Deep Dive: Street Fighter Logic Systems

Executive Summary: Reading This Document

This document formalizes Street Fighter's combat systems and Ryu's martial philosophy using predicate logic and mathematical notation. To effectively navigate this content:

Logical Symbols: Familiarize yourself with the symbol legend. Key operators include:
- → (implies): Represents cause and effect in combat
- ∧ (and): Shows combined conditions
- ∀ (for all): Indicates universal principles
Structure: Each section progresses from fundamental concepts to advanced applications:
- Core principles and predicates
- Technical implementation
- Philosophical context
- Street Fighter lore integration
Context: Each logical statement is accompanied by:
- Natural language explanation
- Street Fighter context
- Practical application notes

The document merges formal logic with Street Fighter's rich lore, particularly focusing on Ryu's journey from student to master. Code implementations follow theoretical concepts, providing a complete framework for understanding both the technical and philosophical aspects of the combat system.

1. Street Fighter Core Systems in Logical Form

1.1 Character State Predicates

In Street Fighter, character states form the foundation of decision-making:

Core State Predicates:

isGrounded(x)

Formal Definition: ∀x [ Position(x).y = 0 ∧ ¬inHitstun(x)]

"A character is grounded when their Y position is 0 and they're not in hitstun."

SF Context: Determines when Ryu can perform ground normals or throws.

hasChargeMeter(x)

Formal Definition: ∀x [ ChargeTime(x) ≥ RequiredTime ∧ Direction(x) = Backward]

"A character has charge when they've held back for the required time."

SF Context: Used for special moves like Guile's Sonic Boom.

1.2 Ansatsuken Core Principles

Satsui no Hado Control:

∀x [
    hasSatsui(x) →
    (
        increasedPower(x) ∧
        ¬hasMuDo(x) ∧
        shouldSuppressUrge(x)
    )
]

SF Context: Ryu's constant battle against the dark hadou.

1.2 Street Fighter Specific Move Properties

Move Classification Logic:

isReversalMove(m)

∀m [
    isReversalMove(m) ↔
    (hasInvincibility(m) ∧
     startupFrames(m) ≤ 5 ∧
     meterCost(m) > 0)
]

"A move is a reversal if it has invincibility, fast startup, and costs meter."

SF Context: Dragon Punch (DP) with meter is a reversal.

isAntiAir(m)

∀m [
    isAntiAir(m) ↔
    (hitboxHeight(m) > characterHeight ∧
     upperBodyInvuln(m) ∧
     startupFrames(m) ≤ 7)
]

"A move is an anti-air if it has upward hitboxes, upper body invulnerability, and quick startup."

SF Context: Ryu's Standing Heavy Punch or DP.

1.3 Street Fighter Combo Systems

Combo Validation Logic:

isValidCombo(m1, m2)

∀m1,m2 [
    isValidCombo(m1,m2) ↔
    (hitstun(m1) > startupFrames(m2) ∧
     pushbackDistance(m1) ≤ range(m2) ∧
     cancelWindow(m1) ∧
     canCancelInto(m1,m2))
]

"A combo is valid if the second move can start before hitstun ends, is in range, and can be canceled into."

SF Context: Ryu's cr.MK into Hadoken combo.

Target Combo Logic:

∀x,m1,m2 [
    (performsMove(x,m1) ∧
     isTargetCombo(m1,m2) ∧
     inputWindow(m2) < 6)
    →
    shouldBuffer(x,m2)
]

SF Context: Buffering Ken's b.MP into HP target combo.

Frame Trap Decision Making:

∀x,y [
    (opponentTechPattern(y, "aggressive") ∧
     hasFrameAdvantage(x) ∧
     distance(x,y) ≤ throwRange)
    →
    (shouldDelayButton(x) ∨ shouldThrow(x))
]

"Against aggressive opponents, alternate between delayed buttons and throws when at advantage."

2.1 Okizeme Decision Trees

Wakeup Pressure System:

∀x,y [
    isKnockedDown(y) →
    (
        (hasQuickRise(y) → setOkiTiming(x, 11)) ∧
        (hasBackRoll(y) → setOkiTiming(x, 15)) ∧
        (hasVReversal(y) → shouldBait(x))
    )
]

"On knockdown, adjust timing for quick rise or back roll, and bait V-Reversal if available."

Safe Jump Logic:

∀x,y [
    (canSafeJump(x,y) ∧
     hasMeterForReversal(y))
    →
    performSafeJump(x)
]

SF Context: Safe jump timing against DP reversals.

2.2 V-System Resource Management

V-Trigger Decision Making:

∀x [
    shouldActivateVTrigger(x) ↔
    (
        (health(x) < 40% ∧
         hasVTrigger(x) ∧
         ¬isInHitstun(x))
        ∨
        (canConfirmInto(x, "highDamageCombo") ∧
         hasVTrigger(x))
    )
]

"Activate V-Trigger when at low health or to confirm into high damage."

V-Reversal Usage:

∀x,y,m [
    shouldVReversal(x) ↔
    (
        isBlocking(x) ∧
        hasVGauge(x) ∧
        (
            (pressure(y) > threshold ∧
             health(x) < 30%)
            ∨
            isSetupMove(lastMove(y))
        )
    )
]

SF Context: V-Reversal against heavy pressure or setup moves.

3.1 Matchup-Specific Adaptations

Character Archetype Responses:

Zoner Matchup Logic:

∀x,y [
    isZoner(y) →
    (
        (projectileOnScreen(y) →
            (shouldNeutralJump(x) ∨ shouldEX(x))) ∧
        (distance(x,y) < rushdownRange →
            maintainPressure(x))
    )
]

SF Context: Ryu vs Guile matchup strategies.

Grappler Counter-Strategy:

∀x,y [
    isGrappler(y) →
    (
        (distance(x,y) = throwRange →
            shouldPreemptiveButton(x)) ∧
        (hasCommandGrab(y) →
            maintainDistance(x, "mid"))
    )
]

SF Context: Keeping Zangief out with Ryu's cr.MK.

Specific Character Counters:

∀x,y [
    (character(y) = "Dhalsim" ∧
     limb(y, "extended"))
    →
    (shouldTatsu(x) ∨ shouldEXFireball(x))
]

"Against Dhalsim's extended limbs, use Tatsumaki or EX Fireball to punish."

3.2 Situational Awareness Systems

Corner Control:

∀x,y [
    (hasCornerPressure(x,y) ∧
     opponentTendency(y, "reversal"))
    →
    (
        shouldShimmy(x) ∨
        (blockString(x) ∧
         waitForReversal(x))
    )
]

SF Context: Baiting and punishing desperate DPs in corner.

Stage Position Awareness:

∀x,y,p [
    stagePosition(p) ∧
    (
        (p = "corner" → increasePressure(x)) ∧
        (p = "midscreen" → maintainNeutral(x)) ∧
        (p = "backToCorner" → shouldEscape(x))
    )
]

3.3 Advanced Pattern Recognition

Player Habit Analysis:

∀x,y,s [
    (situation(s) ∧
     observedResponse(y,s) > 3)
    →
    (
        addToPatternDB(y,s) ∧
        calculateCounter(x,s)
    )
]

"After observing an opponent's response to a situation multiple times, add it to the pattern database and calculate counters."

Adaptation Triggers:

∀x,y [
    (successfulCounter(y,x) > 2)
    →
    (
        shouldChangePattern(x) ∧
        updateStrategy(x, getAlternateStrategy())
    )
]

SF Context: Adapting when opponent has downloaded your patterns.

3.4 Meta-Game Considerations

Round-Based Adaptations:

∀x,r [
    (roundNumber(r) > 1)
    →
    (
        analyzePreviousRound(r-1) ∧
        (
            (lostPreviousRound(x) →
                changeGameplan(x, "aggressive")) ∨
            (wonPreviousRound(x) →
                maintainGameplan(x))
        )
    )
]

"Adapt strategy based on previous round results."

Tournament Context:

∀x,m [
    isTournamentMatch(m) →
    (
        (matchPoint(x) →
            playConservative(x)) ∧
        (eliminationGame(m) →
            minimizeRisks(x))
    )
]

SF Context: Adjusting playstyle based on tournament situation.

4.1 Implementation Architecture

Decision Tree Structure:

class StreetFighterNode {
    condition: Predicate
    weight: float
    priority: number
    actions: Action[]
    children: StreetFighterNode[]
    frameData: FrameData

    evaluate(): Action {
        if (this.condition.test()) {
            return this.getBestAction()
        }
        return this.defaultAction
    }

    getBestAction(): Action {
        return this.actions
            .filter(a => this.isViable(a))
            .sort((a, b) => this.calculateUtility(b) - this.calculateUtility(a))[0]
    }

    calculateUtility(action: Action): number {
        return action.damage * action.successRate * this.weight
            + (action.frameAdvantage > 0 ? 1.5 : 1.0)
            - (action.meterCost * 0.8)
    }
}

Each node in the decision tree evaluates frame-perfect conditions and calculates optimal responses.

Frame-Perfect Execution System:

class FrameManager {
    currentFrame: number
    inputBuffer: Input[]
    frameData: Map

    update(gameState: GameState) {
        this.currentFrame++
        this.processInputBuffer()
        this.checkFrameAdvantage()
        this.updateHitConfirms()
    }

    isInStartup(move: Move): boolean {
        return this.currentFrame - move.startFrame < this.frameData.get(move.id).startup
    }

    isInRecovery(move: Move): boolean {
        return this.currentFrame - move.startFrame < this.frameData.get(move.id).recovery
    }
}

4.2 Real-Time Pattern Recognition

Pattern Tracking System:

class PatternTracker {
    patterns: Map
    frequency: Map
    counters: Map

    recordPattern(situation: GameState, response: Action) {
        const pattern = this.createPattern(situation, response)
        this.updateFrequency(pattern)
        this.updateCounters(pattern)
    }

    suggestCounter(pattern: Pattern): Action {
        return this.counters.get(pattern.id)
            .sort((a, b) => this.getSuccessRate(b) - this.getSuccessRate(a))[0]
    }
}

Real-time pattern recognition system that adapts to opponent tendencies.

4.3 State Machine Implementation

Character State Management:

class FighterStateMachine {
    currentState: FighterState
    transitions: Map
    frameData: FrameData

    update(input: Input, gameState: GameState) {
        const nextState = this.getNextState(input, gameState)
        if (this.canTransition(this.currentState, nextState)) {
            this.executeTransition(nextState)
        }
    }

    canTransition(from: FighterState, to: FighterState): boolean {
        return this.transitions.has(`${from.id}->${to.id}`)
            && this.checkTransitionConditions(from, to)
    }
}

State machine handling character states and transitions.

4.4 Performance Optimization

Critical Performance Considerations:

Frame Budget Management:

const FRAME_BUDGET_MS = 16.67  // 60fps target
const MAX_PREDICTION_DEPTH = 3  // Limit prediction tree depth
const CACHE_DURATION_FRAMES = 6 // Cache predictions for 6 frames

Decision Caching:

class DecisionCache {
    cache: Map

    getCachedDecision(state: GameState): Decision | null {
        const key = this.getStateHash(state)
        const cached = this.cache.get(key)
        if (cached && !this.isStale(cached)) {
            return cached.decision
        }
        return null
    }
}

Priority Queue for Decisions:

class DecisionPriorityQueue {
    queue: PriorityQueue

    addDecision(decision: Decision) {
        const priority = this.calculatePriority(decision)
        this.queue.enqueue(decision, priority)
    }

    getNextDecision(): Decision {
        return this.queue.dequeue()
    }
}

4.5 System Integration

Main Game Loop Integration:

class StreetFighterAI {
    decisionTree: StreetFighterNode
    frameManager: FrameManager
    patternTracker: PatternTracker
    stateMachine: FighterStateMachine
    cache: DecisionCache

    update(gameState: GameState) {
        // Update all systems
        this.frameManager.update(gameState)
        this.stateMachine.update(gameState)
        this.patternTracker.update(gameState)

        // Get optimal action
        const action = this.getOptimalAction(gameState)

        // Execute action
        this.executeAction(action)
    }

    getOptimalAction(gameState: GameState): Action {
        // Check cache first
        const cached = this.cache.getCachedDecision(gameState)
        if (cached) return cached

        // Calculate new optimal action
        const action = this.decisionTree.evaluate()

        // Cache result
        this.cache.cacheDecision(gameState, action)

        return action
    }
}

Denjin Enhancement:

∀m [
    isDenjinCharged(m) →
    (
        frameAdvantage(m) += 2 ∧
        damage(m) *= 1.5 ∧
        hasStunProperty(m)
    )
]

SF Context: Ryu's mastery of the electrical properties of Hadou.

Mu no Ken (Fist of Nothingness):

∀x [
    hasMuState(x) →
    (
        perfectParryRate(x) *= 1.5 ∧
        counterHitDamage(x) *= 1.25 ∧
        ¬canUseSatsui(x)
    )
]

SF Context: Ryu's ultimate state of consciousness, transcending the Satsui no Hado.

1.3 The Path of the True Warrior

Gouken's Teachings:

∀x [
    isGoukenStudent(x) →
    (
        useHadouForDefense(x) ∧
        ¬seekDestructivePower(x) ∧
        (training(x) → spiritualGrowth(x))
    )
]

SF Context: The foundational principles taught by Master Gouken.

Ken Masters Rivalry:

∀x,y [
    (isRyu(x) ∧ isKen(y)) →
    (
        pushesEachOtherForward(x,y) ∧
        sharedTechniques(x,y) ∧
        distinctStyles(x,y)
    )
]

SF Context: The eternal rivalry that drives both warriors to greater heights.

Shoryuken Evolution:

∀x [
    mastersShinShoryuken(x) →
    (
        damage(shoryuken) *= 2 ∧
        addProperty(shoryuken, "airborne_invincible") ∧
        requiresMomentOfMu(x)
    )
]

SF Context: The pinnacle of Ryu's dragon punch mastery.

Akuma Encounter Protocol:

∀x,y [
    (isRyu(x) ∧ isAkuma(y)) →
    (
        detectKillingIntent(y) ∧
        (satsuitemptation(x) *= 3) ∧
        (
            hasMuState(x) →
            canResistRage(x)
        )
    )
]

SF Context: The ultimate test of Ryu's control over the dark hadou.

World Warrior Journey:

∀x,t [
    isWorldWarrior(x) →
    (
        (encounterNewStyle(x,t) →
            expandTechnique(x,t)) ∧
        (faceAdversity(x) →
            growStronger(x)) ∧
        seeksTrueMeaning(x)
    )
]

SF Context: Ryu's never-ending journey of self-improvement.

The Answer in Battle:

∀x [
    seeksTrueMeaning(x) →
    (
        (fightWithHonor(x) ∧
         respectOpponent(x)) →
        (
            gainInsight(x) ∧
            approachEnlightenment(x)
        )
    )
]

SF Context: Ryu's philosophy that true growth comes through honorable combat.

Hadou Evolution Path:

∀x [
    mastersDenjinHadou(x) →
    (
        (baseHadoken → shakunetsuHadoken) ∧
        (shakunetsuHadoken → denjinHadoken) ∧
        (denjinHadoken → shinHadoken)
    )
]

SF Context: The evolution of Ryu's Hadou techniques from basic energy projection to mastery of both fire and electric properties.

Satsui no Hado Stages:

∀x [
    embracesSatsui(x) →
    (
        (stage1 → chokusenhadoken) ∧
        (stage2 → ashurasenku) ∧
        (stage3 → messatsuGouHadou) ∧
        (stage4 → shunGokuSatsu)
    )
]

SF Context: The dark progression of techniques if Ryu were to fully embrace the killing intent.

Dojo Training Principles:

∀x,t [
    isTrainingDay(t) →
    (
        (meditateAtDawn(x) ∧
         practiceKata(x) ∧
         sparWithKen(x)) →
        (
            improveSpirit(x) ∧
            refineTechnique(x) ∧
            strengthenBonds(x)
        )
    )
]

SF Context: Daily life at Gouken's dojo, where Ryu and Ken trained together.

Sakura's Mentorship:

∀x,y [
    (isRyu(x) ∧ isSakura(y)) →
    (
        inspiresDetermination(x,y) ∧
        teachesHumility(x,y) ∧
        (
            seekingGuidance(y) →
            reflectsOnJourney(x)
        )
    )
]

SF Context: Ryu's relationship with his most dedicated follower, showing how teaching others leads to self-discovery.

Gouken's Final Lesson:

∀x [
    understandsPower(x) →
    (
        powerForDefense(x) ∧
        strengthForProtection(x) ∧
        victoryThroughPeace(x)
    )
]

SF Context: The ultimate teaching that helped Ryu resist the Satsui no Hado.

Sagat's Honor Match:

∀x,y [
    (isRyu(x) ∧ isSagat(y)) →
    (
        respectfulBattle(x,y) ∧
        overcomesPastSin(x) ∧
        (
            fightWithHonor(x,y) →
            mutualGrowth(x,y)
        )
    )
]

SF Context: The redemption match between Ryu and Sagat, where both warriors sought to overcome their past.

Power of Nothingness Awakening:

∀x [
    awakensNothingness(x) →
    (
        transcendsDuality(x) ∧
        achievesBalance(x) ∧
        (
            fightingIntent(x) →
            pureAction(x)
        )
    )
]

SF Context: Ryu's ultimate achievement, mastering the Power of Nothingness taught by Gouken.

World Warrior Encounters:

∀x,y [
    encountersWarrior(x,y) →
    (
        studiesTechnique(x,y) ∧
        respectsTradition(x,y) ∧
        (
            learnsFighting(x,y) →
            understandsCulture(x,y)
        )
    )
]

SF Context: Ryu's encounters with fighters worldwide, learning not just techniques but cultural wisdom.

5.1 The Complete Martial Code of Ansatsuken

Fundamental Principles:

∀x [
    followsAnsatsuken(x) →
    (
        respectsLife(x) ∧
        seeksPerfection(x) ∧
        maintainsBalance(x) ∧
        (
            facesChallenge(x) →
            growsStronger(x)
        )
    )
]

SF Context: The core tenets of Ansatsuken as taught by Gouken, emphasizing the preservation of life.

The Three Virtues:

∀x [
    masterOfVirtues(x) →
    (
        (hasHumility(x) ∧
         ¬seeksGlory(x)) ∧
        (hasDiscipline(x) ∧
         dailyTraining(x)) ∧
        (hasWisdom(x) ∧
         understandsBalance(x))
    )
]

SF Context: The three core virtues Gouken taught to both Ryu and Ken.

Path of the True Warrior:

∀x,t [
    walksTruePath(x) →
    (
        (meditateDaily(x) ∧
         trainBody(x) ∧
         cultivateSpirit(x)) ∧
        (
            encounterDarkness(x) →
            findLight(x)
        ) ∧
        (
            gainPower(x) →
            maintainHumility(x)
        )
    )
]

SF Context: Ryu's daily practice to maintain balance between power and control.

The Five Battle Principles:

∀x [
    mastersBattlePrinciples(x) →
    (
        (readOpponent(x) ∧
         anticipateIntent(x)) ∧
        (maintainDistance(x) ∧
         controlSpace(x)) ∧
        (timePrecisely(x) ∧
         seizeOpportunity(x)) ∧
        (adaptStrategy(x) ∧
         overcomeWeakness(x)) ∧
        (showRespect(x) ∧
         honorOpponent(x))
    )
]

SF Context: The fundamental combat principles of Ansatsuken, passed down through generations.

Ki Energy Mastery:

∀x [
    mastersKi(x) →
    (
        canChannelHadou(x) ∧
        (
            (focusKi(x) →
                increasePower(x)) ∧
            (balanceKi(x) →
                maintainControl(x)) ∧
            (flowKi(x) →
                achieveHarmony(x))
        )
    )
]

SF Context: The foundation of Hadou techniques and spiritual growth.

Mental Fortitude:

∀x [
    hasMentalFortitude(x) →
    (
        (facesFailure(x) →
            learnsLesson(x)) ∧
        (facesTemptation(x) →
            maintainsPurity(x)) ∧
        (facesFear(x) →
            findsStrength(x)) ∧
        (
            inBattle(x) →
            remainsFocused(x)
        )
    )
]

SF Context: The mental discipline required to resist the Satsui no Hado.

Teaching and Legacy:

∀x,y [
    isTeacher(x) →
    (
        (sharesKnowledge(x,y) ∧
         guidesGrowth(x,y)) ∧
        (
            makesMistake(y) →
            providesGuidance(x,y)
        ) ∧
        (
            showsPromise(y) →
            nurtureTalent(x,y)
        )
    )
]

SF Context: Ryu's responsibility to pass on Gouken's teachings, as shown with Sakura.