A. M. Turing. Practical forms of type theory. The journal of symbolic logic, vol. 13 (1948), pp. 80–94.

1949 ◽  
Vol 14 (1) ◽  
pp. 67-68
Author(s):  
Maurice L'abbé
Keyword(s):  
Type Theory ◽  
Symbolic Logic

scholarly journals Group-Assign: Type Theoretic Framework for Human AI Orchestration

2021 ◽  
Author(s):  
Aik Beng Ng ◽  
Simon See ◽  
Zhangsheng Lai ◽  
Shaowei Lin
Keyword(s):  
Type Theory ◽  
Information Age ◽  
Symbolic Logic ◽  
Human Language ◽  
Theoretic Description

In today’s Information Age, we work under the constant drive to be more productive. Unsurprisingly, we progress towards being an AI-augmented workforce where we are augmented by AI assistants and collaborate with each other (and their AI assistants) at scale. In the context of humans, a human language suffices to describe and orchestrate our intents (and corresponding actions) with others. This, however, is clearly insufficient in the context of humans and machines. To achieve this, communication across a network of different humans and machines is crucial. With this objective, our research scope covers and presents a type theoretic framework and language built upon type theory (a branch of symbolic logic in mathematics), to enable the collaboration within a network of humans and AI assistants. While the idea of human-machine or human-computer collaboration is not new, to the best of our knowledge, we are one of the first to propose the use of type theory to orchestrate and describe human-machine collaboration. In our proposed work, we define a fundamental set of type theoretic rules and abstract functions Group and Assign to achieve the type theoretic description, composition and orchestration of intents and implementations for an AI-augmented workforce.

Type Theory and Formal Proof

2009 ◽  
Author(s):  
Rob Nederpelt ◽  
Herman Geuvers
Keyword(s):  
Type Theory ◽  
Formal Proof

Computational Models for Multilayered Composite Shells with Application to Tires

1996 ◽  
Vol 24 (1) ◽  
pp. 11-38 ◽  
Author(s):  
G. M. Kulikov
Keyword(s):  
Type Theory ◽  
Computational Models ◽  
Geometrical Nonlinearity ◽  
Higher Order ◽  
Stress Strain ◽  
Strain Fields ◽  
First Order ◽  
Timoshenko Type ◽  
Joint Influence ◽  
Discrete Layer

Abstract This paper focuses on four tire computational models based on two-dimensional shear deformation theories, namely, the first-order Timoshenko-type theory, the higher-order Timoshenko-type theory, the first-order discrete-layer theory, and the higher-order discrete-layer theory. The joint influence of anisotropy, geometrical nonlinearity, and laminated material response on the tire stress-strain fields is examined. The comparative analysis of stresses and strains of the cord-rubber tire on the basis of these four shell computational models is given. Results show that neglecting the effect of anisotropy leads to an incorrect description of the stress-strain fields even in bias-ply tires.

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