base-model.nlogo

globals [
  hypothesis-value ;actual Boolean value of the instantiated hypothesis (world model)
  evidence-list ;List to store the actual values of the nodes designated as evidence (world model)
  optimal-posterior ;the optimal belief p(HYP| evidence list) about the hypothesis given access to all evidence nodes' actual values
  Bayes-net ;causal structure of the world model and of the agents' faithful subjective representations thereof
  hypothesis-node ;specification/ selection of the hypothesis nodes
  evidence-nodes  ;specification/ selection of the evidence nodes
  arguments ;list used to count the uses of each argument
  number-of-evidence ;number of pieces of evidence
  evidence-probabilities-list ;marginal probabilities of each piece of evidence given the actual value of the hypothesis
]

turtles-own [
  agent-evidence-list ;stores which parcels/pieces of evidence this agent has seen
  agent-belief ;current degree of belief in the hypothesis
  current-evidence ;list index of the currently handled piece of evidence
  last-heard ;the number of the last-heard piece of evidence
  draws ;How many more draws before this agent reaches max-draws?
  initial-draws-list ;used to store which pieces of evidence this agent pre-drew last time
  heard ;list of indexes of the pieces of evidence this agent has already encountered
  update-total ;list of evidence-strengths for this agent
  initial-belief ;this agent's prior about HYP from before they drew or heard any evidence
  recency-list ;list of evidence this agent has encountered, from least to most recent (no duplicated)
]

extensions [r Nw]

;******************************************************************
;MAIN MODEL FLOW **************************************************
;******************************************************************


to setup
  my-clear-all
  reset-ticks

  carefully [
    loadDAG ;all routines to do with loading or modifying DAGs can be found at the bottom of this code file
  ][
    print "EXCEPTION: Please ensure you are providing a valid R-file in the chosen location."
    print error-message
    stop
  ]

  if reset-world-? [
    carefully [
      reset-evidence
    ][
      print "EXCEPTION: please ensure that your custom settings for the Bayesian network are sound."
      print error-message
      stop
    ]
    set reset-agents-initial-evidence-? true ;a new world necessitates new initial draws
  ]

  compute-optimal-posterior

  if reset-social-network-? [
    clear-turtles
    carefully [
      if network = "wheel" [create-turtles number-of-agents create-network-wheel]
    ][
      print "EXCEPTION: please ensure that your wheel network contains at least three agents."
      stop
    ]
    if network = "complete" [create-turtles number-of-agents create-network-complete]
    if network = "small-world" [
       carefully [
      create-network-small-world
    ][
      print "EXCEPTION: To create a small-world network, please make sure that [k] is less than half of [number-of-agents]."
      print error-message
      stop
      ]
    ]
    if network = "null" [create-turtles number-of-agents create-network-null]

    set reset-agents-initial-evidence-? true ;a new network structure necessitates freshly initialized agents
  ]

  initializeAgents

  setupPlots
end

to go

  if check-stoping-conditions [stop] ;Optionally, the simulation stops when all agents know all the evidence or when max-ticks is reached.

  if show-me-? [
    show (word "--------------------------------------------")
    show (word "NEW TICK: " ticks)
    show (word "--------------------------------------------")
    show (word "Step 1: Inquiry")
    show (word "--------------------------------------------")
  ]

  ask turtles [
    if shouldInquire? [
      collectEvidence "random"
    ]
  ]

if show-me-? [
    show (word "--------------------------------------------")
    show (word "Step 2: COMMUNICATION")
    show (word "--------------------------------------------")
  ]

  ask turtles [
    if shouldShare? [
      if share = "impact" [impactShare]
      if share = "random" [randomShare]
      if share = "recent" [simpleRecentShare]
    ]

  ]

  plotArguments
  tick


 end

;******************************************************************
;INQUIRY AND REASONING SUBROUTINES ********************************
;******************************************************************

to compute-posterior
;This is called whenever an agent receives a new piece of evidence (parcel). The procedure computes the posterior belief in the hypothesis, given ALL currently recorded pieces of evidence.
  let b0 agent-belief
  let b1 0

  ;***********************************************************************************************************************************
  ;the following block creates a string that is later used to query the R instance

  let heard-sorted sort heard ;recall that heard just stores indexes, so sort applies

  let rQuery (word "cpquery("Bayes-net", event = ("Hypothesis-node" == 'yes'), evidence = (")

  let x 0 ;iterates through all eNodes
  let y 0 ;keeps track of the additions to the rQuery string
  while [x < number-of-evidence] [

    if member? x heard-sorted [
      set rQuery (word rQuery ""item x evidence-nodes" == '" item x agent-evidence-list"'")
      set y y + 1
      if y < length heard-sorted [set rQuery (word rQuery " & ")]
    ]
    set x x + 1
  ]

   set rQuery (word rQuery "))")

  if show-me-? [print (word "The rQuery for compute-optimal-posterior is " rQuery)]

  ;***********************************************************************************************************************************


  ;Here again, we repeat the query to counteract approximation errors.

  if approximation = "repeater" [
    repeat repeater [
      let m r:get rQuery
      set b1 (b1 + m)
    ]
    set b1 (b1 / repeater)
  ]

  if approximation = "seed"[
    r:eval (word "set.seed("seed") ")
    set b1 r:get rQuery
  ]

  if show-me-? [show (word "my posterior: " b1)]

  ;This computes the "relative" update: it records how the agent's belief has changed through this particular piece of evidence.
  let update-r b1 - b0
  ;set update-relative replace-item last-heard update-relative update-r

  compute-singular

  if show-me-? [show (word "update-total: " update-total)]

  set agent-belief  b1
  change-colors
end

to compute-singular ;It computes how much the last received piece of evidence would have changed the agent's belief had this been the first piece of evidence they heard (relative to the original prior).
;In this way, the agents record the isolated diagnosticity of the evidence.
;This is called whenever a new posterior is calculated.
  if last-heard != "none"
  [

    ;***********************************************************************************************************************************
    ;the following block creates a string that is later used to query the R instance
    let rQuery (word "cpquery("Bayes-net", event = ("Hypothesis-node" == 'yes'), evidence = (")
    set rQuery (word rQuery ""item last-heard evidence-nodes" == '" item last-heard evidence-list "' ))")
    ;***********************************************************************************************************************************

    let r 0
    if approximation = "repeater"[
      repeat repeater [
        let v r:get rQuery
        set r (r + v)
      ]
      set r (r / repeater)
    ]
    if approximation = "seed"[
      r:eval (word "set.seed("seed") ")
      set r r:get rQuery
    ]

  if show-me-? [
  show (word "singular posterior: " rQuery ": " r)]
  set update-total replace-item last-heard update-total (r - initial-belief)
  ]
end

to change-colors
;changes the agents' colors, given their belief in the hypothesis node.
  if agent-belief = initial-belief [set color grey]
  if agent-belief > initial-belief [set color green]
  if agent-belief < initial-belief [set color red]
end

to collectEvidence [number] ;number is either the index of the piece of evidence to be collected, or the string "random"
  let i number

  if number = "random" [
    ;select the index of an hitherto unknown piece of evidence;
    let nIndices n-values length agent-evidence-list [ ? -> ifelse-value (item ? agent-evidence-list = "-") [?][false]]
    set nIndices filter [x -> x != false] nIndices
    set i one-of nIndices
  ]

  ;Computation and recording of new evidence

  set heard lput i heard

  set recency-list lput i recency-list

  set last-heard i

  if item i agent-evidence-list = "-"[
    set agent-evidence-list replace-item i agent-evidence-list item i evidence-list
  ]

  if show-me-? [show (word "I drew item " i "; my list: " agent-evidence-list)]
  if show-me-? and share = "recent" [show (word "recency-list: " recency-list)]
  compute-posterior
  set draws draws - 1

end

to-report shouldInquire? ;Each round, the agents may collect a new piece of evidence, but only given three conditions hold:

  ifelse draws > 0 [ ;Condition 1: They must still have "draws" (see interface).
    let p random-float 1
    ifelse p < curiosity [ ; Condition 2: They must be curious enough
      ifelse length heard  < number-of-evidence [ ;Condition 3: They must not know all the evidence already
        report true
      ][
        if show-me-? [show (word "I already know all pieces of evidence." )]
          report false
      ]
    ][
      if show-me-? [show (word "I am not curious this round.")]
      report false
    ]
  ][
    if show-me-? [show (word "I have no more draws left.")]
    report false
  ]

end

to compute-optimal-posterior

  let rQuery (word "cpquery("Bayes-net", event = ("Hypothesis-node" == 'yes'), evidence = (")

  let x 0
  while [x < number-of-evidence] [
    set rQuery (word rQuery "" item x evidence-nodes " == '" item x evidence-list "' ")
    set x x + 1
    if x < number-of-evidence [set rQuery (word rQuery " & ")]
  ]
  set rQuery (word rQuery "))")

  if show-me-? [print (word "The rQuery for compute-optimal-posterior is " rQuery)]

  if approximation = "repeater"[
    repeat repeater [
      let m r:get rQuery
      set optimal-posterior (optimal-posterior + m)
    ]
    set optimal-posterior (optimal-posterior / repeater)
  ]
  if approximation = "seed"[
    r:eval (word "set.seed("seed") ")
    set optimal-posterior r:get rQuery
  ]
  if show-me-? [show (word "The optimal posterior is " optimal-posterior)]
end

;******************************************************************
;COMMUNICATION SUBROUTINES ****************************************
;******************************************************************
to-report shouldShare?
  ;Three conditions need to obtain for agents to share evidence:
  ;1. They have already heard of a piece of evidence
  ;2. They need to be chatty enough
  ;3. They need to pass the conviction threshold
  ifelse length heard > 0 [
    let x random-float 1
    ifelse x < chattiness [

      let lowerBound (initial-belief - initial-belief * conviction-threshold)
      let upperBound (initial-belief + (1 - initial-belief) * conviction-threshold)

      ifelse (agent-belief < lowerBound OR agent-belief > upperBound)[
        report true
      ][
        if show-me-? [show (word "My belief does not pass the threshold.")]
        report false
      ]
    ][
      if show-me-? [show (word "I am not chatty right now.")]
      report false
    ]
  ][
    if show-me-? [show (word "I don't know anything, so I cannot share evidence.")]
    report false
  ]
end

to receiveShare [sharedPiece] ;sharedPiece is the list index the shared piece of evidence

  ;*****************************************************************************************************
  ;upon receiving a piece of evidence via communication, agents put it to the top of their simple-memory
  if   member? sharedPiece recency-list [
    set recency-list remove sharedPiece recency-list
  ]
  set recency-list lput sharedPiece recency-list
  if show-me-? and share = "recent" [show (word "recency-list: " recency-list)]
  ;*****************************************************************************************************

  ;Link-neighbors only accept the piece of evidence if they have not yet seen the parcel
  ifelse item sharedPiece [agent-evidence-list] of self != "-" [
    if show-me-? [show (word "I've heard " sharedPiece " before, thanks " [who] of myself". My list: " agent-evidence-list)]
  ][
    set agent-evidence-list replace-item sharedPiece agent-evidence-list (item sharedPiece evidence-list)
    set heard lput sharedPiece heard
    set last-heard sharedPiece
    compute-posterior


    if plotting-type = "received as novel" [ask myself [countArguments]]

    if show-me-? [show (word [who] of myself " told me " sharedPiece ", now I entertain:" agent-evidence-list " and believe " agent-belief"." )]
  ]
  if plotting-type = "sent to" [ask myself [countArguments]]
end

to randomshare
;This is the simplest of the sharing procedures: the agent chooses a random piece of evidence they have heard and shares it with their neighbours.
  let sharedPiece one-of heard
  if show-me-? [show (word "I want to communicate " sharedPiece)]
  set current-evidence sharedPiece
 if plotting-type = "uttered" [countArguments]


  ask link-neighbors [receiveShare sharedPiece]
end

to impactshare
;Strategic sharing procedures: the agent chooses the piece of evidence that most convinced them of their current position. They measure this by consulting ther "update-total" string.

  let sharedPiece "-"

  ;*************************************************************************************************************************************
  ;agents select the strongest positive piece of evidence if believing in HYP more than they started out, strongest negative piece of evidence otherwise
  ifelse agent-belief > initial-belief [
    let n max update-total
    set sharedPiece position n update-total
  ][
    let n min update-total
    set sharedPiece position n update-total
  ]
  ;*************************************************************************************************************************************

  if show-me-? [ show (word "I communicate " sharedPiece) ]
  set current-evidence sharedPiece
  if plotting-type = "uttered" [countArguments]

  ask link-neighbors [receiveShare sharedPiece]
end

to simplerecentshare

  ifelse length recency-list >= 1  [
    let sharedPiece "-"
    let n random-float 1

    ;*************************************************************************************************************************************
    ;agents have a 90% chance of sharing the last piece of evidence they encountered and–iff they have recently encountered more than once
    ;piece–a 10% chance of sharing the second to last

    ifelse n < 0.9 OR length recency-list = 1 [ ;HERE IS THE PROBABILITY OF PICKING THE MOST RECENT EVIDENCE
      set sharedPiece last recency-list
    ][
      let simple-memory-derivative (remove last recency-list recency-list)
      set sharedPiece one-of simple-memory-derivative
    ]
    ;*************************************************************************************************************************************

    if show-me-? [show (word "I want to communicate " sharedPiece)]

    set current-evidence sharedPiece
    if plotting-type = "uttered" [countArguments]
    if show-me-? [show (word "recency-list: " recency-list)]

    ask link-neighbors [receiveShare sharedPiece]

  ][
    if show-me-? [show (word "I don't remember anything from last round.")]
  ]
end

;******************************************************************
;NETWORK CREATION SUBROUTINES *************************************
;******************************************************************

to create-network-small-world
    nw:generate-watts-strogatz turtles links number-of-agents k rewiring-probability
  layout-circle sort turtles 10
end

to create-network-complete
  ask turtles [ create-links-with other turtles ]
  layout-circle sort turtles  10
end

to create-network-null
  layout-circle sort turtles  10
end

to create-network-cycle
  [turtle-list]
  let previous-turtle 0
  foreach turtle-list [ [cur-turtle] ->
    ask cur-turtle [
      ifelse previous-turtle != 0 [
        create-link-with previous-turtle
        set previous-turtle self
      ][
        create-link-with last turtle-list
        set previous-turtle self
      ]
    ]
  ]
  layout-circle sort turtles 10
end

to create-network-wheel
  let turtle-list sort turtles
  create-network-cycle but-first turtle-list
  ask first turtle-list [
    setxy 0 0
    create-links-with other turtles
  ]
end

;******************************************************************
;MISCELLANEOUS SUBROUTINES ****************************************
;******************************************************************

to initializeAgents

  ask turtles [

    ;******************************************************************************************************
    ;This is the agent's initial belief in the hypothesis, determined by the CPT.
    let rQuery (word "cpquery("Bayes-net", event = ("Hypothesis-node" == 'yes'), evidence = TRUE)")

    let r 0
    if approximation = "repeater"[
      repeat repeater [let v r:get rQuery
        set r (r + v)]
      set r (r / repeater)]
    if approximation = "seed"[
      r:eval (word "set.seed("seed") ")
      let v r:get rQuery
      set r v ]

    set agent-belief r
    set initial-belief r
    ;******************************************************************************************************

    set agent-evidence-list []
    set heard [] ;Stores which pieces of evidence the agent has heard, in order of reception.
    set recency-list []
    set last-heard "none" ;Stores the piece of evidence the agent has last heard.
    set draws maximum-draws ;Agents may only "draw" from the evidence a limited amount of times. If maximum-draws = number-of-evidence, then full information is assured
    set update-total [] ;Stores the size of the "total" update: P(HYP|E_{i+1}) - P(HYP); where E_{i+1} is what the agent has just learned.

    repeat number-of-evidence [
      set agent-evidence-list lput "-" agent-evidence-list
      set update-total lput "-" update-total
    ]

    ;******************************************************************************************************
    ;Pre-draws
    ;[UI toggle] Either each agent performs random initial draws, or they re-draw their previous initial draws
    ifelse reset-agents-initial-evidence-? [
      repeat initial-draws [collectEvidence "random"]
      set initial-draws-list agent-evidence-list
    ][
      set agent-evidence-list initial-draws-list
      let x 0
      while [x < number-of-evidence] [
        if item x agent-evidence-list != "-" [collectEvidence x]
        set x x + 1
      ]
    ]
    ;******************************************************************************************************

    change-colors

    if show-me-? [show (word "my list " agent-evidence-list)]
  ]

end

to reset-evidence
  let c random-float 1
  ifelse c < hypothesis-probability [set hypothesis-value "yes"][set hypothesis-value "no"]

  set evidence-probabilities-list []
  repeat number-of-evidence [
    set evidence-probabilities-list lput "-" evidence-probabilities-list
  ]
  set evidence-list []

  ;*********************************************************************************************************************************************
  ;For each piece of evidence, the rquery (using either seed or repeater) determines the conditional probability given the actual value of HYP
  ;Then, we use that probability to determine the actual value of each piece  of evidence
  let x 0
  while [x < number-of-evidence] [
    let r 0

    if approximation = "repeater" [
      repeat repeater[
      set r r + (r:get (word "cpquery(" Bayes-net ", event = ("item x evidence-nodes" == 'yes'), evidence = (" Hypothesis-node " == '" hypothesis-value "'))"))
    ]
    set r r / repeater
    ]

    if approximation = "seed" [
      r:eval (word "set.seed("seed") ")
      set r (r:get (word "cpquery(" Bayes-net ", event = ("item x evidence-nodes" == 'yes'), evidence = (" Hypothesis-node " == '" hypothesis-value "'))"))
    ]

    let n random-float 1
    ifelse (n < r) [set evidence-list lput "yes" evidence-list][set evidence-list lput "no" evidence-list ]
    set evidence-probabilities-list (replace-item x evidence-probabilities-list (precision r 2))



    set x x + 1
  ]
  ;*********************************************************************************************************************************************



  if show-me-?[
    show  (word "Probabilities that evidence nodes are true, given truth/falsity of hypothesis: " evidence-probabilities-list)
    show (word "Evidence list " evidence-list)
  ]

  set arguments [] ;resets arguments counter
  repeat number-of-evidence [
      set arguments lput 0 arguments
  ]

  if maximum-draws > number-of-evidence [
    set maximum-draws number-of-evidence
    print "Note: automatically adjusted [maximum-draws]."
  ]
  if initial-draws > maximum-draws [
    set initial-draws maximum-draws
    print "Note: automatically adjusted [initial-draws]."
  ]

 end

to my-clear-all
show (word "------------------------")
  show "**NEW RUN**"
  show (word "------------------------")

  ; manually clears the globals we want to reset, leaves retain-me alone.
  clear-ticks
  set optimal-posterior 0

  clear-patches
  clear-drawing
  clear-all-plots
  clear-output
end

to countArguments
  if current-evidence != "null" [set arguments replace-item current-evidence arguments (item current-evidence arguments + 1)] ;counts current evidence as an argument used
end

to setupPlots
  let x 0
  while [x < number-of-evidence] [
    create-temporary-plot-pen item x evidence-nodes
    ifelse x < 13 [set-plot-pen-color 5 + (x * 10)][set-plot-pen-color 0]
    set x x + 1
  ]
  update-plots
end

to plotArguments

  let x 0
  while [x < number-of-evidence] [
    set-current-plot-pen item x evidence-nodes
    plot item x arguments
    set x x + 1
  ]

  set arguments [] ;resets arguments counter
  repeat number-of-evidence [
    set arguments lput 0 arguments

    ]
end

to-report  check-stoping-conditions
  let stop? false

  if stop-at-full-information-? [
    if not any? turtles with [length heard  < number-of-evidence ][
      show "*** State of full information reached ***"
      set stop? true
    ]
  ]

  if stop-at-max-ticks-? [
    if ticks >= max-ticks [
      show "*** Upper tick-limit reached ***"
      set stop? true
    ]
  ]


  report stop?
end

;******************************************************************
;DAG-RELATED SUBROUTINES ******************************************
;******************************************************************

to loadDAG
  r:eval "library (bnlearn)" ;the R library that lets us use Bayes' nets

  if causal-structure = "big net"[LoadBigNet]
  if causal-structure = "small net"[LoadSmallNet]
  if causal-structure = "asia" [loadAsiaNet]
  if causal-structure = "alarm" [loadAlarmNet]
  if causal-structure = "Vole" [loadVoleNET]
  if causal-structure = "WetGrass" [loadWetGrassNet]
  if causal-structure = "SallyClark" [loadSallyClarkNet]

  if causal-structure = "custom" [
    ;######Upload your custom net here. Either use a whole file via using the UI and this line: <r:eval (word "source('" pathToCustomDAG "')")>
    ;OR copy paste the R script's lines here. Needed:  1. a dag, b. a probability distribution/data fitted onto the dag ("bn.fit")
    ;Make sure each line is embedded like so:  r:eval "R-SCRIPT-LINE". Make sure the syntax is correct (e.g., R is sensitive to small differences such as punctuation).
    ;#####################COPY-PASTE BEGIN


      r:eval (word "source('" path-to-custom-DAG "')")



    ;#####################COPY-PASTE END
    useCustomEvidenceAndHypothesisNodes
  ]


  set Bayes-net "bn"
  set number-of-evidence length evidence-nodes
end

to useCustomEvidenceAndHypothesisNodes
  set evidence-nodes []
  let tempString evidence-nodes-custom-DAG

  while [position "\n" tempString != FALSE] [
    let nextNode  (substring tempString 0 position "\n" tempString)
    set evidence-nodes lput nextNode evidence-nodes
    repeat (position "\n" tempString + 1) [set tempString (but-first tempString)]
  ]
  set evidence-nodes lput tempString evidence-nodes

  set hypothesis-node hypothesis-node-custom-DAG
end

to loadAsiaNet
   r:eval  "data(asia)"
   r:eval  "dag <- model2network('[A][S][T|A][L|S][B|S][D|B:E][E|T:L][X|E]')"
   r:eval  "bn <- bn.fit(dag, asia)"

  ifelse custom-evidence-and-hypothesis-? = false [
    set hypothesis-node "L"
    set evidence-nodes ["A" "S" "T" "B" "D" "X"]
  ][useCustomEvidenceAndHypothesisNodes]

end

to loadVoleNET
r:eval "dag1 <- model2network('[M1][M2][M3|M1:M2][Vole_present][H0|M3:Vole_present][H1|H0][H5][E6|H5][A3|H5:H1][E7|H5:A3:H1][A1][E1|Vole_present:A1][A2|H0][E2|A2:Vole_present][H3][E5|H3][H2|H0][H4|H3][E4|H4][E3|H2:H4][Auxilliary|H2:H4][Constraint|Auxilliary]')"
r:eval "cptM1 <- array(c(0.5,0.5), dim = 2, dimnames = list(M1 = c('no', 'yes')))"
r:eval "cptM2 <- array(c(0.5,0.5), dim = 2, dimnames = list(M2 = c('no', 'yes')))"
r:eval "cptVole_present <- array(c(0.5,0.5), dim = 2, dimnames = list(Vole_present = c('no', 'yes')))"
r:eval "cptA1 <- array(c(0.5,0.5), dim = 2, dimnames = list(A1 = c('no', 'yes')))"
r:eval "cptH3 <- array(c(0.5,0.5), dim = 2, dimnames = list(H3 = c('no', 'yes')))"
r:eval "cptH5 <- array(c(0.5,0.5), dim = 2, dimnames = list(H5 = c('no', 'yes')))"
r:eval "cptH1 <- array(c(1,0,0.5,0.5), dim = c(2,2), dimnames = list(H1 = c('no', 'yes'), H0 =c('no', 'yes')))"
r:eval "cptH2 <- array(c(0.9,0.1,0.3,0.7), dim = c(2,2), dimnames = list(H2 = c('no', 'yes'), H0 =c('no', 'yes')))"
r:eval "cptH2 <- array(c(0.9,0.1,0.3,0.7), dim = c(2,2), dimnames = list(H2 = c('no', 'yes'), H0 =c('no', 'yes')))"
r:eval "cptE5 <- array(c(0.99,0.01,0.1,0.9), dim = c(2,2), dimnames = list(E5 = c('no', 'yes'), H3 =c('no', 'yes')))"
r:eval "cptH4 <- array(c(1.0,0.0,0.1,0.9), dim = c(2,2), dimnames = list(H4 = c('no', 'yes'), H3 =c('no', 'yes')))"
r:eval "cptE4 <- array(c(0.99,0.01,0,1), dim = c(2,2), dimnames = list(E4 = c('no', 'yes'), H4 =c('no', 'yes')))"
r:eval "cptConstraint <- array(c(0.283,0.717,0.45,0.55,1,0), dim = c(2,3), dimnames = list(Constraint = c('no', 'yes'), Auxilliary = c('H2','H4','impossible')))"
r:eval "cptA2 <- array(c(0,1,0.9,0.1), dim = c(2,2), dimnames = list(A2 = c('no', 'yes'), H0 =c('no', 'yes')))"
r:eval "cptE6 <- array(c(0.99,0.01,0.1,0.9), dim = c(2,2), dimnames = list(E6 = c('no', 'yes'), H5 =c('no', 'yes')))"
r:eval "cptM3 <- array(c(0.9,0.1,0.3,0.7,0.4,0.6,0.2,0.8), dim = c(2,2,2),  dimnames = list(M3 = c('no','yes'),M2 = c('no', 'yes'),M1 = c('no', 'yes')))"
r:eval "cptH0 <- array(c(1.0,0.0,1.0,0.0,0.5,0.5,0.3,0.7), dim = c(2,2,2), dimnames = list(H0 = c('no','yes'),M3 = c('no', 'yes'),Vole_present = c('no', 'yes')))"
r:eval "cptE3 <- array(c(1,0,0.99,0.01,0,1,0,1), dim = c(2,2,2), dimnames = list(E3 = c('no','yes'), H4 = c('no', 'yes'), H2= c('no', 'yes')))"
r:eval "cptAuxilliary <-array(c(0,0,1,0,1,0,1,0,0,0,0,1), dim = c(3,2,2), dimnames = list(Auxilliary = c('H2','H4','impossible'), H4 = c('no', 'yes'), H2= c('no', 'yes')))"
r:eval "cptE1 <- array(c(0.5,0.5,0.5,0.5,1,0,0,1), dim = c(2,2,2), dimnames = list(E1 = c('no','yes'), Vole_present= c('no', 'yes'), A1= c('no', 'yes')))"
r:eval "cptE2 <- array(c(0,1,0.4,0.6,0,1,1,0), dim = c(2,2,2), dimnames = list(E2 = c('no','yes'), Vole_present= c('no', 'yes'), A2= c('no', 'yes')))"
r:eval "cptA3 <- array(c(0.9,0.1,0.001,0.999,1,0,0.3,0.7), dim = c(2,2,2),  dimnames = list(A3 = c('no','yes'), H1= c('no', 'yes'), H5= c('no', 'yes')))"
r:eval "cptE7 <- array(c(1,0,1,0,0.2,0.8,1,0,1,0,0.4,0.6,0.01,0.99,0,1),dim = c(2,2,2,2), dimnames = list(E7 = c('no','yes'), A3= c('no', 'yes'), H5= c('no', 'yes'),H1= c('no', 'yes')))"
r:eval "cpt1 <- list( H0 = cptH0, M1 = cptM1, M2 = cptM2, M3 = cptM3, Vole_present = cptVole_present, E1 = cptE1, A1 = cptA1, E2 = cptE2, A2 = cptA2, H1 = cptH1, H5 = cptH5, E6 = cptE6, E7 = cptE7, A3 = cptA3, H2 = cptH2, H3 = cptH3, H4 = cptH4, E3 = cptE3, E4 = cptE4, E5 = cptE5, Auxilliary = cptAuxilliary, Constraint = cptConstraint)"
r:eval "bn <- custom.fit(dag1, cpt1)"

  ifelse custom-evidence-and-hypothesis-? = false [
    set hypothesis-node "H0"
    set evidence-nodes ["E1" "E2" "E3" "E4" "E5" "E6" "E7"]
  ][
    useCustomEvidenceAndHypothesisNodes
  ]

end

to loadAlarmNet
  r:eval "data(alarm)"
  r:eval "dag <- model2network('[HIST|LVF][CVP|LVV][PCWP|LVV][HYP][LVV|HYP:LVF][LVF][STKV|HYP:LVF][ERLO][HRBP|ERLO:HR][HREK|ERCA:HR][ERCA][HRSA|ERCA:HR][ANES][APL][TPR|APL][ECO2|ACO2:VLNG][KINK][MINV|INT:VLNG][FIO2][PVS|FIO2:VALV][SAO2|PVS:SHNT][PAP|PMB][PMB][SHNT|INT:PMB][INT][PRSS|INT:KINK:VTUB][DISC][MVS][VMCH|MVS][VTUB|DISC:VMCH][VLNG|INT:KINK:VTUB][VALV|INT:VLNG][ACO2|VALV][CCHL|ACO2:ANES:SAO2:TPR][HR|CCHL][CO|HR:STKV][BP|CO:TPR]')"
  r:eval  "bn <- bn.fit(dag, alarm)"

  ifelse custom-evidence-and-hypothesis-? = false [
    set hypothesis-node "CVP"
    set evidence-nodes ["HIST" "CO"]
  ][
    useCustomEvidenceAndHypothesisNodes
  ]

end

to loadWetGrassNet

r:eval "library (bnlearn)"

r:eval "dag1 <- model2network('[Rain][Sprinkler][Watson|Rain][Holmes|Rain:Sprinkler]')"

r:eval "cptRain <- array(c(0.2,0.8), dim = 2, dimnames = list(Rain = c('yes', 'no')))"
r:eval "cptSprinkler <- array(c(0.1,0.9), dim = 2, dimnames = list(Sprinkler = c('yes', 'no')))"
r:eval "cptWatson <- array(c(1.0,0.0,0.2,0.8), dim = c(2,2), dimnames = list(Watson = c('yes', 'no'),Rain = c('yes', 'no')))"
r:eval "cptHolmes <- array(c(1.0, 0.0, 0.9, 0.1,1.0,0.0,0.0,1.0), dim = c(2,2,2), dimnames = list(Holmes = c('yes', 'no'), Rain = c('yes', 'no'), Sprinkler = c('yes', 'no')) )"
r:eval "cpt1 <- list(Rain = cptRain,Sprinkler = cptSprinkler, Watson = cptWatson,  Holmes =cptHolmes)"
r:eval "bn <- custom.fit(dag1, cpt1)"

  ifelse custom-evidence-and-hypothesis-? = false [
    set hypothesis-node "Sprinkler"
    set evidence-nodes ["Holmes" "Watson"]
  ][
    useCustomEvidenceAndHypothesisNodes
  ]

end

to loadSallyClarkNet

  ;NOTE: I changed SIDS to NO and MURDER to YES.
r:eval "dag1 <- model2network('[ChildACause][ChildBCause|ChildACause][Guilty|Findings][Findings|ChildACause:ChildBCause][ChildABruising|ChildACause][ChildADisease|ChildACause][ChildBBruising|ChildBCause][ChildBDisease|ChildBCause]')"
r:eval "cptChildACause <- array(c(0.921659,0.07834101), dim = 2, dimnames = list(ChildACause = c('no', 'yes')))"
r:eval "cptChildBCause <- array(c(0.9993604, 6.3959067E-4,1.4622862E-4, 0.9998538), dim = c(2, 2), dimnames = list(ChildBCause = c('no', 'yes'),ChildACause = c('no', 'yes')))"
r:eval "cptChildABruising <- array(c(0.99,0.01,0.95,0.05), dim = c(2, 2), dimnames = list(ChildABruising = c('no', 'yes'), ChildACause = c('no', 'yes')))"
r:eval "cptChildBBruising <- array(c(0.99,0.01,0.95,0.05), dim = c(2, 2), dimnames = list(ChildBBruising = c('no', 'yes'), ChildBCause = c('no', 'yes')))"
r:eval "cptChildADisease <- array(c(0.95,0.05,0.999,0.001), dim = c(2, 2), dimnames = list(ChildADisease = c('no', 'yes'),ChildACause = c('no', 'yes')))"
r:eval "cptChildBDisease <- array(c(0.95,0.05,0.999,0.001), dim = c(2, 2), dimnames = list(ChildBDisease = c('no', 'yes'),ChildBCause = c('no', 'yes')))"
r:eval "cptGuilty <- array(c(0.0,1.0,0.0,1.0,1.0,0.0), dim = c(2, 3), dimnames = list(Guilty = c('no', 'yes'), Findings = c('Both Murdered', 'Either Murdered', 'Neither Murdered')))"
r:eval "cptFindings <- array(c(0.0,0.0,1.0,0.0,1.0,0.0,0.0,1.0,0.0,1.0,0.0,0.0), dim = c(3,2,2), dimnames = list(Findings = c('Both Murdered', 'Either Murdered', 'Neither Murdered'), ChildBCause = c('no', 'yes'), ChildACause = c('no', 'yes')))"
r:eval "cpt1 <- list(ChildABruising = cptChildABruising, ChildADisease = cptChildADisease, ChildBBruising = cptChildBBruising, ChildBDisease = cptChildBDisease, ChildACause = cptChildACause, ChildBCause = cptChildBCause, Findings = cptFindings, Guilty = cptGuilty)"
r:eval "bn <- custom.fit(dag1, cpt1)"

  ifelse custom-evidence-and-hypothesis-? = false [
    set hypothesis-node "Guilty"
    set evidence-nodes ["ChildADisease" "ChildBDisease" "ChildABruising" "ChildBBruising"]
  ][
    useCustomEvidenceAndHypothesisNodes
  ]

end

to loadBigNet
  r:eval  "dag1 <- model2network('[A][B|A][C|A][D|A][one|B][two|B][three|B][four|C][five|C][six|C][seven|D][eight|D][nine|D]')"
  r:eval  "cptA <- array(c(0.5,0.5), dim = 2, dimnames = list(A = c('yes', 'no')))"
  r:eval  "cptB <- array(c(0.9, 0.1, 0.1, 0.9), dim = c(2, 2), dimnames = list(B = c('yes', 'no'), A = c('yes', 'no')))"
  r:eval  "cptC <- array(c(0.5, 0.5, 0.5, 0.5), dim = c(2, 2), dimnames = list(C = c('yes', 'no'), A = c('yes', 'no')))"
  r:eval  "cptD <- array(c(0.1, 0.9, 0.9, 0.1), dim = c(2, 2), dimnames = list(D = c('yes', 'no'), A = c('yes', 'no')))"
  r:eval  "cptone <- array(c(0.9, 0.1, 0.1, 0.9), dim = c(2, 2), dimnames = list(one = c('yes', 'no'), B = c('yes', 'no')))"
  r:eval  "cpttwo <- array(c(0.8, 0.2, 0.2, 0.8), dim = c(2, 2), dimnames = list(two = c('yes', 'no'), B = c('yes', 'no')))"
  r:eval  "cptthree <- array(c(0.7, 0.3, 0.3, 0.7), dim = c(2, 2), dimnames = list(three = c('yes', 'no'), B = c('yes', 'no')))"
  r:eval  "cptfour <- array(c(0.9, 0.1, 0.1, 0.9), dim = c(2, 2), dimnames = list(four = c('yes', 'no'), C = c('yes', 'no')))"
  r:eval  "cptfive <- array(c(0.8, 0.2, 0.2, 0.8), dim = c(2, 2), dimnames = list(five = c('yes', 'no'), C = c('yes', 'no')))"
  r:eval  "cptsix <- array(c(0.7, 0.3, 0.3, 0.7), dim = c(2, 2), dimnames = list(six = c('yes', 'no'), C = c('yes', 'no')))"
  r:eval  "cptseven <- array(c(0.9, 0.1, 0.1, 0.9), dim = c(2, 2), dimnames = list(seven = c('yes', 'no'), D = c('yes', 'no')))"
  r:eval  "cpteight <- array(c(0.8, 0.2, 0.2, 0.8), dim = c(2, 2), dimnames = list(eight = c('yes', 'no'), D = c('yes', 'no')))"
  r:eval  "cptnine <- array(c(0.7, 0.3, 0.3, 0.7), dim = c(2, 2), dimnames = list(nine = c('yes', 'no'), D = c('yes', 'no')))"
  r:eval  "cpt1 <- list(A = cptA, B = cptB, C = cptC, D = cptD, one = cptone, two = cpttwo, three = cptthree, four = cptfour, five = cptfive, six = cptsix, seven = cptseven, eight = cpteight, nine = cptnine)"
  r:eval  "bn <- custom.fit(dag1, cpt1)"

  ifelse custom-evidence-and-hypothesis-? = false [
    set hypothesis-node "A"
    set evidence-nodes [ "one" "two" "three" "four" "five" "six" "seven" "eight" "nine"]
  ][
    useCustomEvidenceAndHypothesisNodes
  ]
end

to loadSmallNet
  r:eval  "dag <- model2network('[V][CS|V][VT|V][M|CS][I|CS][WHO|VT][RS|VT]')"
  r:eval  "cptV <- array(c(0.5,0.5), dim = 2, dimnames = list(A = c('yes', 'no')))"
  r:eval  "cptCS <- array(c(0.9, 0.1, 0.1, 0.9), dim = c(2, 2), dimnames = list(CS = c('yes', 'no'), V = c('yes', 'no')))"
  r:eval  "cptVT <- array(c(0.8, 0.2, 0.2, 0.8), dim = c(2, 2), dimnames = list(VT = c('yes', 'no'), V = c('yes', 'no')))"
  r:eval  "cptI  <- array(c(0.7, 0.3, 0.3, 0.7), dim = c(2, 2), dimnames = list(I = c('yes', 'no'), CS = c('yes', 'no')))"
  r:eval  "cptM  <- array(c(0.8, 0.2, 0.2, 0.8), dim = c(2, 2), dimnames = list(M = c('yes', 'no'), CS = c('yes', 'no')))"
  r:eval  "cptWHO <- array(c(0.8, 0.2, 0.2, 0.8), dim = c(2, 2), dimnames = list(WHO = c('yes', 'no'), VT = c('yes', 'no')))"
  r:eval  "cptRS <- array(c(0.2, 0.8, 0.8, 0.2), dim = c(2, 2), dimnames = list(RS = c('yes', 'no'), VT = c('yes', 'no')))"
  r:eval  "cpt <- list(V = cptV, VT = cptVT, CS = cptCS, I = cptI, M = cptM, WHO = cptWHO, RS = cptRS)"
  r:eval  "bn <- custom.fit(dag, cpt)"

  ifelse custom-evidence-and-hypothesis-? = false [
    set evidence-nodes ["I" "M" "WHO" "RS"]
    set hypothesis-node "V"
  ][
    useCustomEvidenceAndHypothesisNodes
  ]
end
@#$#@#$#@
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Histogram of beliefs
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If you want to load a [causal-structure] via an external R-file, please manually enter the [path-to-custom-DAG]. In addition, please decide upon a [hypothesis-node-custom-DAG], and upon [evidence-nodes-custom-DAG].\n\nIf you are using a pre-set [causal-structure], you may either use the preset [evidence-nodes] and [hypothesis-node], or enter your own selection and toggle [custom-evidence-and-hypothesis-?] on.
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@#$#@#$#@
## WHAT IS IT?

NormAN 1.0 is the first implementation of the NormAN framework. NormAN – short for Normative Argument Exchange across Networks – is a framework for agent-based modelling of argument exchange in social networks, first presented in ’A Bayesian Agent-Based Framework for Argument Exchange Across Networks’. A detailed explanation of all model parameters can be found there. (Full reference: Assaad, L., Fuchs, R., Jalalimanesh, A., Phillips, K., Schöppl, L. & Hahn, U. (2023). ’A Bayesian Agent-Based Framework for Argument Exchange Across Networks’.) 

**This is the model’s process in a nutshell:** To argue about a central claim, agents exchange arguments for believing that claim to be true or false. What evidence exists is determined by the world and its causal structure: for example, if a patient has lung cancer, it is more likely than not that they have shortness of breath. NormAN uses this to generate ‘worlds’ in which argument exchange takes place. Agents can collect evidence from the world and they can communicate with one another by sharing that evidence as arguments across the social network.

To capture this process, NormAN has three components: a ground truth ‘world’ model, individual agents, and the social network across which these agents communicate. 

* The ground truth world determines the true state of the claim at issue, along with the evidence for it that could be discovered in principle. 

* Agents receive evidence about that world (through inquiry) and may communicate that evidence to others as arguments and receive it in turn. Agents aggregate all evidence/arguments that they have encountered to form a degree of belief in the target
claim. To this end, they use Bayes’ rule. 

* Communication, finally, takes place across a social network.

NormAN 1.0 offers the user the possibility to change each of these components and thus explore a variety of different argumentation scenarios. The model captures different communication styles, different world models and social networks. Issues that can be addressed with NormAN include (but are not limited to): polarization and the emergence of consensus, the diffusion of arguments across social networks, the truth-tracking potential of deliberative bodies, and many more.

## HOW TO USE IT?

Follow these steps to quickly initialize the model: 

1. When first opening the model, make sure ‘reset-world-?’
and ‘reset-social-network-?’ are on. 
2. The World: choose a ‘causal-structure’ (chooser). 
3. The social network:
choose a ‘social-network’ (chooser) and a ‘number-of-agents’ (slider). 
4. Click setup: the social network will appear in the interface, the right bottom monitor will show a histogram of agent-beliefs and the middle output will
show which pieces of evidence are true. 
5. Press ‘go’ to start the simulation 

By clicking ‘setup’, users can wholly re-initialize the model, or keep some model facets fixed. Switching ‘reset-world-?’ on resets the truth values of the evidence nodes when ‘ setup’ is pressed. ‘reset-social-network-?’ resets all agents and the social network that connects them. ‘reset-agents-initial-evidence-?’ resets the set of evidence that each agent starts with upon initialization (only relevant if initial-draws>0). Note that because these facets are interconnected, ‘reset-world-?’ triggers‘reset-agents-initial-evidence?’ and so does ‘reset-social-network-?’.

If you would like to monitor what each agent does each round, toggle on ‘show-me-?’: each agent will output their exact step-by-step behaviour as lines in the Command Center. 

The ‘plotting-type’ chooser gives three options for visualizing the frequency of shared arguments (in the plot entitled ‘The rise and fall of arguments’): ‘uttered’ tracks how many times a piece of evidence has been shared each round. ‘sent-to’ tracks how many agents an argument was sent to. ‘received-as-novel’ tracks how many times
an argument was received as a novelty by an agent.

## THINGS TO NOTICE

There are many things to notice. For example, notice how the dynamics of the evidence exchange (illustrated in the window ‘The rise and fall of arguments’) change when you alter the agents’ sharing rule (e.g., from impact to random). Also, observe how using less dense social networks (e.g., from complete to wheel) slows down the evolution of the agents’ beliefs.

## THINGS TO TRY

A phenomenon of interest in NormAN is whether agents reach a consensus (see window ‘Histogram of beliefs’). This will depend on all the factors mentioned above, and changing any model component can help or hinder consensus building. It is, therefore, a worthwhile endeavour to determine which parameter combinations lead to consensus.

## EXTENDING THE MODEL

As explained in ‘A Bayesian Agent-Based Framework for Argument Exchange Across Networks’ (Assaad et al., 2023), NormAN can (and should be) extended in many ways. One thing you can do easily is add new Bayesian networks to NormAN. Additional Bayesian networks must be written in bnlearn code (as in our code) and can be transferred to the NetLogo model via a path to an external R (bnlearn) file by entering the file path in ‘path-to-custom-dag’. Alternatively, you can "copy and paste" the bnlearn file into our NetLogo code (in the designated area at the bottom). Here is the step-by-step protocol to do this: 

1. Create bnlearn code of a Bayesian network.
2. In the UI: Select ‘causal-net = custom’. Specify which nodes ought to count as evidence (‘evidence-Nodes- Custom-DAG’) and hypothesis. Make sure you write each node’s name into one separate line (as in the preset). 
3. Go into the code. Copy and paste the code into the indicated slot (under "LoadCustomNet“). Make sure each line is embedded like so: r:eval "library(bnlearn)“. Make sure the syntax is correct (e.g., R is sensitive to differences such in punctuation, and NetLogo prefers ‘<-’ to ‘=’). Lastly, note that the evidence and hypothesis nodes must take the values ‘yes’ and ‘no’. In the preset ‘Sally Clark’ network, for instance, we changed the values ‘SIDS’ to ‘no’ and ‘murder’ to ‘yes’.

For those who are familiar with NetLogo, it should also be straightforwardly possible to add new communication rules and new social networks.

## CREDITS AND REFERENCES

**SOFTWARE**

* **NetLogo R extension**
Thiele, JC; Grimm, V (2010). “NetLogo meets R: Linking agent-based models with a toolbox for their analysis.” Environmental Modelling and Software, Volume 25, Issue 8: 972 - 974 [DOI: 10.1016/j.envsoft.2010.02.008]

* **bnlearn package**
Scutari M (2010). “Learning Bayesian Networks with the bnlearn R Package.” Journal of Statistical Software, 35(3), 1–22. doi:10.18637/jss.v035.i03.

**SOCIAL NETWORKS**

* **NetLogo Nw Extension and small-world networks**
<https://ccl.northwestern.edu/netlogo/docs/nw.htmlnw:generate-watts-strogatz> 
Wilensky, U. (2015). NetLogo Small Worlds model.http://ccl.northwestern.edu/netlogo/models/SmallWorlds. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.

* **Wheel and Cycle**
Frey, Daniel, and Dunja Šešelja. “Robustness and idealizations in agent-based models of scientific interaction.” The British Journal for the Philosophy of Science (2020).
https://github.com/daimpi/SocNetABM/tree/RobIdeal.

**BAYESIAN NETWORKS**

* **Alarm**
Accessed via bnlearn ‘Bayesian Network Repository’- www.bnlearn.com/bnrepository/ (updated Nov 2022). Originally found in: I. A. Beinlich, H. J. Suermondt, R. M. Chavez, and G. F. Cooper. The ALARM Monitoring System: A Case Study with Two Probabilistic Inference Techniques for Belief Networks. In Proceedings of the 2nd European Conference on Artificial Intelligence in Medicine, pages 247-256. Springer-Verlag, 1989.

* **Asia**
Accessed via bnlearn ‘Bayesian Network Repository’- www.bnlearn.com/bnrepository/ (updated Nov 2022). Originally found in: S. Lauritzen, and D. Spiegelhalter. Local Computation with Probabilities on Graphical Structures and their Application to Expert Systems (with discussion). Journal of the Royal Statistical Society: Series B (Statistical Methodology), 50(2):157-224, 1988.

* **Wet Grass**
Accessed via ‘agena.ai.modeller’ software (version 9336, www.agena.ai) model library. Originally found in: F. V. Jensen. Introduction to Bayesian Networks. Springer-Verlag, 1996.

* **Sally Clark**
Accessed via ‘agena.ai.modeller’ software (version 9336, www.agena.ai) model library. The AgenaRisk software contains a model library with executable versions of all models found in this book: F. Norman, and M. Neil. Risk assessment and decision analysis with Bayesian networks. Crc Press, 2018. Discussed in: N. Fenton. Assessing evidence and testing appropriate hypotheses. Sci Justice, 54(6):502–504, 2014. https://doi.org/10.1016/j.scijus.2014.10.007.

* **Vole**
Accessed via ‘agena.ai.modeller’ software (version 9336, www.agena.ai) model library. The AgenaRisk software contains a model library with executable versions of all models found in this book: F. Norman, and M. Neil. Risk assessment and decision analysis with Bayesian networks. Crc Press, 2018. Originally found in: Lagnado, D. A. “Thinking about evidence.” In Proceedings of the British Academy, vol. 171, pp. 183-223. Oxford, UK: Oxford University Press, 2011. Revised by: F. Norman, M. Neil, and D. A. Lagnado. A general structure for legal arguments about evidence using Bayesian networks. Cognitive science, 37(1): 61-102, 2013.

## HOW TO CITE
Assaad, L., Fuchs, R., Jalalimanesh, A., Phillips, K., Schöppl, L. & Hahn, U. (2023). “A Bayesian Agent-Based Framework for Argument Exchange Across Networks”.
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