SML (Stack-Map-Loglang) 📐

English | 中文

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SML (English)

An experimental formal semantic deduction engine and logical language (Loglang) architecture based on a 6-Stack, 1-Stream, 1-Register, and 8-Map concatenative state machine.

Note

STATUS: EXPERIMENTAL SPECIFICATION & PROTOTYPE (v1.2)
This project is currently an experimental formal specification and prototype. The core reduction engine has been validated against a comprehensive suite of 10 representative benchmark cases (covering a 31-variable full-scale stress test, deeply nested and coordinate relative clauses, generalized quantifiers, donkey sentences, scale semantics, dynamic permutation pipelines, and tri-level negation).

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🚀 Overview

Traditional formal semantics (e.g., Montague Grammar) typically relies on compositional syntactic trees, type-driven functional application, and Quantifier Raising (QR). Conversely, classical logical languages (such as Lojban) encode predicates as rigid, predetermined tuple slots (x₁, ..., xₙ), which often introduces substantial lexical memorization burdens and necessitates elidable terminators (ku, vau, kei, etc.) to resolve structural ambiguities.

SML (Stack-Map-Loglang) v1.2 explores an alternative, tree-free operational model: a linear concatenative abstract machine with relational graph construction and quantifier closure.

By treating all lexical content as unary base sets (:S), dynamic event reification (Ω), and binary relations (:R), SML establishes an incremental state-transition system. Coupled with higher-order continuation closures on a Wait Stack (WT), a dual-track restrictor/nuclear scope mapping (Imap / Omap), a single scalar focus register (⟨F⟩), and a permutation pipeline (PR), SML resolves complex quantifier scopings, nested/coordinate relative clauses, and tri-level negations without syntax trees or structural closing delimiters.

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🏗️ Abstract Machine Model (v1.2)

State = ⟨ IP, NM, QN, WT, CM, PR, OP, ⟨F⟩, Imap, Omap, Qmap, Smap, Mmap, Fmap, Emap, Map ⟩

1. The 6 Stacks + 1 Stream + 1 Scalar Register (Right end is Top)

Component	Identifier	Description
Input Stack	IP	Queue of tokens, instruction blocks, and unpacked macros awaiting execution.
Number Stream	NM	Infinite generator of fresh, monotonically increasing integer IDs (1, 2, 3, ...).
Quantifier Queue	QN	Queue storing entity IDs awaiting quantifier closure (Build !).
Wait Stack	WT	Staging area for higher-order continuation closures (λa. B), intermediate entities, and modifier polarities.
Component Stack	CM	Storage for active arguments and their truth polarities (Polarity Entity).
Permutation Stack	PR	Buffer and pipeline for permutation operations and dynamic combinator adjustments (Traverse !).
Output Stack	OP	Immediate working memory for atomic reductions, boolean logic, and relation triggers.
Focus Register	⟨F⟩	Scalar integer register tracking the core host entity currently undergoing clause closure.

2. The 8 Associative Maps (Keys are Entity IDs)

Map	Identifier	Function
Restrictor Map	Imap	Accumulates nominal restrictions and relative clause formulas inside {α_i ∈ S_i | Imap[i]}.
Nuclear Scope Map	Omap	Accumulates asserted predicate propositions.
Quantifier Map	Qmap	Maps entity variables to generalized quantifier forces (default: Exist / ∃).
Base Set Map	Smap	Maps entity IDs to base category names or event domains (e.g., "Cat", "Ω").
Mode Map	Mmap	Polarity mode: True writes relations to Imap (Inner), False writes to Omap (Outer).
Focus Flag Map	Fmap	Identifies whether an entity is a protected host of an active relative clause.
Environment Map	Emap	Dynamic variable alias registry for cross-clause pronoun coreference (Upload / Download).
Lexical Macro Map	Map	Global dictionary mapping lexical set strings to their predicate frame macros.

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💡 Key Architectural Features (v1.2)

• Noun-Verb Parity:
  Verbs and nouns are unified as unary sets (:S). Verbal predicate frames are dynamically unpacked via Map, allowing verbs to natively host relative clauses and higher-order adjuncts just like nouns.
• Currying Continuation Closures on WT:
  Pre-modifiers and relation builders are staged on WT as λ-closures, resolving surface word-order mismatches through post-order beta-substitutions without syntax trees.
• Generalized Quantifier Duality (Imap vs Omap):
  Quantification cleanly separates restrictors from nuclear scopes, naturally accommodating Generalized Quantifiers (such as proportional quantifiers, e.g., More Than Half).
• Single Scalar Focus Register with Invariant Restoration:
  Replacing dedicated clause stacks with ⟨F⟩ and atomic Release macros allows both nested and coordinate relative clauses to evaluate with automatic host reset.
• Permutation Pipeline (PR) and Church-Peano Recursion:
  High-arity quantifiers and permutation adjustments are driven by a dynamic permutation stack and list-peeling recursion, preventing fixed-arity macro combinatorial explosion.
• Tri-Level Orthogonal Negation System:
  Local relation negation on WT, constituent role negation on CM, and propositional negation on QN are completely decoupled, eliminating scope drift.

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🌐 Linguistic Philosophy: The Relational "Annotation" Model

Rather than hardcoding rigid metaphysical assumptions into the grammar (e.g., prescribing a specific tense logic, or baking in a fixed Kripkean possible-world modal frame), SML treats language as an open topological graph construction and quantifier closure process:

• Grammar as an Agnostic Canvas:
  The core abstract machine enforces only topological conservation and generalized quantifier closure. It does not dictate how speakers must conceptualize time, space, or probability.
• Semantics as Progressive Annotation:
  Complex linguistic phenomena are represented as iterative binary relations (R) attached to entities (S) or events (Ω):
  • Tense & Aspect: Relational spatiotemporal coordinates attached to event entities (e.g., Occurred_At(e, t)).
  • Modality & Probability: Graded attributes (e.g., Probability(e, 0.5)) rather than rigid modal operators.
  • Degree Semantics: Gradable adjectives and adverbs are treated as measurement relations over normalized scale sets (0~1:S).
  • Questions: Represented via named placeholder variables awaiting contextual resolution.
• Arbitrary Tree and DAG Topologies:
  Because postfix chains construct arbitrary nested relational trees, and dynamic anaphora (Upload / Download) enables cross-branch coreference, the system naturally expresses arbitrary Directed Acyclic Graphs (DAGs).

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📂 Repository Structure

.
├── English/
│   ├── Examples.txt         # Complete execution traces for 10 benchmark test sentences
│   ├── Others.txt           # Linguistic philosophy, annotative model, and Two-Pass pipeline
│   ├── RuleSet.txt          # Formal 29 reduction rules and abstract machine specification
│   └── SurfaceSyntax.md     # Surface syntax guide and macro behavior specification
├── 中文/
│   ├── 例句.txt              # 10 个完整基准测试例句推导与机器状态输出记录
│   ├── 其他.txt              # 语言哲学、关系批注模型与自然语言化演进备忘录
│   ├── 规则集.txt            # 29 条形式规约规则与状态机底层规范
│   └── 表层语法.md          # 表层语法结构、宏观栈语义与核心宏模板速查
├── src/
│   └── Main.hs              # Reference implementation (Haskell prototype)
└── README.md                # Project documentation (Bilingual)

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📝 Design, Authorship & AI Disclosure

• Theoretical Foundations & System Design:
  The formal logical framework, the 6-Stack 1-Stream 1-Register 8-Map abstract machine, the relational annotation model, the 29 reduction rules, and the macro calculus were conceived, formulated, and designed entirely and independently by the author.
• Surface Syntax Document Notice:
  The surface syntax specifications (English/SurfaceSyntax.md and 中文/表层语法.md) were compiled with AI assistance. The author explained the specific functionality of each macro bullet-by-bullet in conversational terms. The AI was then instructed to organize and structure these notes into the formal specification. Because AI synthesis may introduce subtle descriptive discrepancies, in case of any inconsistency between the surface syntax document and actual engine behavior, please treat Examples.txt / 例句.txt as the definitive ground truth.

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SML (中文)

基于“六栈一流水一标量寄存器八映射”（6-Stack 1-Stream 1-Register 8-Map）串接式状态机的形式语义推导引擎与逻辑语言（Loglang）架构。

Note

当前状态：试验性形式规范与原型系统 (v1.2)
本项目目前处于试验性形式规范与原型机探索阶段。核心状态机规约引擎已在 10 个具有代表性的典型基准用例（涵盖包含 31 个变量的超长长难句极限压力测试、多层嵌套动词定语从句、广义受限量词、经典驴子句、标度语义学、置换栈动态流水线以及三轨否定）上完成了推导自洽性验证。

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🚀 项目概述

经典形式语义学（如蒙太格语法）高度依赖句法树递归、类型驱动的应用与量词提升（QR）；而传统人造逻辑语（如 Lojban）则普遍将谓词固定为刚性的位点结构（x₁, ..., xₙ），这不仅带来了沉重的词汇位点记忆负担，还需要依靠庞杂的括号终止符（ku, vau, kei 等）来消除句法歧义。

SML (Stack-Map-Loglang) v1.2 探索了一种去语法树化的串接式线性状态机路径。

系统将语言中的实词统一抽象为单目基底集合（:S），动作统一本体化为一阶事件个体（Ω），多元关系统一分解为二元谓词（:R）。通过等待栈（WT）上的高阶延续闭包、限制域与核域的双轨映射（Imap / Omap）、焦点单值寄存器（⟨F⟩）与排列流水线栈（PR），SML 旨在不构建显式句法树、不书写闭合括号的前提下，线性求解复杂量词辖域、深层嵌套与并列定语从句，以及细粒度题元否定。

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🏗️ 抽象机模型 (v1.2)

State = ⟨ IP, NM, QN, WT, CM, PR, OP, ⟨F⟩, Imap, Omap, Qmap, Smap, Mmap, Fmap, Emap, Map ⟩

1. 六个线性栈 + 一个自然数流 + 一个标量寄存器（均以右端为栈顶）

组件名称	缩写标识	功能说明
输入栈	IP	待执行的指令块、Token 流与解包后的宏指令序列。
数字流	NM	预置无限递增自然数生成器（1, 2, 3, ...），为新实体分配全局唯一数值标号。
量化栈	QN	论元实体排队栈，维护等待执行受限量词闭包（Build !）的实体队列。
等待栈	WT	暂存区，维护高阶柯里化延续闭包（λa. B）、实体中间态及修饰语极性。
成分栈	CM	规约完毕的论元实体及真值极性游标栈（格式为 Polarity Entity）。
排列栈	PR	置换群操作流水线，用于动态调整量化置换元组与执行顺序（Traverse !）。
输出栈	OP	即时运算与规约工作台，执行原子规约、布尔逻辑及关系连接触发。
焦点寄存器	⟨F⟩	标量整数寄存器，记录当前正在执行闭包的核心宿主实体标号。

2. 八个关联映射表（键均为实体数字标号）

映射表	缩写标识	用途说明
限制域映射	Imap	累积名词内涵修饰与定语从句条件（{α_i ∈ S_i | Imap[i]}）。
核域映射	Omap	累积主谓陈述命题。
量化映射	Qmap	记录实体的广义量词类型（缺省为 Exist / ∃）。
集合映射	Smap	记录实体所属的基底类别名称或事件空间（如 "猫", "Ω"）。
模式映射	Mmap	写入模式布尔值：True 表示内模式（写入 Imap），False 表示外模式（写入 Omap）。
焦点标记	Fmap	标记该实体是否为当前定语从句受保护的宿主。
环境映射	Emap	动态变量别名映射，用于跨子句代词照应与驴子句消解（Upload / Download）。
全局宏映射	Map	全局词汇字典，建立从集合名称字符串到对应格框宏代码的映射。

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💡 v1.2 核心设计特征

• 名谓词本体平权（Noun-Verb Parity）：
  动词不再拥有特殊的固定语法位点，而是作为普通的集合词（:S）进入成分栈。在遇到执行触发时，通过全局字典 Map 动态解构出二元题元格框与主事件 Ω，使动词天然能像名词一样接受定语从句修饰。
• WT 栈柯里化延续闭包（Currying Continuation）：
  将关系修饰与延迟装配抽象为驻留在 WT 栈上的高阶 λ 闭包，当宿主实体就位时自动触发代换求值，消除了串接式语言逆波兰序与人类前置修饰语习惯的冲突。
• 广义量词双轨切分（Imap 与 Omap 对偶）：
  严格划分限制域与核域，配合模式翻转，原生支持蒙太格广义量词理论（GQ Theory，如“多于一半”等比例量词）。
• 标量焦点寄存器 ⟨F⟩ 与宿主原位复位：
  通过 释放宏（探测 Fmap 并按需引渡）与原子复位机制，废除冗余的专用从句栈，且对称统一了嵌套从句与并列从句。
• 排列栈流水线与皮亚诺列表递归：
  引入置换群生成元思想与列表剥离递归（Church-Peano 计数），消除了传统固定元数量化宏的阶乘爆炸问题。
• 完备的三轨正交否定系统：
  局部关系修饰否定（局部否定宏 on WT）、题元成分独立否定（句内否定宏 on CM）与主陈述命题全局求反（整体否定宏 on QN）完全解耦，作用域永不漂移。

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🌐 语言学哲学：开放的“关系批注模型”

SML 在语言哲学上放弃了在语法底层硬编码特定形而上学或物理学模型的做法（不预设特定的绝对时空观，也不在语法中硬编码固定的克里普克可能世界集合）：

• 语法作为不可知论拓扑画布：
  底层抽象机仅保障拓扑守恒（ΔR = ΔS）与广义受限量词闭包的严密性，把世界观的解释权彻底交还给说话者。
• 语言即批注（Annotative Model）：
  浩瀚的语言学范畴被统一为向核心实体或事件追加的二元修饰边（R）：
  • 时态与体貌：作为事件变元的二元时空坐标挂载（如 发生于(e, t)、参考系(e, 地表)）；
  • 情态与可能性：作为渐进的程度与证据批注（如 可能性(e, 0.5)、证据源(e, 亲眼所见)）；
  • 标度语义学：形容词与副词被视作在规范化度量区间（如 0~1:S）上的二元测度关系与量化变换；
  • 疑问句：视为保留未封闭占位符变元（Named Holes）的开放模板查询。
• 从树状修饰到有向无环图（DAG）：
  串接操作能够构造任意深度的嵌套修饰树；配合代词照应机制（Upload / Download），各分支节点可跨作用域建立有向边，使语言表达力自然覆盖任意有向无环图（DAG）。

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📂 仓库目录结构

.
├── English/
│   ├── Examples.txt         # 10 个基准测试例句运行追踪完整记录 (英文版)
│   ├── Others.txt           # 架构设计思想、关系批注模型与双阶段解析备忘录 (英文版)
│   ├── RuleSet.txt          # 29 条形式规约规则与状态机底层规范 (英文版)
│   └── SurfaceSyntax.md     # 表层语法规范与宏观栈语义速查 (英文版)
├── 中文/
│   ├── 例句.txt              # 10 个完整基准测试例句推导与机器状态输出记录
│   ├── 其他.txt              # 语言哲学、关系批注模型与自然语言化演进备忘录
│   ├── 规则集.txt            # 29 条形式规约规则与状态机底层规范
│   └── 表层语法.md          # 表层语法结构、宏观栈语义与核心宏模板速查
├── src/
│   └── Main.hs              # 规约状态机参考实现代码（Haskell 原型）
└── README.md                # 双语项目主文档

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📝 关于设计、原创性与 AI 辅助说明

• 系统理论与内核设计：
  SML 的理论基石、“六栈一流水一标量寄存器八映射”抽象机模型、关系批注模型、29 条状态转移规约规则体系以及量化消解代数，完全由作者本人独立构思、数学化定义并实现。
• 表层语法文档说明：
  表层语法规范文件（中文/表层语法.md 与 English/SurfaceSyntax.md）是由作者以逐条列点、口语化的方式详细说明每个宏的具体功能，由 AI 协助整理归纳而成。由于 AI 在整理转化过程中可能存在局部的理解偏差或疏漏，当前阶段若发现表层语法描述与实际推导行为存在不一致，请一律以 例句.txt / Examples.txt 的实际推导结果为准。作者会在后续版本中对表层语法的正规文法进行人工审校与严密规范。