 @@ Learning new facts and increasing their activation strength is also part of the
 
 \bigskip
 \small\textit{Note}. Table~\ref{tab:prodcompa} shows a production with the condition that the operation variable must be ``subtract'', and argument1 and 2 must have any values x and y.
-If selected, it starts retrieval of the result of x - y from declarative memory.
+If selected, it starts retrieval of the result of $x - y$ from declarative memory.
 Production 2 (Table~\ref{tab:prodcompb}) is selected when the operation value is subtract as well, and the retrieval variable is filled with a value z.
 It then starts a motor process to press button z.
 When the model executes both productions after another, it starts the production compilation process with the current model state.
@@ -190,9 +191,25 @@ That means for each combination of x, y and z a different specific production ca
 
 \subsection*{Task}
 
-\todo[inline]{Modified Frensch/Elio Task. 7 mathematical procedures, learning differently based on presentation order}
+To investigate model behavior and potentially compare it to results from human experiments, it was decided to use an adapted version of the setup described in \citet{Frensch_1991}, which was first used in \citet{Elio_1986}.
+Subjects are put in charge of determining the quality of water samples by performing simple mathematical operations with given indicator values per water sample.
+A water sample has an algae, a solids and multiple toxin and sandstone values, which are randomly generated for each sample.
+There are six different 2-step equations that use these values and a seventh equation using all previously calculated results to determine the final result (see Table~\ref{tab:proc}).
+To solve a procedure, subjects have to locate the values of used variables on the screen.
+Some variables show multiple values, procedures using them indicate how it should be selected after an underscore.
+For example x\_2 means taking the second value of variable x.
+Other procedures require finding the maximum or minimum value of a variable or of previous solutions.
+An example of how the screen could look during a trial is shown in Figure~\ref{fig:frensch}.
+
+The experiment starts with 75 training trials, each representing a water sample, in which a random choice of 6 procedures has to be solved in the order they are presented.
+The last procedure is always picked in the selection process, as it uses all previous results for a water sample to calculate the final solution.
+Afterwards 50 testing trials take place, in which the third procedure from the training phase is switched for the unpicked one.
+There are three conditions that determine the order in which procedures are presented in the training phase, however the procedure for the final result is always last.
+In the fixed condition, the order is randomized once at the start and stays constant during all trials.
+In the random condition, procedure order is randomized between each trial.
+In the blocked condition, the first procedure has to be solved for all trials before moving on to the second procedure, etc.
+The testing phase always uses fixed order.
 
-(Task description, kommt noch)
 
 How modeled:
 Improvements in task performance are mainly dependent on production compilation, as the order and how efficiently the mathematical operations are performed are the main subject of the task.
@@ -227,6 +244,20 @@ Six of them are used in the training phase, in the testing phase one procedure i
 The bottom procedure is always included as it calculates the total water quality.
 \end{table}
 
+\begin{figure}[H]
+    \centering
+    \caption{Screenshot of experiment display}
+    \label{fig:frensch}
+        \includegraphics[width=1.1\textwidth]{exp_screen.png}
+
+    \bigskip
+    \raggedright\small\textit{Note}. Example water sample presenting in an experiment using the adapted task from \citet{Frensch_1991}.
+    In the first procedure, a subject has to find the smaller of $Sandstein_{1} + Gifte_{1}$ and $Algen$.
+    First they need to find the value of $Algen$ and the first values in the lists of $Sandstein$ and $Gifte$ to substitute them into the equation.
+    Next they can calculate the sum inside the parenthesis and put the smaller value between it and $Algen$ as the result.
+
+  \end{figure}
+
 \section*{Model}
 
 \todo[inline]{chunktypes, pre-knowledge}
@@ -334,15 +365,6 @@ Since operations use both the full numbers and their digits, a set of production
     \bigskip
     \raggedright\small\textit{Note}. When each production is executed depending on state. Either example for one operation or figures for all?\end{figure}
 
-\begin{figure}[H]
-    \centering
-    \caption{Screenshot of experiment display}
-    \label{fig:frensch}
-        %\includegraphics[width=1.1\textwidth]{frensch.png}
-
-    \bigskip
-    \raggedright\small\textit{Note}. Example water sample as shown to a subject.\end{figure}
-
 \section*{Results}
 
 Without enabling the subsymbolic system and its learning algorithms, the average time the model takes to solve a specific procedure stays the same over the experiment (Figure~\ref{fig:RT}).
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