TreeOfThoughts.nb

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Based on the repo and paper \[OpenCurlyDoubleQuote]Tree of Thoughts: \
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Language models have proven effective problem solvers across a wide range of \
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Thoughts (ToT) is a decision making framework introduced in (1) that \
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intermediate step. ToT allows LMs to perform deliberate decision making by \
considering multiple different reasoning paths and self-evaluating choices to \
decide the next course of action, as well as looking ahead or backtracking \
when necessary to make global choices. In this project, we implement the Tree \
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solution for the game of 24, and begin to explore the use of this framework \
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 "Game of 24 is a mathematical reasoning challenge, where the goal is to use \
4 numbers and basic arithmetic operations (+-*/) to obtain 24. \nFor example, \
given input \[OpenCurlyDoubleQuote]4 9 10 13\[CloseCurlyDoubleQuote], a \
solution output could be \[OpenCurlyDoubleQuote](10-4)*(13-9)=24\
\[CloseCurlyDoubleQuote].\n\nIn order to approach Game of 24 within the Tree \
of Thoughts framework we must first break it down into steps. A natural way \
to do this is to take two numbers at a time and apply an arithmetic operation\
\n13 - 10 = 3\nAfter this operation we have used two of our numbers and have \
two left (4 and 9) in addition to our result (3) so we have:\nStep 1: 13 - 10 \
= 3 (left: 4 9 3)\nAfter two more steps we can reach the solution:\nStep 2: 9 \
- 3 = 6 (left: 4 6)\nStep 3: 4 * 6 = 24 (left: 24)\nNow that we have reached \
24 we can construct our solution:\nAnswer: 4 * (9 - (13 - 10)) = 24\n\nBefore \
we proceed toward our solution with Tree of Thoughts, we provide some \
motivation as to why ToT or similar frameworks are very helpful for problem \
solving with LLMs.\n\nFirst let\[CloseCurlyQuote]s look at how ChatGPT, in \
this case GPT-4 approaches solving this problem. Using the steps we provided \
above we will provide a 1-shot chain of thought (CoT) reasoning prompt using \
a handy function built into Wolfram Language as of version 13.3, LLMFunction \
(3).\n\n",
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Cell["\<\
Attempting to Solve Game of 24 with Chain of Thought Prompting\
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those numbers in your answer.\nInput: 4 4 6 8\nSteps:\n4 + 8 = 12 (left: 4 6 \
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With a 1-shot prompt GPT-4 gets close to a solution obtaining a result of 26 \
and recognizing its mistake, states (falsely) that there is no way to obtain \
24 with these numbers.

We can improve the performance with this approach by using more examples. \
Below we provide a 5-shot chain of thought prompt:\
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In the 5-shot chain of thought case, GPT-4 provides a valid solution to the \
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With more difficult inputs, GPT-4 is unable to find a solution with the \
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\>", "Text",
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Cell["\<\
Generate Thoughts with the Propose Prompt (1-shot learning example)\
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Cell["\<\
Tree of Thoughts improves language models\[CloseCurlyQuote] problem solving \
ability by enabling them to explore a branching web of possible decisions. At \
any given step in our problem solving process we consider several options, \
evaluate them, and keep the best options in our set of options. The first \
step for any given input (either the task input or numbers left after an \
operation) is to generate a list of proposed options we can consider.\
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After we have generated a list of proposals we need to evaluate them so we \
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numerical values to form a rough heuristic for evaluating a particular \
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In order to produce a solution to the task, we must write the final equation \
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Our solveTask function runs iteratively for four steps generating proposals, \
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How can we extend the tree of thoughts methodology to other types of problems \
with less well defined solutions and thought spaces? We can look at using \
language models to solve coding challenges such as those presented in An \
Elementary Introduction to the Wolfram Language (4). 

Below are a few selected exercises from the book.\
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 CellLabel->
  "In[1160]:=",ExpressionUUID->"26031e5a-df31-4008-b40d-bce70837dee1"],

Cell["\<\
Unlike the case of Game of 24, there is no obvious way to break down any \
given coding problem into a series of steps that we can use for Tree of \
Thoughts. One approach is to ask GPT-4 to help us break down a problem.\
\>", "Text",
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Cell[BoxData[
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you break this problem down into a step by step procedure you could use to \
arrive at an answer?\>\"", ",", 
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Cell[BoxData["\<\"Step 1: Generate a list of the first 5 natural \
numbers.\\n\\nWolfram language has a built-in function `Range[]` that can \
help us generate a list of the first 5 natural numbers. `Range[5]` will give \
us `{1, 2, 3, 4, 5}`.\\n\\nStep 2: Square each of the numbers in the list.\\n\
\\nIn Wolfram language, you can use `Map[]` or `/@` to apply a function to \
each element in the list. `#^2& /@ Range[5]` will give us a list of the \
squares of the first 5 natural numbers.\\n\\nStep 3: Cube each of the numbers \
in the list.\\n\\nSimilarly, `#^3& /@ Range[5]` will give us a list of the \
cubes of the first 5 natural numbers.\\n\\nStep 4: Combine the list of \
squares and cubes.\\n\\nYou can use `Join[]` to combine the two lists. \
`Join[#^2& /@ Range[5], #^3& /@ Range[5]]` will give us a combined list of \
the first 5 squares and cubes.\\n\\nStep 5: Sort the combined list into \
order.\\n\\nFinally, you can use `Sort[]` to sort the combined list into \
ascending order. `Sort[Join[#^2& /@ Range[5], #^3& /@ Range[5]]]` will give \
us the sorted combined list.\\n\\nPutting it all together, the Wolfram \
language code to solve the problem is:\\n\\n`Sort[Join[#^2& /@ Range[5], #^3& \
/@ Range[5]]]`\"\>"], "Output",
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Cell["\<\
In this case, GPT-4 is not only able to reproduce some reasonable steps but \
also generates a valid answer for the problem. These steps can be used to \
generate a prompt that can help us solve more challenging problems. 

In order to make our chain of thought prompt for proposals we use the above \
prompt to generate steps for a number of problems. We sample a subset of the \
steps produced and suggest the model to provide a possible next step.\
\>", "Text",
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Cell[BoxData[
 RowBox[{
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  "proposalPrompt", " ", "=", " ", 
   "\"\<Given a task and a list of steps generate the likely next step that \
gets closer to achieving the task.\nTask: Make a combined list of the first 5 \
squares and cubes (numbers raised to the power 3), sorted into order.\nSteps:\
\n1. Generate a list of the first five natural numbers. In Wolfram Language, \
you can do this with the Range[] function, as Range[5].\n2. Square each \
number in the list. This can be done by applying the power operator ^ to the \
list, as Range[5]^2. Wolfram Language will automatically apply the operation \
to each element of the list.\n3. Cube each number in the list. This is done \
in the same way as the squaring operation, but with 3 as the exponent, as \
Range[5]^3.\nPossible next step:\n4. Join the list of squares and the list of \
cubes into a single list. The Join[] function can be used for this, as \
Join[Range[5]^2, Range[5]^3].\nTask: Make a line plot of the numerical phase \
of the moon for each of the next 30 days.\nSteps:\n1. Generate a list of the \
next 30 days. In Wolfram Language, you can use the Today function to get \
today's date, and you can add n days to this date with Today + n Quantity[1, \
\\\"Days\\\"]. If you use the Table[] function to do this for n from 0 to 29, \
you get a list of the dates of the next 30 days.\nPossible next step:\n2. For \
each date in this list, calculate the numerical phase of the moon. The \
MoonPhase[] function in Wolfram Language does exactly this. So \
Table[MoonPhase[Today + n Quantity[1, \\\"Days\\\"]], {n, 30}] generates a \
list of the moon phases for the next 30 days\nTask: In the digit lists for \
the first 1000 squares, find those that begin with 9 and end with 0 or 1.\n\
Steps:\n1. Generate a list of the squares of the first 1000 natural numbers. \
This can be done using the Range[] function and the power operator ^, as \
Range[1000]^2.\n2. Convert each number in this list to a list of its digits. \
The IntegerDigits[] function can be used for this, so \
IntegerDigits[Range[1000]^2] gives a list of lists, where each inner list is \
the digit list of a square.\nPossible next step:\n3. Search this list of \
lists for lists that begin with 9 and end with either 0 or 1. The Cases[] \
function in Wolfram Language can be used for this. The pattern {9, __, 0 | 1} \
matches any list that begins with 9 (9) and ends with either 0 or 1 (0 | 1), \
with any number of any digits in between (__). Therefore, \
Cases[IntegerDigits[Range[1000]^2], {9, __, 0 | 1}] returns all lists of \
digits that represent squares beginning with 9 and ending with 0 or 1.\n\
Input: `input`\nSteps: \n`steps`\nPossible next step:\n\>\""}], 
  ";"}]], "Input",
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Cell["\<\
Similar to the case for Game of 24 we can ask the model to evaluate a \
proposal, in this case asking it whether a set of steps will accomplish \
(sure), is reasonable (likely) or cannot produce the desired result \
(impossible).\
\>", "Text",
 CellChangeTimes->{{3.8981816774672127`*^9, 
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Cell[BoxData[
 RowBox[{"evaluateProposalPrompt", " ", "=", " ", 
  "\"\<Evaluate if following the procedure given in the steps will accomplish \
the given task (sure/likely/impossible)\nTask: Find the second-to-last digit \
of 2^32.\nSteps:\n1. Calculate the number 2^32. In Wolfram Language, this is \
done simply as 2^32.\n2. Convert the result into a list of digits. Wolfram \
Language provides the function IntegerDigits[] for this purpose.\n3. Reverse \
the order of the list of digits. This can be done with the Reverse[] \
function. Reversing the list of digits will allow us to directly address the \
second-to-last digit as the second element of the reversed list (since \
Wolfram Language uses 1-based indexing).\n4. Extract the second element from \
the reversed list of digits. This can be done with the Part[] function (which \
is often abbreviated as [[ ]]), using 2 as the index.\nsure\nTask: Make a \
combined list of the first 5 squares and cubes (numbers raised to the power \
3), sorted into order.\nSteps:\n1. Generate a list of the first five natural \
numbers. In Wolfram Language, you can do this with the Range[] function, as \
Range[5].\n2. Square each number in the list. This can be done by applying \
the power operator ^ to the list, as Range[5]^2. Wolfram Language will \
automatically apply the operation to each element of the list.\n3. Cube each \
number in the list. This is done in the same way as the squaring operation, \
but with 3 as the exponent, as Range[5]^3.\nI cannot accomplish the task now, \
but the steps are reasonable\nlikely\nTask: Make a graph with 50 nodes, in \
which node i connects to node i+1.\nSteps:\n1. Generate a list of numbers \
from 1 to 49. In Wolfram Language, you can do this using the Table[] function \
as Table[i, {i, 49}]. However, for this task, we are not just generating a \
list of numbers; we are generating a list of directed edges between nodes.\n\
2. For each number i in this list, create an edge from node i + 1 to node i. \
This can be done using the -> operator in Wolfram Language. So the command \
Table[i + 1 -> i, {i, 49}] generates a list of edges where each node i (for i \
from 1 to 49) is connected to node i + 1.\n3. Create a graph from this list \
of edges. Wolfram Language has a Graph[] function that can take a list of \
edges as input and generate a corresponding graph.\nimpossible\nTask: Make a \
line plot of the numerical phase of the moon for each of the next 30 days.\n\
Steps: \n1. Generate a list of the next 30 days. In Wolfram Language, you can \
use the Today function to get today's date, and you can add n days to this \
date with Today + n Quantity[1, \\\"Days\\\"]. If you use the Table[] \
function to do this for n from 0 to 29, you get a list of the dates of the \
next 30 days.\n2. For each date in this list, calculate the numerical phase \
of the moon. The MoonPhase[] function in Wolfram Language does exactly this. \
So Table[MoonPhase[Today + n + 1 Quantity[1, \\\"Days\\\"]], {n, 30}] \
generates a list of the moon phases for the next 30 days\n3. Create a line \
plot of this list of moon phases. You can use the ListLinePlot[] function for \
this. Therefore, ListLinePlot[Table[MoonPhase[Today + n + 1 Quantity[1, \
\\\"Days\\\"]], {n, 30}]] creates the desired plot.\nimpossible\nTask: In the \
digit lists for the first 1000 squares, find those that begin with 9 and end \
with 0 or 1.\nSteps:\n1. Generate a list of the squares of the first 1000 \
natural numbers. This can be done using the Range[] function and the power \
operator ^, as Range[1000]^2.\n2. Convert each number in this list to a list \
of its digits. The IntegerDigits[] function can be used for this, so \
IntegerDigits[Range[1000]^2] gives a list of lists, where each inner list is \
the digit list of a square.\n3. Search this list of lists for lists that \
begin with 9 and end with either 0 or 1. The Cases[] function in Wolfram \
Language can be used for this. The pattern {9, __, 0 | 1} matches any list \
that begins with 9 (9) and ends with either 0 or 1 (0 | 1), with any number \
of any digits in between (__). Therefore, Cases[IntegerDigits[Range[1000]^2], \
{9, __, 0 | 1}] returns all lists of digits that represent squares beginning \
with 9 and ending with 0 or 1.\nsure\nTask: `input`\nSteps:\n`steps`\n\
\>\""}]], "Input",
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Cell["\<\
In order to produce a solution to the coding challenge we ask the model to \
produce an answer for the problem given a series of steps.\
\>", "Text",
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Cell[BoxData[
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  RowBox[{
  "answerPrompt", " ", "=", 
   "\"\<Follow the steps given to write a single line of Wolfram language \
code that satisfies the given task.\nTask: Find the second-to-last digit of \
2^32.\nSteps:\n1. Calculate the number 2^32. In Wolfram Language, this is \
done simply as 2^32.\n2. Convert the result into a list of digits. Wolfram \
Language provides the function IntegerDigits[] for this purpose.\n3. Reverse \
the order of the list of digits. This can be done with the Reverse[] \
function. Reversing the list of digits will allow us to directly address the \
second-to-last digit as the second element of the reversed list (since \
Wolfram Language uses 1-based indexing).\n4. Extract the second element from \
the reversed list of digits. This can be done with the Part[] function (which \
is often abbreviated as [[ ]]), using 2 as the index.\nAnswer: (2^32 // \
IntegerDigits // Reverse)[[2]]\nTask: Make a combined list of the first 5 \
squares and cubes (numbers raised to the power 3), sorted into order.\nSteps:\
\n1. Generate a list of the first five natural numbers. In Wolfram Language, \
you can do this with the Range[] function, as Range[5].\n2. Square each \
number in the list. This can be done by applying the power operator ^ to the \
list, as Range[5]^2. Wolfram Language will automatically apply the operation \
to each element of the list.\n3. Cube each number in the list. This is done \
in the same way as the squaring operation, but with 3 as the exponent, as \
Range[5]^3.\n4. Join the list of squares and the list of cubes into a single \
list. The Join[] function can be used for this, as Join[Range[5]^2, \
Range[5]^3].\n5. Sort the combined list into order. This can be done with the \
Sort[] function, as Sort[Join[Range[5]^2, Range[5]^3]].\nAnswer: \
Sort[Join[Range[5]^2,Range[5]^3]]\nTask: Make a graph with 50 nodes, in which \
node i connects to node i+1.\nSteps:\n1. Generate a list of numbers from 1 to \
49. In Wolfram Language, you can do this using the Table[] function as \
Table[i, {i, 49}]. However, for this task, we are not just generating a list \
of numbers; we are generating a list of directed edges between nodes.\n2. For \
each number i in this list, create an edge from node i to node i + 1. This \
can be done using the -> operator in Wolfram Language. So the command Table[i \
-> i + 1, {i, 49}] generates a list of edges where each node i (for i from 1 \
to 49) is connected to node i + 1.\n3. Create a graph from this list of \
edges. Wolfram Language has a Graph[] function that can take a list of edges \
as input and generate a corresponding graph.\nAnswer: Graph[Table[i -> i + 1, \
{i, 49}]]\nTask: Make a line plot of the numerical phase of the moon for each \
of the next 30 days.\nSteps:\n1. Generate a list of the next 30 days. In \
Wolfram Language, you can use the Today function to get today's date, and you \
can add n days to this date with Today + n Quantity[1, \\\"Days\\\"]. If you \
use the Table[] function to do this for n from 0 to 29, you get a list of the \
dates of the next 30 days.\n2. For each date in this list, calculate the \
numerical phase of the moon. The MoonPhase[] function in Wolfram Language \
does exactly this. So Table[MoonPhase[Today + n Quantity[1, \\\"Days\\\"]], \
{n, 30}] generates a list of the moon phases for the next 30 days\n3. Create \
a line plot of this list of moon phases. You can use the ListLinePlot[] \
function for this. Therefore, ListLinePlot[Table[MoonPhase[Today + n \
Quantity[1, \\\"Days\\\"]], {n, 30}]] creates the desired plot.\nAnswer: \
ListLinePlot[Table[MoonPhase[Today + n Quantity[1,\\\"Days\\\"]],{n,30}]]\n\
Task: In the digit lists for the first 1000 squares, find those that begin \
with 9 and end with 0 or 1.\nSteps:\n1. Generate a list of the squares of the \
first 1000 natural numbers. This can be done using the Range[] function and \
the power operator ^, as Range[1000]^2.\n2. Convert each number in this list \
to a list of its digits. The IntegerDigits[] function can be used for this, \
so IntegerDigits[Range[1000]^2] gives a list of lists, where each inner list \
is the digit list of a square.\n3. Search this list of lists for lists that \
begin with 9 and end with either 0 or 1. The Cases[] function in Wolfram \
Language can be used for this. The pattern {9, __, 0 | 1} matches any list \
that begins with 9 (9) and ends with either 0 or 1 (0 | 1), with any number \
of any digits in between (__). Therefore, Cases[IntegerDigits[Range[1000]^2], \
{9, __, 0 | 1}] returns all lists of digits that represent squares beginning \
with 9 and ending with 0 or 1.\nAnswer: \
Cases[IntegerDigits[Range[1000]^2],{9,__,0 | 1}]\nTask: `input`\nSteps:\n\
`steps`\n\>\""}], ";"}]], "Input",
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Cell["\<\
Once we have produced an answer, we can evaluate the answer and judge whether \
it produced the desired result.\
\>", "Text",
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Cell[BoxData[
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  "evaluateAnswerPrompt", " ", "=", " ", 
   "\"\<Given a task and an answer, give a judgement (sure/impossible) if the \
answer is correct, i.e. the line of code provided in the answer, when \
evaluated will give the result specified in the task.\nTask: Find the \
second-to-last digit of 2^32.\nAnswer: (2^32 // IntegerDigits // \
Reverse)[[2]]\nJudge: \nsure\nTask: Find the second-to-last digit of 2^32.\n\
Answer: (2^32 // IntegerDigits // Reverse)[[1]]\nJudge: \nimpossible\nTask: \
Make a graph with 50 nodes, in which node i connects to node i+1.\nAnswer: \
Graph[Table[i -> i + 1, {i, 49}]]\nJudge:\nsure\nTask: Make a graph with 50 \
nodes, in which node i connects to node i+1.\nAnswer: Graph[Table[i -> i + 1, \
{i, 50}]]\nJudge:\nimpossible\nTask: Make a combined list of the first 5 \
squares and cubes (numbers raised to the power 3), sorted into order.\n\
Answer: Sort[Join[Range[5]^2,Range[5]^3]]\nJudge:\nsure\nTask: Make a \
combined list of the first 5 squares and cubes (numbers raised to the power \
3), sorted into order.\nAnswer: Sort[Table[i^2, {i, 5}], Table[i^3, {i, 5}]]\n\
Judge:\nimpossible\nTask: `input`\nAnswer: `answer`\nJudge:\n\>\""}], 
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Cell[CellGroupData[{

Cell["Conclusion", "Section",
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Cell["\<\
We investigated the use of the Tree of Thoughts framework to extend language \
models\[CloseCurlyQuote] problem solving ability for difficult problems that \
require exploring a diversity of intermediate thoughts. We used the newly \
introduced LLMFunction capability in Wolfram Language to reproduce the ToT \
algorithm for the Game of 24. We visualized the results of exploring and \
evaluating proposals for intermediate steps in this game. We produce and \
visualize a solution to the game by exploring the Tree of Thoughts. Finally \
we begin to explore extending this framework to solving coding challenges, \
providing prompts that could be used toward this end.\
\>", "Text",
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Cell[CellGroupData[{

Cell["Acknowledgment", "Section",
 CellChangeTimes->{{3.898181901737294*^9, 
  3.898181918224023*^9}},ExpressionUUID->"11ba11a1-f3ce-4fb1-84b7-\
f86894fd4aed"],

Cell["\<\
I\[CloseCurlyQuote]d like to thank Jofre Espigule, my project mentor, for his \
extensive support and mentorship and helpful ideas throughout the course of \
my project. Thanks also to Steven Wolfram, Mads, Xerxes, Yi, Danielle, \
Stephanie and all the other mentors and TAs that made Wolfram Summer School \
2023 possible.\
\>", "Text",
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  3.898111000373991*^9}},ExpressionUUID->"5b9c9186-b220-4d66-abe5-\
5e5eca71744e"],

Cell["\<\
Tree of Thoughts: Deliberate Problem Solving with Large Language Models - \
https://arxiv.org/abs/2305.10601\
\>", "ItemNumbered",
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  3.898111217290008*^9, 
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e134441eb28b"],

Cell["\<\
Chain-of-Thought Prompting Elicits Reasoning in Large Language Models - \
https://arxiv.org/abs/2201.11903\
\>", "ItemNumbered",
 CellChangeTimes->{{3.898111084514639*^9, 3.898111105972838*^9}, 
   3.898111194089982*^9, {3.898111332889427*^9, 3.898111332891592*^9}, {
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   3.898111870333172*^9}},ExpressionUUID->"d21c92f4-4769-4ee1-866a-\
107c61484574"],

Cell["\<\
The New World of LLM Functions: Integrating LLM Technology into the Wolfram \
Language  - \
https://writings.stephenwolfram.com/2023/05/the-new-world-of-llm-functions-\
integrating-llm-technology-into-the-wolfram-language/\
\>", "ItemNumbered",
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   3.898111194089982*^9, {3.898111332889427*^9, 3.898111332891592*^9}, {
   3.898116563095736*^9, 
   3.8981166027198477`*^9}},ExpressionUUID->"f7dc59b1-9876-49cc-bf00-\
0d66101b0673"],

Cell["\<\
An Elementary Introduction to the Wolfram Language - \
https://www.wolfram.com/language/elementary-introduction/3rd-ed/\
\>", "ItemNumbered",
 CellChangeTimes->{{3.898111084514639*^9, 3.898111105972838*^9}, 
   3.898111194089982*^9, {3.898111332889427*^9, 3.898111332891592*^9}, {
   3.898180973875125*^9, 
   3.898180992613706*^9}},ExpressionUUID->"3b27ee7a-e2e4-4801-9392-\
46796527d747"],

Cell["\<\
Progressive-Hint Prompting Improves Reasoning in Large Language Models - \
https://arxiv.org/abs/2304.09797\
\>", "ItemNumbered",
 CellChangeTimes->{{3.898111084514639*^9, 3.898111105972838*^9}, 
   3.898111194089982*^9, {3.898111332889427*^9, 
   3.898111332891592*^9}},ExpressionUUID->"bbc21954-2693-4032-8be1-\
0a5665f276e1"],

Cell["\<\
Language Models as Zero-Shot Planners: Extracting Actionable Knowledge for \
Embodied Agents - https://arxiv.org/abs/2201.07207\
\>", "ItemNumbered",
 CellChangeTimes->{{3.898111084514639*^9, 3.898111105972838*^9}, 
   3.898111194089982*^9, {3.898111333364408*^9, 3.898111345903925*^9}, {
   3.8981114168271723`*^9, 
   3.898111416829645*^9}},ExpressionUUID->"e68b363d-b377-46a0-9b5f-\
5fc13ccee7a4"],

Cell["\<\
Inner Monologue: Embodied Reasoning through Planning with Language Models - \
https://arxiv.org/abs/2207.05608\
\>", "ItemNumbered",
 CellChangeTimes->{{3.898111084514639*^9, 3.898111105972838*^9}, 
   3.898111194089982*^9, {3.898111333364408*^9, 3.898111345903925*^9}, {
   3.898111417158288*^9, 
   3.898111424633131*^9}},ExpressionUUID->"89cfa329-f01f-4484-bf81-\
9631488d507e"],

Cell["\<\
OpenAI GPT-4 Technical Report - https://arxiv.org/abs/2303.08774\
\>", "ItemNumbered",
 CellChangeTimes->{{3.898111084514639*^9, 3.898111105972838*^9}, 
   3.898111194089982*^9, {3.898111333364408*^9, 3.898111345903925*^9}, {
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4c47785084c6"],

Cell["\<\
Reflexion: Language Agents with Verbal Reinforcement Learning - \
https://arxiv.org/abs/2303.11366\
\>", "ItemNumbered",
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   3.898111194089982*^9, {3.898111333364408*^9, 3.898111345903925*^9}, {
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   3.898111714207839*^9}},ExpressionUUID->"11de69cd-f35e-40be-afeb-\
dc113e8070f8"],

Cell["\<\
S.A. Sloman. The empirical case for two systems of reasoning. Psychological \
bulletin, 119(1): 3,1996.\
\>", "ItemNumbered",
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