Logic-Thinking MCP Server

# PDSL Examples Collection **Version:** 0.1.0 This document contains 25+ comprehensive examples covering all major use cases for PDSL. ## Table of Contents 1. [Basic Examples](#basic-examples) 2. [Medical Diagnosis](#medical-diagnosis) 3. [Weather Prediction](#weather-prediction) 4. [Fault Diagnosis](#fault-diagnosis) 5. [Risk Assessment](#risk-assessment) 6. [Natural Language Understanding](#natural-language-understanding) 7. [Sensor Fusion](#sensor-fusion) 8. [Game AI](#game-ai) 9. [Financial Forecasting](#financial-forecasting) 10. [Advanced Patterns](#advanced-patterns) ## Basic Examples ### Example 1: Coin Flip Simple probabilistic model: ```pdsl probabilistic_model CoinFlip { # Fair coin 0.5 :: heads 0.5 :: tails query heads } ``` **Output:** `heads: 0.5` ### Example 2: Biased Die Annotated disjunction with six outcomes: ```pdsl probabilistic_model BiasedDie { # Biased towards 6 0.1 :: roll(1); 0.1 :: roll(2); 0.1 :: roll(3); 0.15 :: roll(4); 0.15 :: roll(5); 0.4 :: roll(6) query roll(6) } ``` **Output:** `roll(6): 0.4` ### Example 3: Conditional Probability Bird flight with exceptions: ```pdsl probabilistic_model BirdFlight { # Birds bird(sparrow) bird(penguin) bird(eagle) penguin(penguin) # Flight probability 0.95 :: flies(X) :- bird(X), not penguin(X) 0.0 :: flies(X) :- penguin(X) query flies(sparrow) query flies(penguin) query flies(eagle) } ``` **Output:** - `flies(sparrow): 0.95` - `flies(penguin): 0.0` - `flies(eagle): 0.95` ## Medical Diagnosis ### Example 4: Simple Diagnosis Fever and disease: ```pdsl probabilistic_model SimpleDiagnosis { # Prior: 1% chance of flu 0.01 :: flu # Likelihood: 90% fever if flu 0.9 :: fever :- flu # Background fever rate: 5% 0.05 :: fever :- not flu # Patient has fever observe fever # What's P(flu | fever)? query flu } ``` **Output:** `flu: 0.154` (Bayes' theorem: 15.4%) ### Example 5: Multi-Disease Diagnosis Multiple diseases and symptoms: ```pdsl probabilistic_model MultiDiseaseDiagnosis { # Priors 0.01 :: disease(flu) 0.001 :: disease(covid) 0.005 :: disease(cold) 0.0001 :: disease(pneumonia) # Symptoms for flu 0.9 :: symptom(fever) :- disease(flu) 0.8 :: symptom(cough) :- disease(flu) 0.6 :: symptom(fatigue) :- disease(flu) # Symptoms for covid 0.95 :: symptom(fever) :- disease(covid) 0.85 :: symptom(cough) :- disease(covid) 0.9 :: symptom(fatigue) :- disease(covid) 0.7 :: symptom(loss_of_smell) :- disease(covid) # Symptoms for cold 0.3 :: symptom(fever) :- disease(cold) 0.9 :: symptom(cough) :- disease(cold) 0.4 :: symptom(fatigue) :- disease(cold) # Symptoms for pneumonia 0.95 :: symptom(fever) :- disease(pneumonia) 0.95 :: symptom(cough) :- disease(pneumonia) 0.8 :: symptom(fatigue) :- disease(pneumonia) 0.7 :: symptom(chest_pain) :- disease(pneumonia) # Background symptom rates 0.05 :: symptom(fever) 0.1 :: symptom(cough) 0.15 :: symptom(fatigue) # Observations observe symptom(fever) observe symptom(cough) observe symptom(fatigue) # Queries query disease(flu) query disease(covid) query disease(cold) query disease(pneumonia) } ``` ### Example 6: Disease Progression Temporal disease model: ```pdsl probabilistic_model DiseaseProgression { # Initial infection 0.1 :: infected(day1) # Progression over time 0.8 :: infected(day2) :- infected(day1) 0.7 :: infected(day3) :- infected(day2) 0.5 :: infected(day4) :- infected(day3) # Symptoms appear with delay 0.3 :: symptoms(day1) :- infected(day1) 0.7 :: symptoms(day2) :- infected(day2) 0.9 :: symptoms(day3) :- infected(day3) 0.95 :: symptoms(day4) :- infected(day4) # Observed symptoms on day 3 observe symptoms(day3) # When did infection start? query infected(day1) query infected(day2) query infected(day3) } ``` ## Weather Prediction ### Example 7: Simple Weather Rain and clouds: ```pdsl probabilistic_model SimpleWeather { # Base probability of rain 0.2 :: rain # Cloudy depends on rain 0.9 :: cloudy :- rain 0.3 :: cloudy :- not rain # Observed clouds observe cloudy # Chance of rain? query rain } ``` ### Example 8: Multi-Day Weather Weather dependencies across days: ```pdsl probabilistic_model MultiDayWeather { # Day 1 weather (independent) 0.3 :: rain(day1) # Day 2 depends on day 1 0.6 :: rain(day2) :- rain(day1) 0.2 :: rain(day2) :- not rain(day1) # Day 3 depends on day 2 0.7 :: rain(day3) :- rain(day2) 0.15 :: rain(day3) :- not rain(day2) # Temperature inversely related to rain 0.2 :: cold(D) :- rain(D) 0.6 :: cold(D) :- not rain(D) # Observations observe rain(day1) observe cold(day2) # Predictions query rain(day2) query rain(day3) query cold(day3) } ``` ### Example 9: Seasonal Weather Weather patterns by season: ```pdsl probabilistic_model SeasonalWeather { # Season facts season(summer) # Rain probabilities by season 0.15 :: rain :- season(summer) 0.4 :: rain :- season(spring) 0.5 :: rain :- season(fall) 0.35 :: rain :- season(winter) # Temperature by season 0.8 :: temp(hot) :- season(summer), not rain 0.4 :: temp(hot) :- season(summer), rain 0.5 :: temp(mild) :- season(spring) 0.5 :: temp(mild) :- season(fall) 0.7 :: temp(cold) :- season(winter) query rain query temp(hot) } ``` ## Fault Diagnosis ### Example 10: Computer System Faults Hardware and software failures: ```pdsl probabilistic_model ComputerFaults { # Component reliability 0.95 :: working(cpu) 0.98 :: working(memory) 0.90 :: working(disk) 0.85 :: working(power_supply) # System boot depends on components 0.99 :: boots :- working(cpu), working(memory), working(power_supply) 0.0 :: boots :- not working(cpu) 0.0 :: boots :- not working(power_supply) # Slow performance 0.8 :: slow :- not working(disk) 0.7 :: slow :- not working(memory) 0.1 :: slow # Observations observe not boots # Which component failed? query working(cpu) query working(memory) query working(power_supply) } ``` ### Example 11: Network Fault Diagnosis Network topology failures: ```pdsl probabilistic_model NetworkFaults { # Node reliability 0.98 :: up(server1) 0.98 :: up(server2) 0.95 :: up(router1) 0.95 :: up(router2) 0.99 :: up(gateway) # Connectivity rules connected(server1, client) :- up(server1), up(router1), up(gateway) connected(server2, client) :- up(server2), up(router2), up(gateway) # Service availability (redundant servers) service_available :- connected(server1, client) service_available :- connected(server2, client) # Cascade failures 0.7 :: up(router1) :- not up(gateway) 0.7 :: up(router2) :- not up(gateway) # Observation: service down observe not service_available # Diagnose query up(server1) query up(server2) query up(gateway) query up(router1) } ``` ### Example 12: Manufacturing Defects Production line quality control: ```pdsl probabilistic_model ManufacturingQC { # Machine states 0.95 :: machine_ok(machine1) 0.93 :: machine_ok(machine2) 0.97 :: machine_ok(machine3) # Material quality 0.98 :: material_ok # Product quality depends on machines and materials 0.99 :: product_ok :- machine_ok(machine1), machine_ok(machine2), machine_ok(machine3), material_ok 0.7 :: product_ok :- not machine_ok(machine1), machine_ok(machine2), machine_ok(machine3), material_ok 0.8 :: product_ok :- machine_ok(machine1), not machine_ok(machine2), machine_ok(machine3), material_ok 0.75 :: product_ok :- machine_ok(machine1), machine_ok(machine2), not machine_ok(machine3), material_ok 0.5 :: product_ok :- machine_ok(machine1), machine_ok(machine2), machine_ok(machine3), not material_ok # Test results 0.98 :: test_pass :- product_ok 0.05 :: test_pass :- not product_ok # Observed test failure observe not test_pass # Root cause? query machine_ok(machine1) query machine_ok(machine2) query machine_ok(machine3) query material_ok } ``` ## Risk Assessment ### Example 13: Credit Risk Loan default prediction: ```pdsl probabilistic_model CreditRisk { # Applicant characteristics income(high) employment(stable) credit_score(good) # Default probabilities 0.01 :: defaults :- income(high), credit_score(excellent) 0.03 :: defaults :- income(high), credit_score(good) 0.08 :: defaults :- income(medium), credit_score(good) 0.15 :: defaults :- income(low), credit_score(fair) 0.35 :: defaults :- income(low), credit_score(poor) # Employment stability effect 0.7 :: defaults :- defaults, not employment(stable) query defaults } ``` ### Example 14: Cybersecurity Risk Attack probability assessment: ```pdsl probabilistic_model CyberSecurityRisk { # Threat level 0.3 :: threat(high) 0.5 :: threat(medium) 0.2 :: threat(low) # Vulnerability assessment 0.8 :: vulnerable :- threat(high) 0.4 :: vulnerable :- threat(medium) 0.1 :: vulnerable :- threat(low) # Security measures 0.95 :: firewall_active 0.90 :: ids_active 0.85 :: patch_updated # Attack success 0.7 :: attack_success :- vulnerable, not firewall_active 0.5 :: attack_success :- vulnerable, not ids_active 0.4 :: attack_success :- vulnerable, not patch_updated 0.1 :: attack_success :- vulnerable, firewall_active, ids_active, patch_updated # Data breach 0.8 :: data_breach :- attack_success # Observations observe threat(high) observe firewall_active # Risk queries query attack_success query data_breach } ``` ### Example 15: Investment Risk Portfolio risk analysis: ```pdsl probabilistic_model InvestmentRisk { # Market conditions 0.25 :: market(bull); 0.5 :: market(neutral); 0.25 :: market(bear) # Stock performance 0.7 :: stock_up(tech) :- market(bull) 0.3 :: stock_up(tech) :- market(neutral) 0.1 :: stock_up(tech) :- market(bear) 0.6 :: stock_up(energy) :- market(bull) 0.4 :: stock_up(energy) :- market(neutral) 0.2 :: stock_up(energy) :- market(bear) # Portfolio performance 0.8 :: portfolio_gain :- stock_up(tech), stock_up(energy) 0.5 :: portfolio_gain :- stock_up(tech), not stock_up(energy) 0.4 :: portfolio_gain :- not stock_up(tech), stock_up(energy) 0.1 :: portfolio_gain :- not stock_up(tech), not stock_up(energy) # Observations observe stock_up(tech) # Queries query portfolio_gain query market(bull) } ``` ## Natural Language Understanding ### Example 16: Word Sense Disambiguation Disambiguate word meanings: ```pdsl probabilistic_model WordSenseDisambiguation { # Context words context(bank) context(river) context(water) # Word senses 0.6 :: sense(bank, financial) 0.4 :: sense(bank, riverbank) # Contextual preferences 0.9 :: sense(bank, riverbank) :- context(river) 0.8 :: sense(bank, riverbank) :- context(water) 0.9 :: sense(bank, financial) :- context(money) 0.8 :: sense(bank, financial) :- context(account) # Observe context observe context(river) observe context(water) # Which sense? query sense(bank, financial) query sense(bank, riverbank) } ``` ### Example 17: Sentiment Analysis Text sentiment classification: ```pdsl probabilistic_model SentimentAnalysis { # Word indicators word(excellent) word(great) word(terrible) # Sentiment probabilities 0.9 :: sentiment(positive) :- word(excellent) 0.85 :: sentiment(positive) :- word(great) 0.1 :: sentiment(positive) :- word(terrible) 0.05 :: sentiment(negative) :- word(excellent) 0.1 :: sentiment(negative) :- word(great) 0.95 :: sentiment(negative) :- word(terrible) # Default sentiment 0.5 :: sentiment(neutral) # Observations observe word(excellent) observe word(great) # Classify query sentiment(positive) query sentiment(negative) query sentiment(neutral) } ``` ### Example 18: Intent Classification Chatbot intent detection: ```pdsl probabilistic_model IntentClassification { # Detected keywords keyword(book) keyword(flight) keyword(tomorrow) # Intent priors 0.3 :: intent(book_flight) 0.25 :: intent(book_hotel) 0.2 :: intent(check_weather) 0.15 :: intent(set_reminder) 0.1 :: intent(other) # Keyword-intent associations 0.9 :: intent(book_flight) :- keyword(book), keyword(flight) 0.8 :: intent(book_hotel) :- keyword(book), keyword(hotel) 0.85 :: intent(check_weather) :- keyword(weather) 0.8 :: intent(set_reminder) :- keyword(remind), keyword(tomorrow) # Observations observe keyword(book) observe keyword(flight) observe keyword(tomorrow) # Classify intent query intent(book_flight) query intent(book_hotel) query intent(set_reminder) } ``` ## Sensor Fusion ### Example 19: Robot Localization Multiple sensor readings: ```pdsl probabilistic_model RobotLocalization { # Possible locations 0.25 :: location(room1); 0.25 :: location(room2); 0.25 :: location(hallway); 0.25 :: location(kitchen) # GPS reading (noisy) 0.8 :: gps_reading(X) :- location(X) 0.1 :: gps_reading(Y) :- location(X), adjacent(X, Y) # Vision sensor 0.9 :: sees(table) :- location(kitchen) 0.85 :: sees(bed) :- location(room1) 0.85 :: sees(desk) :- location(room2) # Adjacency facts adjacent(room1, hallway) adjacent(room2, hallway) adjacent(hallway, kitchen) # Observations observe gps_reading(kitchen) observe sees(table) # Where is robot? query location(kitchen) query location(hallway) } ``` ### Example 20: Multi-Sensor Object Detection Fusing camera and LIDAR: ```pdsl probabilistic_model ObjectDetection { # Object presence 0.1 :: object_present(car) 0.05 :: object_present(pedestrian) 0.02 :: object_present(bicycle) # Camera detection 0.95 :: camera_detects(X) :- object_present(X) 0.05 :: camera_detects(X) # False positive # LIDAR detection 0.98 :: lidar_detects(X) :- object_present(X) 0.02 :: lidar_detects(X) # False positive # Fusion: higher confidence if both agree 0.99 :: confirmed(X) :- camera_detects(X), lidar_detects(X) # Observations observe camera_detects(car) observe lidar_detects(car) # Query query object_present(car) query confirmed(car) } ``` ## Game AI ### Example 21: Enemy Behavior Prediction Predict opponent actions: ```pdsl probabilistic_model EnemyBehavior { # Enemy state enemy_health(low) player_distance(close) # Action probabilities 0.7 :: action(retreat) :- enemy_health(low) 0.2 :: action(attack) :- enemy_health(low) 0.3 :: action(retreat) :- enemy_health(high) 0.6 :: action(attack) :- enemy_health(high) # Distance modifies behavior 0.8 :: action(attack) :- player_distance(close), enemy_health(high) 0.9 :: action(retreat) :- player_distance(close), enemy_health(low) # Observations observe enemy_health(low) observe player_distance(close) # Predict query action(retreat) query action(attack) } ``` ### Example 22: Loot Drop System Probabilistic item generation: ```pdsl probabilistic_model LootDrop { # Enemy type enemy(boss) # Rarity tiers 0.5 :: rarity(common); 0.3 :: rarity(rare); 0.15 :: rarity(epic); 0.05 :: rarity(legendary) # Boss modifiers 0.3 :: rarity(common) :- enemy(boss) 0.3 :: rarity(rare) :- enemy(boss) 0.25 :: rarity(epic) :- enemy(boss) 0.15 :: rarity(legendary) :- enemy(boss) # Item types by rarity 0.7 :: item_type(weapon) :- rarity(legendary) 0.3 :: item_type(armor) :- rarity(legendary) 0.5 :: item_type(weapon) :- rarity(epic) 0.5 :: item_type(armor) :- rarity(epic) # Observations observe enemy(boss) # What drops? query rarity(legendary) query item_type(weapon) } ``` ### Example 23: Dialogue System NPC conversation choices: ```pdsl probabilistic_model DialogueSystem { # Player reputation reputation(high) # NPC mood 0.6 :: mood(friendly) 0.3 :: mood(neutral) 0.1 :: mood(hostile) # Response probabilities 0.9 :: response(helpful) :- mood(friendly), reputation(high) 0.7 :: response(helpful) :- mood(friendly), reputation(medium) 0.5 :: response(helpful) :- mood(neutral), reputation(high) 0.8 :: response(hostile) :- mood(hostile) 0.3 :: response(hostile) :- mood(neutral), reputation(low) # Quest offering 0.8 :: offers_quest :- response(helpful) 0.1 :: offers_quest :- response(neutral) # Observations observe reputation(high) observe mood(friendly) # Queries query response(helpful) query offers_quest } ``` ## Financial Forecasting ### Example 24: Stock Price Movement Short-term price prediction: ```pdsl probabilistic_model StockPriceMovement { # Market indicators 0.3 :: indicator(volume_high) 0.25 :: indicator(rsi_overbought) 0.2 :: indicator(macd_bullish) # Price movement 0.6 :: price(up) :- indicator(macd_bullish), not indicator(rsi_overbought) 0.7 :: price(up) :- indicator(volume_high), indicator(macd_bullish) 0.3 :: price(down) :- indicator(rsi_overbought) 0.4 :: price(down) :- not indicator(volume_high), not indicator(macd_bullish) # Observations observe indicator(macd_bullish) observe indicator(volume_high) # Forecast query price(up) query price(down) } ``` ### Example 25: Economic Recession Prediction Macro-economic indicators: ```pdsl probabilistic_model RecessionPrediction { # Economic indicators 0.15 :: indicator(unemployment_rising) 0.2 :: indicator(yield_curve_inverted) 0.1 :: indicator(gdp_declining) 0.12 :: indicator(consumer_confidence_low) # Recession probability 0.7 :: recession :- indicator(yield_curve_inverted), indicator(unemployment_rising) 0.8 :: recession :- indicator(gdp_declining), indicator(unemployment_rising) 0.6 :: recession :- indicator(consumer_confidence_low), indicator(gdp_declining) # Base recession rate 0.05 :: recession # Observations observe indicator(yield_curve_inverted) observe indicator(unemployment_rising) # Forecast query recession } ``` ## Advanced Patterns ### Example 26: Parameter Learning Learn probabilities from data: ```pdsl probabilistic_model ParameterLearning { # Unknown probabilities (to be learned) p1 :: symptom(fever) :- disease(flu) p2 :: symptom(cough) :- disease(flu) p3 :: disease(flu) # Learn from dataset learn parameters from dataset("medical_records.csv") # Query with learned parameters query disease(flu) } ``` ### Example 27: Recursive Probabilistic Model Transitive relations: ```pdsl probabilistic_model TransitiveFriendship { # Base friendships 0.8 :: friends(alice, bob) 0.7 :: friends(bob, carol) 0.6 :: friends(carol, dave) # Transitive friendship (friends of friends) 0.6 :: connected(X, Y) :- friends(X, Y) 0.4 :: connected(X, Z) :- friends(X, Y), connected(Y, Z) # Query transitive connection query connected(alice, dave) } ``` ### Example 28: Temporal Reasoning Event sequences: ```pdsl probabilistic_model TemporalEvents { # Initial event 0.3 :: event(start, t1) # Event propagation over time 0.8 :: event(progress, t2) :- event(start, t1) 0.7 :: event(progress, t3) :- event(progress, t2) 0.6 :: event(complete, t4) :- event(progress, t3) # Observations at different times observe event(start, t1) observe event(progress, t2) # Predict future query event(complete, t4) } ``` ### Example 29: Noisy-OR Model Multiple independent causes: ```pdsl probabilistic_model NoisyOR { # Multiple causes 0.1 :: cause(fire) 0.05 :: cause(earthquake) 0.02 :: cause(power_surge) # Effect with noisy-OR combination 0.95 :: effect(alarm) :- cause(fire) 0.9 :: effect(alarm) :- cause(earthquake) 0.7 :: effect(alarm) :- cause(power_surge) # False alarm rate 0.01 :: effect(alarm) # Observation observe effect(alarm) # Diagnose causes query cause(fire) query cause(earthquake) query cause(power_surge) } ``` ### Example 30: Hidden Markov Model Sequence prediction: ```pdsl probabilistic_model HiddenMarkov { # Initial state 0.6 :: state(sunny, t1); 0.4 :: state(rainy, t1) # Transition probabilities 0.8 :: state(sunny, t2) :- state(sunny, t1) 0.2 :: state(rainy, t2) :- state(sunny, t1) 0.4 :: state(sunny, t2) :- state(rainy, t1) 0.6 :: state(rainy, t2) :- state(rainy, t1) # Observations (emissions) 0.9 :: observe_sun :- state(sunny, t1) 0.2 :: observe_sun :- state(rainy, t1) # Observation observe observe_sun # Infer hidden state query state(sunny, t1) query state(rainy, t2) } ``` ## Usage Tips ### Running Examples ```bash # Save example to file echo "..." > example.pdsl # Run with PDSL interpreter logic-thinking probabilistic example.pdsl # Or compile to ProbLog logic-thinking compile example.pdsl > example.pl problog example.pl ``` ### Modifying Examples 1. **Adjust probabilities** to match your domain 2. **Add observations** to condition on evidence 3. **Add queries** to explore different scenarios 4. **Combine examples** for complex models ### Best Practices 1. **Start simple** - Begin with basic facts and rules 2. **Validate probabilities** - Ensure they sum correctly 3. **Test incrementally** - Add complexity gradually 4. **Document assumptions** - Use comments liberally 5. **Compare outputs** - Verify results make intuitive sense ## Additional Resources - [Quickstart Guide](PROBABILISTIC_DSL_QUICKSTART.md) - [Language Specification](PROBABILISTIC_DSL_SPECIFICATION.md) - [ProbLog Translation](PROBABILISTIC_DSL_PROBLOG_TRANSLATION.md) --- **These examples demonstrate the full expressive power of PDSL across diverse application domains.**