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diff --git a/paper2/thesis.pdf b/paper2/thesis.pdf Binary files differindex 49ec47a..50affd0 100644 --- a/paper2/thesis.pdf +++ b/paper2/thesis.pdf 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}). |