AGI reasoning using Kyburg module a hybrid morphological parsing write out all the math for me in a dissertation so a developer can start working on it
Here is a mathematical and conceptual framework, written at a dissertation-ready level, for your hybrid model. This is structured so a developer can begin implementation, and it incorporates the Kyburg-style probability, root-pattern morphology, and the Gödel-based intuition bounds you described.
Let:
- $$ l $$: The language or domain (e.g., set of all valid statements, commands, or actions).
- $$ S
$$: A statement, command, or construct in $$ l $$. - $$ w \subseteq l
$$: The subset of $$ l $$ where $$ S $$ is supported by current evidence or context. - $$ p, q $$: Probabilistic parameters (e.g., lower and upper probability bounds, belief/plausibility, or point probability).
- $$ \text{PROB}_{w,l}(S) = (p, q)
$$: The probability assignment for $$ S $$ in language $$ l$$, with support set $$ w $$.
Given an input $$ S $$, parse it into its root-pattern components:
where $$ \text{MorphParse} $$ decomposes $$ S $$ into roots, patterns, and parameters relevant to $$ l $$.
Define the probability assignment as:
where:
- $$ w = { S' \in l \mid \text{support}(S', p, q) = \text{True} } $$
- $$ p, q $$ are determined by the most specific reference class and available evidence, following Kyburg’s rules for interval probability.
For Dempster-Shafer:
where $$ \text{Bel}(S) $$ and $$ \text{Pl}(S) $$ are belief and plausibility functions.
For Bayesian:
where $$ P(S) $$ is the Bayesian probability.
For mathematical or logical domains, define computational intuition as:
- Gödel incompleteness: Lower bound, reflecting the possibility that $$ S $$ is true but unprovable in $$ l $$ ([1][2]).
- Gödel completeness: Upper bound, reflecting the provable (or refutable) status of $$ S $$ in $$ l $$.
For a formal system $$ F $$, Gödel’s first incompleteness theorem states:
- There exists a sentence $$ G_F $$ such that if $$ F $$ is consistent, $$ F \not\vdash G_F $$ and $$ F \not\vdash \neg G_F $$.
- Thus, for some $$ S
$$, the interval is nontrivial: $$ (\text{incompleteness}, \text{completeness}) $$.
Define an EIE function:
If $$ \text{EIE} \neq \text{None} $$:
- Generate a clarifying question $$ Q(S, \text{EIE}) $$ for the user.
- Receive user response $$ S' $$.
- Update $$ S \leftarrow S'
$$, re-parse, and repeat until $$ \text{EIE} = \text{None} $$.
Because $$ w, l, S, p, q $$ are abstract variables, this framework applies to any domain:
- $$ l $$: Natural language, game commands, mathematical logic, etc.
- $$ S
$$: Any statement or action in $$ l $$. - $$ w $$: Context-specific support set.
- $$ p, q $$: Chosen probability semantics for the domain.
def process_input(S, l):
while True:
roots, patterns = MorphParse(S)
w, p, q = ProbabilisticAssignment(roots, patterns, l)
error = EIE(S, w, p, q)
if error is not None:
question = GenerateQuestion(S, error)
S = GetUserResponse(question)
else:
Execute(S, w, p, q)
breakGiven $$ S $$ in a formal system $$ F $$:
- Compute $$ \text{PROB}_{F}(S) = (\text{Gödel incompleteness}, \text{Gödel completeness}) $$.
- If $$ S $$ is independent (by Gödel), the interval is nontrivial ([1][2]).
- If $$ S $$ is provable or refutable, the interval collapses to a point.
- Each module (morphological parsing, probabilistic assignment, EIE detection, dialogue) should be implemented as an independent, testable component.
- Use existing libraries for probabilistic reasoning and natural language parsing where possible.
- Ensure all variables are abstract and parameterizable for cross-domain use.
References:
- [1] Stanford Encyclopedia of Philosophy: Gödel's Incompleteness Theorems
- [2] Wikipedia: Gödel's Incompleteness Theorems
This mathematical framework gives developers a precise, modular foundation for building your hybrid, explainable, and domain-general AI system.
Citations:
[1] Gödel's Incompleteness Theorems https://plato.stanford.edu/entries/goedel-incompleteness/
[2] Gödel's incompleteness theorems - Wikipedia https://en.wikipedia.org/wiki/G%C3%B6del's_incompleteness_theorems
[3] How Gödel's Proof Works | Quanta Magazine https://www.quantamagazine.org/how-godels-proof-works-20200714/
[4] Most general formulation of Gödel's incompleteness theorems https://mathoverflow.net/questions/32318/most-general-formulation-of-g%C3%B6dels-incompleteness-theorems
[5] [PDF] Gödel's Incompleteness Theorem https://www.math.uni-hamburg.de/home/khomskii/recursion/Goedel.pdf
[6] Gödel's Incompleteness Theorem - Marcus du Sautoy - YouTube https://www.youtube.com/watch?v=I4pQbo5MQOs
[7] A concrete example of Gödel's Incompleteness theorem https://math.stackexchange.com/questions/63038/a-concrete-example-of-g%C3%B6dels-incompleteness-theorem
[8] How can you formalize the metamathematics conventionally used to ... https://mathoverflow.net/questions/307080/how-can-you-formalize-the-metamathematics-conventionally-used-to-state-godel-s-t
Perfect! Here’s a downloadable, all-in-one file containing everything you need to set up your Kyburg Morphological Parsing Engine repository. Just download the files, or copy their contents, and upload them to your new GitHub repository (kyburg-morphology or any name you choose).
# Kyburg Morphological Parsing Engine
This repository contains a data-driven, language-agnostic morphological parsing module, inspired by Semitic (e.g., Hebrew) verbal morphology. It is intended as a component of the Kyburg AGI project and is ready for use or extension in Python, Java, and other environments.
## Features
- Systematic, compositional morphology for English verbs.
- Portable: Integrate with Python, Java, Verse, or any language.
- Data-driven: Patterns defined in `morphology_patterns.json`.
- NLP-ready: For both input and output transformation.
## Quick Start
### Python
```python
from morphology_engine import MorphologyEngine
engine = MorphologyEngine()
print(engine.generate("grow", "causative")) # maGROWen
print(engine.parse("maGROWen")) # ('grow', 'causative')
```
### Java
See `MorphologyEngine.java` for a minimal working version.
## Patterns
See [`morphology_patterns.json`](./morphology_patterns.json) for all supported morphological templates.
## Documentation
See [`docs/MORPHOLOGY_ENGINE.md`](./docs/MORPHOLOGY_ENGINE.md) for full technical details.
## Contributing
1. Fork this repo
2. Add/modify morphological templates or code
3. Open a pull request!
---
**Maintainer:** [314project](https://github.com/314project){
"simple": {"template": "{ROOT}", "description": "To X"},
"causative": {"template": "ma{ROOT}en", "description": "To cause to X"},
"intensive": {"template": "i{ROOT}itate", "description": "To do X intensely"},
"passive": {"template": "{ROOT}ed", "description": "To be Xed"},
"reflexive": {"template": "se{ROOT}", "description": "To X oneself"},
"repetitive": {"template": "re{ROOT}", "description": "To X again"}
}import json
import re
class MorphologyEngine:
def __init__(self, patterns_file="morphology_patterns.json"):
with open(patterns_file) as f:
self.patterns = json.load(f)
def generate(self, root, pattern_name):
pattern = self.patterns[pattern_name]["template"]
return pattern.replace("{ROOT}", root.upper())
def parse(self, word):
for name, pat in self.patterns.items():
regex = pat['template'].replace('{ROOT}', r'([A-Z]+)')
match = re.fullmatch(regex, word)
if match:
return match.group(1).lower(), name
return None, Noneimport java.util.Map;
import java.util.regex.*;
import java.nio.file.*;
import com.fasterxml.jackson.databind.ObjectMapper;
public class MorphologyEngine {
private Map<String, Map<String, String>> patterns;
public MorphologyEngine(String jsonPath) throws Exception {
ObjectMapper mapper = new ObjectMapper();
patterns = mapper.readValue(
Files.readAllBytes(Paths.get(jsonPath)),
Map.class
);
}
public String generate(String root, String patternName) {
String pattern = patterns.get(patternName).get("template");
return pattern.replace("{ROOT}", root.toUpperCase());
}
public ParseResult parse(String word) {
for (Map.Entry<String, Map<String, String>> entry : patterns.entrySet()) {
String name = entry.getKey();
String pat = entry.getValue().get("template").replace("{ROOT}", "([A-Z]+)");
Pattern regex = Pattern.compile(pat);
Matcher matcher = regex.matcher(word);
if (matcher.matches()) {
return new ParseResult(matcher.group(1).toLowerCase(), name);
}
}
return null;
}
public static class ParseResult {
public final String root;
public final String pattern;
public ParseResult(String root, String pattern) {
this.root = root;
this.pattern = pattern;
}
}
}# Python
__pycache__/
*.pyc
# Java
*.class
*.jar
# OS generated
.DS_Store
Thumbs.db# Kyburg AGI Morphological Parsing Module
This module implements systematic, templatic morphological parsing for English verbs, inspired by Semitic morphology. It is designed for integration into the Kyburg AGI project and supports Python, Java, and other languages.
## Features
- **Data-driven**: Morphological rules in `morphology_patterns.json`
- **Language-agnostic**: Core logic can be used in any language
- **NLP Interface**: Generates and parses verb forms for input/output
## Usage
### 1. Define Patterns
See `morphology_patterns.json`:
```json
{
"causative": {"template": "ma{ROOT}en", "description": "to cause to X"}
}
```
### 2. Generate a Form
```python
engine = MorphologyEngine()
word = engine.generate("grow", "causative") # maGROWen
```
### 3. Parse a Form
```python
root, pattern = engine.parse("maGROWen") # ("grow", "causative")
```
### 4. Extend
Add new patterns to the JSON file. All bindings (Python, Java, etc.) will support them.
## Example Patterns
| Name | Template | Meaning |
|------------|-----------------|---------------------|
| simple | {ROOT} | To X |
| causative | ma{ROOT}en | To cause to X |
| intensive | i{ROOT}itate | To do X intensely |
| passive | {ROOT}ed | To be Xed |
| reflexive | se{ROOT} | To X oneself |
| repetitive | re{ROOT} | To X again |
## Integration
- Use as a Python/Java library.
- Or wrap as a REST API for cross-language use.
- Or embed in your AGI's NLP pipeline.
---
**Maintainer:** [314project](https://github.com/314project)new addition go to https://www.perplexity.ai/search/this-sounds-familiar-https-you-e9vK_g0NSTuoRm0.c5CpSg
You can now:
- Create a new repo on GitHub.
- Upload these files (copy-paste or upload directly).
- Share your repo link with other developers!
If you want a step-by-step guide for uploading, or want to add more features (like a REST API or Verse code), just let me know!