A New AI Research Introduces a Unique Approach to Indirect Reasoning (IR) Using Contrapositive and Contradiction Ideas for Automated Reasoning

With the rapid increase in the popularity of Artificial Intelligence (AI) and Large Language Models (LLMs), there has been a growing interest in augmenting the reasoning capabilities of LLMs to handle increasingly complex tasks. Existing methods, such as Chain-of-Thought and Self-Consistency, mostly function inside the Direct Reasoning (DR) paradigm. Even while these techniques work well in some situations, they struggle to solve problems in the actual world that are difficult to solve with logic alone. 

To address these limitations, a team of researchers from Nanjing University of Science and Technology, JD Explore Academy, Yunnan University and the University of Sydney has presented a unique approach to Indirect Reasoning (IR) in recent research to strengthen the reasoning ability of LLMs. This method applies the ideas of contrapositives and contradictions to IR tasks, with a particular emphasis on areas like mathematical proof and factual reasoning.

The suggested methodology has been broken down into two main phases. First, the LLMs’ general comprehension has been enhanced by utilizing the logical equivalency of contrapositives to enrich the facts and rules. Second, a collection of well-constructed prompt templates has been used to encourage LLMs to participate in IR. These templates use a proof-by-contradiction methodology, which is a logical extension of the traditional DR procedure. 

This IR method can be easily integrated with other DR approaches to improve LLMs’ reasoning powers synergistically. Experiments have been carried out on popular LLMs such as Gemini-pro and GPT-3.5-turbo, which have shown the effectiveness of the IR approach. Comparing the results to standard DR methods, a significant improvement was found in the overall accuracy of factual reasoning (27.33%) and mathematical proof (31.43%). The team has shared that the combined use of IR and DR outperformed the use of IR or DR alone, highlighting the effectiveness of the suggested technique. 

The team has summarized their primary contributions as follows.

  1. The idea of indirect reasoning in LLMs has been introduced, with an emphasis on the logical frameworks of contrapositive and contradiction. 
  2. A number of creative prompt templates have been created to encourage licensed lifelong learners to include indirect reasoning in their cognitive processes. These templates lead LLMs through the reasoning phases in an understandable way because they are based on the concepts of contrapositive and contradiction.
  1. The approach starts with the data preprocessing phase by integrating the principles of contradiction and contrapositive. By doing this, the data that LLMs receive is organized in a way that makes using indirect reasoning easier and more natural for the models.
  1. Extensive testing has shown that indirect reasoning performs better than conventional direct reasoning techniques, particularly in situations where direct reasoning is inadequate. 
  1. A  notable improvement has been seen in the overall reasoning skills of the LLMs when the indirect reasoning strategy is applied in combination with current direct reasoning tactics. Combining the advantages of both lines of thinking produces a more potent and adaptable problem-solving tool.

In conclusion, this study is a major advancement in building AI systems with reasoning skills closer to those of humans. With the creation and incorporation of indirect reasoning techniques into LLMs, a wider variety of challenging issues have been addressed with more precision and effectiveness.


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Tanya Malhotra is a final year undergrad from the University of Petroleum & Energy Studies, Dehradun, pursuing BTech in Computer Science Engineering with a specialization in Artificial Intelligence and Machine Learning.
She is a Data Science enthusiast with good analytical and critical thinking, along with an ardent interest in acquiring new skills, leading groups, and managing work in an organized manner.

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