A Theory of Formalisms for Representing Knowledge
Authors: Heng Zhang, Guifei Jiang, Donghui Quan
AAAI 2025 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | To address these issues, we propose a general framework to capture various knowledge representation formalisms in which we are interested. Within the framework, we find a family of universal knowledge representation formalisms, and prove that all universal formalisms are recursively isomorphic. Moreover, we show that all pairwise intertranslatable formalisms that admit the padding property are also recursively isomorphic. These imply that, up to an offline compilation, all universal (or natural and equally expressive) representation formalisms are in fact the same, which thus provides a partial answer to the aforementioned dispute. [...] our goal is to obtain rigorous conclusions from a broad and inclusive framework through meticulous mathematical demonstrations, thereby deepening the understanding of the nature of representation. |
| Researcher Affiliation | Academia | Heng Zhang1 , Guifei Jiang2, Donghui Quan1 1Zhejiang Lab, Hangzhou, Zhejiang 311121, China 2College of Software, Nankai University, Tianjin 300350, China EMAIL, EMAIL, EMAIL |
| Pseudocode | Yes | Procedure 1: The Workflow of M Input: D D and φ Q Output: Accept iff (D, φ) cl(K(M)) 1 Initialize all positions in F to false; 2 Initialize all positions in c to 1; 3 T[0] (M, D, φ); /* Set the root task */ 4 p[0] 1; /* The root has no parent node */ 5 n 1; /* There is one task in the current array */ 6 for k 0 to do 7 for i 0 to min(n 1, k) do 8 /* Simulate multiple tasks in parallel */ 9 Perform the (k i)-th step of T[i] if it exists; 10 if T[i] has just succeeded then 11 F[i] true; |
| Open Source Code | No | The paper does not contain any explicit statements or links indicating that source code for the described methodology is publicly available. The link to 'https://arxiv.org/abs/2412.11855' is for an extended version of the paper, not a code repository. |
| Open Datasets | No | The paper discusses abstract concepts of 'databases' and 'queries' within a theoretical framework. For example, 'Given a database D, a knowledge base K and a query φ, determine whether φ is inferable from D and K.' It does not mention or use any specific, named datasets, nor does it provide any links or citations to publicly available datasets. |
| Dataset Splits | No | The paper focuses on theoretical contributions and does not use any specific datasets that would require splitting into training, validation, or test sets. |
| Hardware Specification | No | The paper is a theoretical work and does not describe any experimental setup that would require hardware specifications. The mention of 'Turing machine' refers to a conceptual model of computation, not physical hardware used for experiments. |
| Software Dependencies | No | The paper is a theoretical work and does not describe any experimental setup that would require specific software dependencies with version numbers. It references logical systems like Prolog and description logics as examples of formalisms, not as software used for implementation. |
| Experiment Setup | No | The paper is purely theoretical, presenting definitions, propositions, and theorems. It does not include any experimental section or details about hyperparameters, training configurations, or model initialization. |