Optimisation of the Analysis of AND-OR Decision Trees
andorR (pronounced ‘Andorra’) is an R package for the analysis and optimisation of expert system AND-OR decision trees. It helps manage the process of gathering evidence and reaching conclusions under uncertainty, aiming to minimize resource use and maximise confidence.
About
AND-OR decision trees (also known as logic trees or Boolean decision trees) provide a structured way to implement expert systems in domains where repeatable, transparent, and standardised decision processes are critical, and where multiple pathways may lead to the same conclusion. Such trees are particularly valuable when decisions are based on a set of binary (TRUE/FALSE) criteria that can be combined using AND and OR logic.
Examples include clinical diagnosis of complex or ambiguous diseases (e.g., Ottawa Ankle Rules, Centor criteria, Alvarado score), transparent policy decisions (e.g., criteria for listing notifiable animal diseases by WOAH or selecting World Heritage sites by UNESCO), and finance and investment management (e.g., stage-gate systems and exclusionary screening).
In each case, determining an accurate answer to each criterion (a leaf in the tree) can require considerable resources (expensive tests, detailed research, extensive data collection). andorR addresses a critical gap for R users by:
- Optimizing the path to a conclusion: It calculates the “influence index” for each unanswered question, guiding the user to the most efficient sequence to reach a decision.
- Managing uncertainty: It propagates semi-quantitative confidence scores through the tree’s logic, allowing for an overall confidence in the conclusion.
- Guiding evidence generation: For a partially resolved tree, it identifies which low-confidence answers are most critical to strengthen through further investigation to boost confidence in the final result.
While the R ecosystem has excellent packages for machine-learning-derived decision trees (e.g., rpart), andorR specifically caters to the interactive, evidence-gathering workflow of expert-defined logic trees, making complex decision processes transparent, reproducible, and resource-efficient.
Installation
You can install andorR directly from GitHub:
# install.packages("remotes") # If you don't have remotes installed
remotes::install_github("epimundi/andorR")Example Usage
Let’s illustrate andorR’s core functionality by loading a predefined ethical investment decision tree, making some initial decisions, and then identifying the most influential remaining questions.
First, load the package and an example tree, and view the tree structure.
library(andorR)
library(knitr)
# Load the example 'ethical' dataset
data(ethical)
tree <- load_tree_df(ethical)
# Initially, the tree is unresolved
print_tree(tree)
#> Tree Rule Answer Confidence
#> Invest in Company X AND
#> |-- Financial Viability AND
#> | |-- Profitability and Growth Signals OR
#> | | |-- FIN1
#> | | |-- FIN2
#> | | `-- FIN3
#> | `-- Solvency and Stability AND
#> | |-- FIN4
#> | `-- FIN5
#> |-- Acceptable Environmental Stewardship OR
#> | |-- Has a Clean Current Record AND
#> | | |-- ENV1
#> | | |-- ENV2
#> | | `-- ENV3
#> | `-- Has a Credible Transition Pathway OR
#> | |-- ENV4
#> | |-- ENV5
#> | `-- ENV6
#> |-- Demonstrable Social Responsibility OR
#> | |-- Shows Excellent Internal Culture OR
#> | | |-- SOC1
#> | | |-- SOC2
#> | | |-- SOC3
#> | | `-- SOC4
#> | `-- Has a Positive External Impact AND
#> | |-- SOC5
#> | |-- SOC6
#> | `-- SOC7
#> `-- Strong Corporate Governance AND
#> |-- GOV1
#> |-- GOV2
#> |-- GOV3
#> |-- GOV4
#> `-- GOV5Get a list of the questions:
questions_df <- get_questions(tree)
display_df <- questions_df[, c("name", "question")]
colnames(display_df) <- c("ID", "Question")
kable(
display_df,
caption = "Ethical investment decision tree questions",
align = 'l',
escape = TRUE,
booktabs = TRUE
) | ID | Question |
|---|---|
| FIN1 | Company demonstrates consistent, high revenue growth. |
| FIN2 | Company maintains a high net profit margin for its industry. |
| FIN3 | Company holds a dominant or rapidly growing market share. |
| FIN4 | Debt-to-Equity ratio is below the industry average. |
| FIN5 | Company generates strong and positive free cash flow. |
| ENV1 | Carbon emissions (Scopes 1 & 2) are verifiably below the industry average. |
| ENV2 | Waste and water usage are minimal and well-managed. |
| ENV3 | Supply chain has strong, audited environmental standards. |
| ENV4 | Company commits a high percentage of R&D to validated green technology. |
| ENV5 | Has ambitious, science-based emission reduction targets (e.g., SBTi certified). |
| ENV6 | Executive compensation is directly and significantly linked to achieving environmental targets. |
| SOC1 | Pays a verified living wage to all global employees. |
| SOC2 | Employee turnover rate is exceptionally low for the industry. |
| SOC3 | Has strong, independently verified diversity & inclusion metrics. |
| SOC4 | Supply chain is robustly and transparently audited for labor rights (no forced/child labor). |
| SOC5 | Products and services provide a clear, net positive social good. |
| SOC6 | Company has a clean record on product safety and consumer protection. |
| SOC7 | No major, unresolved human rights controversies in its operations or supply chain. |
| GOV1 | The board of directors is majority independent and diverse. |
| GOV2 | Executive pay ratio is reasonable and linked to long-term, sustainable value. |
| GOV3 | Political lobbying and donations are transparent and align with stated company values. |
| GOV4 | Has strong shareholder protection rights (e.g., no dual-class shares). |
| GOV5 | Tax practices are transparent and fair (no excessive use of tax havens). |
Ethical investment decision tree questions
Answer some questions
tree <- set_answer(tree, "FIN1", TRUE, 4) # Company shows consistent, high revenue growth (high confidence)
#> Answer for leaf 'FIN1' set to: TRUE with confidence 4/5
tree <- set_answer(tree, "ENV2", FALSE, 3) # Waste and water usage are NOT minimal (medium confidence)
#> Answer for leaf 'ENV2' set to: FALSE with confidence 3/5
# Update the tree to propagate answers and calculate influence indices
tree <- update_tree(tree)
# Print the updated tree
print_tree(tree)
#> Tree Rule Answer Confidence
#> Invest in Company X AND
#> |-- Financial Viability AND
#> | |-- Profitability and Growth Signals OR TRUE 90%
#> | | |-- FIN1 TRUE 4
#> | | |-- FIN2
#> | | `-- FIN3
#> | `-- Solvency and Stability AND
#> | |-- FIN4
#> | `-- FIN5
#> |-- Acceptable Environmental Stewardship OR
#> | |-- Has a Clean Current Record AND FALSE 80%
#> | | |-- ENV1
#> | | |-- ENV2 FALSE 3
#> | | `-- ENV3
#> | `-- Has a Credible Transition Pathway OR
#> | |-- ENV4
#> | |-- ENV5
#> | `-- ENV6
#> |-- Demonstrable Social Responsibility OR
#> | |-- Shows Excellent Internal Culture OR
#> | | |-- SOC1
#> | | |-- SOC2
#> | | |-- SOC3
#> | | `-- SOC4
#> | `-- Has a Positive External Impact AND
#> | |-- SOC5
#> | |-- SOC6
#> | `-- SOC7
#> `-- Strong Corporate Governance AND
#> |-- GOV1
#> |-- GOV2
#> |-- GOV3
#> |-- GOV4
#> `-- GOV5Now that some questions are answered and the tree is updated, we can find the most influential remaining questions to answer to efficiently reach a conclusion. In this case we are sorting by “TRUE”, a ‘rule-in’ approach which ranks influence assuming we respond TRUE. The other options are “FALSE” (‘rule-out’) and “BOTH” (unopinionated).
# Get the top 10 most influential unanswered questions
highest_influence_questions <- get_highest_influence(tree, sort_by = "TRUE", top_n = 10)
display_df <- highest_influence_questions[, c("name", "influence_if_true", "influence_if_false", "question")]
colnames(display_df) <- c("ID", "Inf True", "Inf False", "Question")
kable(
display_df,
caption = "Priority questions based on 'rule-in' strategy",
align = 'l',
escape = TRUE,
booktabs = TRUE
) | ID | Inf True | Inf False | Question |
|---|---|---|---|
| ENV4 | 0.2500000 | 0.3333333 | Company commits a high percentage of R&D to validated green technology. |
| ENV5 | 0.2500000 | 0.3333333 | Has ambitious, science-based emission reduction targets (e.g., SBTi certified). |
| ENV6 | 0.2500000 | 0.3333333 | Executive compensation is directly and significantly linked to achieving environmental targets. |
| SOC1 | 0.2500000 | 0.1250000 | Pays a verified living wage to all global employees. |
| SOC2 | 0.2500000 | 0.1250000 | Employee turnover rate is exceptionally low for the industry. |
| SOC3 | 0.2500000 | 0.1250000 | Has strong, independently verified diversity & inclusion metrics. |
| SOC4 | 0.2500000 | 0.1250000 | Supply chain is robustly and transparently audited for labor rights (no forced/child labor). |
| FIN4 | 0.1250000 | 1.0000000 | Debt-to-Equity ratio is below the industry average. |
| FIN5 | 0.1250000 | 1.0000000 | Company generates strong and positive free cash flow. |
| SOC5 | 0.0833333 | 0.5000000 | Products and services provide a clear, net positive social good. |
Priority questions based on ‘rule-in’ strategy
Answer more questions to complete the tree
tree <- set_answer(tree, "ENV5", TRUE, 3, verbose=FALSE)
tree <- set_answer(tree, "SOC3", TRUE, 3, verbose=FALSE)
tree <- set_answer(tree, "FIN4", TRUE, 2, verbose=FALSE)
tree <- set_answer(tree, "FIN5", TRUE, 1, verbose=FALSE)
tree <- set_answer(tree, "GOV1", TRUE, 0, verbose=FALSE)
tree <- set_answer(tree, "GOV2", TRUE, 0, verbose=FALSE)
tree <- set_answer(tree, "GOV3", TRUE, 0, verbose=FALSE)
tree <- set_answer(tree, "GOV4", TRUE, 0, verbose=FALSE)
tree <- set_answer(tree, "GOV5", TRUE, 0, verbose=FALSE)
tree <- update_tree(tree)
print_tree(tree)
#> Tree Rule Answer Confidence
#> Invest in Company X AND TRUE 0.8%
#> |-- Financial Viability AND TRUE 37.8%
#> | |-- Profitability and Growth Signals OR TRUE 90%
#> | | |-- FIN1 TRUE 4
#> | | |-- FIN2
#> | | `-- FIN3
#> | `-- Solvency and Stability AND TRUE 42%
#> | |-- FIN4 TRUE 2
#> | `-- FIN5 TRUE 1
#> |-- Acceptable Environmental Stewardship OR TRUE 80%
#> | |-- Has a Clean Current Record AND FALSE 80%
#> | | |-- ENV1
#> | | |-- ENV2 FALSE 3
#> | | `-- ENV3
#> | `-- Has a Credible Transition Pathway OR TRUE 80%
#> | |-- ENV4
#> | |-- ENV5 TRUE 3
#> | `-- ENV6
#> |-- Demonstrable Social Responsibility OR TRUE 80%
#> | |-- Shows Excellent Internal Culture OR TRUE 80%
#> | | |-- SOC1
#> | | |-- SOC2
#> | | |-- SOC3 TRUE 3
#> | | `-- SOC4
#> | `-- Has a Positive External Impact AND
#> | |-- SOC5
#> | |-- SOC6
#> | `-- SOC7
#> `-- Strong Corporate Governance AND TRUE 3.1%
#> |-- GOV1 TRUE 0
#> |-- GOV2 TRUE 0
#> |-- GOV3 TRUE 0
#> |-- GOV4 TRUE 0
#> `-- GOV5 TRUE 0The conclusion for the investment decision is TRUE, but the confidence is very low.
Identify the most efficient questions to focus on to increase confidence.
display_df <- get_confidence_boosters(tree)[, c("name", "action", "details", "potential_gain")]
#> ℹ Analysing 12 unanswered questions...✔ Analysed 12 unanswered questions ✔
#> ℹ Analysing 11 existing answers...✔ Analysed 11 existing answers ✔
colnames(display_df) <- c("ID", "Action", "Details", "Potential gain")
kable(
display_df,
caption = "Priority questions to increase confidence",
align = 'l',
escape = TRUE,
booktabs = TRUE
) | ID | Action | Details | Potential gain | |
|---|---|---|---|---|
| GOV1 | GOV1 | Increase Confidence | Current conf: 0/5 | +0.76% |
| GOV2 | GOV2 | Increase Confidence | Current conf: 0/5 | +0.76% |
| GOV3 | GOV3 | Increase Confidence | Current conf: 0/5 | +0.76% |
| GOV4 | GOV4 | Increase Confidence | Current conf: 0/5 | +0.76% |
| GOV5 | GOV5 | Increase Confidence | Current conf: 0/5 | +0.76% |
Priority questions to increase confidence
All elements of Strong Corporate Governance are important in the tree, so more research into the company is required in this area. Let’s update the results after having done a thorough assessment.
tree <- set_answer(tree, "GOV1", TRUE, 5, verbose=FALSE)
tree <- set_answer(tree, "GOV2", TRUE, 5, verbose=FALSE)
tree <- set_answer(tree, "GOV3", TRUE, 5, verbose=FALSE)
tree <- set_answer(tree, "GOV4", TRUE, 5, verbose=FALSE)
tree <- set_answer(tree, "GOV5", TRUE, 5, verbose=FALSE)
tree <- update_tree(tree)
print_tree(tree)
#> Tree Rule Answer Confidence
#> Invest in Company X AND TRUE 24.2%
#> |-- Financial Viability AND TRUE 37.8%
#> | |-- Profitability and Growth Signals OR TRUE 90%
#> | | |-- FIN1 TRUE 4
#> | | |-- FIN2
#> | | `-- FIN3
#> | `-- Solvency and Stability AND TRUE 42%
#> | |-- FIN4 TRUE 2
#> | `-- FIN5 TRUE 1
#> |-- Acceptable Environmental Stewardship OR TRUE 80%
#> | |-- Has a Clean Current Record AND FALSE 80%
#> | | |-- ENV1
#> | | |-- ENV2 FALSE 3
#> | | `-- ENV3
#> | `-- Has a Credible Transition Pathway OR TRUE 80%
#> | |-- ENV4
#> | |-- ENV5 TRUE 3
#> | `-- ENV6
#> |-- Demonstrable Social Responsibility OR TRUE 80%
#> | |-- Shows Excellent Internal Culture OR TRUE 80%
#> | | |-- SOC1
#> | | |-- SOC2
#> | | |-- SOC3 TRUE 3
#> | | `-- SOC4
#> | `-- Has a Positive External Impact AND
#> | |-- SOC5
#> | |-- SOC6
#> | `-- SOC7
#> `-- Strong Corporate Governance AND TRUE 100%
#> |-- GOV1 TRUE 5
#> |-- GOV2 TRUE 5
#> |-- GOV3 TRUE 5
#> |-- GOV4 TRUE 5
#> `-- GOV5 TRUE 5Individually the impact was small but cumulatively the five questions gave a major boost in confidence. Let’s see what we should look at next.
display_df <- get_confidence_boosters(tree)[, c("name", "action", "details", "potential_gain")]
#> ℹ Analysing 12 unanswered questions...✔ Analysed 12 unanswered questions ✔
#> ℹ Analysing 6 existing answers...✔ Analysed 6 existing answers ✔
colnames(display_df) <- c("ID", "Action", "Details", "Potential gain")
kable(
display_df,
caption = "Priority questions to increase confidence",
align = 'l',
escape = TRUE,
booktabs = TRUE
) | ID | Action | Details | Potential gain | |
|---|---|---|---|---|
| FIN5 | FIN5 | Increase Confidence | Current conf: 1/5 | +16.13% |
| FIN4 | FIN4 | Increase Confidence | Current conf: 2/5 | +10.37% |
| ENV4 | ENV4 | Answer New Question | Suggest answering TRUE | +6.05% |
| ENV6 | ENV6 | Answer New Question | Suggest answering TRUE | +6.05% |
| SOC1 | SOC1 | Answer New Question | Suggest answering TRUE | +6.05% |
Priority questions to increase confidence
Let’s do more research on Solvency and Stability, as suggested.
tree <- set_answer(tree, "FIN4", TRUE, 5, verbose=FALSE)
tree <- set_answer(tree, "FIN5", TRUE, 5, verbose=FALSE)
tree <- update_tree(tree)
print_tree(tree)
#> Tree Rule Answer Confidence
#> Invest in Company X AND TRUE 57.6%
#> |-- Financial Viability AND TRUE 90%
#> | |-- Profitability and Growth Signals OR TRUE 90%
#> | | |-- FIN1 TRUE 4
#> | | |-- FIN2
#> | | `-- FIN3
#> | `-- Solvency and Stability AND TRUE 100%
#> | |-- FIN4 TRUE 5
#> | `-- FIN5 TRUE 5
#> |-- Acceptable Environmental Stewardship OR TRUE 80%
#> | |-- Has a Clean Current Record AND FALSE 80%
#> | | |-- ENV1
#> | | |-- ENV2 FALSE 3
#> | | `-- ENV3
#> | `-- Has a Credible Transition Pathway OR TRUE 80%
#> | |-- ENV4
#> | |-- ENV5 TRUE 3
#> | `-- ENV6
#> |-- Demonstrable Social Responsibility OR TRUE 80%
#> | |-- Shows Excellent Internal Culture OR TRUE 80%
#> | | |-- SOC1
#> | | |-- SOC2
#> | | |-- SOC3 TRUE 3
#> | | `-- SOC4
#> | `-- Has a Positive External Impact AND
#> | |-- SOC5
#> | |-- SOC6
#> | `-- SOC7
#> `-- Strong Corporate Governance AND TRUE 100%
#> |-- GOV1 TRUE 5
#> |-- GOV2 TRUE 5
#> |-- GOV3 TRUE 5
#> |-- GOV4 TRUE 5
#> `-- GOV5 TRUE 5This approach to strategic targeted research helps apply resources to the areas where they will have the most impact on the overall conclusion. The process can be repeated until the target level of confidence is reached.
Interactive tool
This manual iterative approach can get a little tedious. The andorR_interactive() function chains these actions together in a CLI interactive loop to automate the process.
── andorR ──────────────────────────────────────────────────────────────────────────────
An analysis and optimisation tool for AND-OR decision trees.
Created by: EpiMundi (<https://epimundi.com>)
Author: Angus Cameron
Email: angus@epimundi.com
Version: 0.2.4
── Help Menu ───────────────────────────────────────────────────────────────────────────
h: Show this help message.
q: Quit the interactive session.
p: Print the current state of the tree.
s: Save the current tree state to an .rds file.
n: Specify a node to edit by typing its name.
1, 2, ...: Select a numbered question from the list to answer.
────────────────────────────────────────────────────────────────────────────────────────
────────────────────────────────────────────────────────────────────────────────────────
── Conclusion Reached! ──
The current result is: TRUE at a confidence of 57.6%
You can now answer more questions or revise existing answers to boost confidence.
────────────────────────────────────────────────────────────────────────────────────────
✔ Analysed 12 unanswered questions ✔
✔ Analysed 4 existing answers ✔
── Questions to Boost Confidence ──
1. [ENV4] Answer New Question Suggest answering TRUE +14.4%
2. [ENV6] Answer New Question Suggest answering TRUE +14.4%
3. [SOC1] Answer New Question Suggest answering TRUE +14.4%
4. [SOC2] Answer New Question Suggest answering TRUE +14.4%
5. [SOC4] Answer New Question Suggest answering TRUE +14.4%
6. [ENV5] Increase Confidence Current conf: 3/5 +14.4%
7. [SOC3] Increase Confidence Current conf: 3/5 +14.4%
8. [FIN2] Answer New Question Suggest answering TRUE +6.4%
9. [FIN3] Answer New Question Suggest answering TRUE +6.4%
10. [FIN1] Increase Confidence Current conf: 4/5 +6.4%
────────────────────────────────────────────────────────────────────────────────────────
Enter a number, 'n', or command (h, p, s, q): API Documentation
Detailed documentation for all functions and their arguments can be found in the package’s reference manual. You can access it in R using ?function_name (e.g., ?update_tree) or by visiting the andorR pkgdown website: https://epimundi.github.io/andorR/