We present a method for using type theory to solve decision making problem. Our method is based on the view that decision making is a special kind of theorem proving activity. An isomorphism between problems and types...We present a method for using type theory to solve decision making problem. Our method is based on the view that decision making is a special kind of theorem proving activity. An isomorphism between problems and types, and solutions and programs has been established to support this view which is much similar to the Curry-Howard isomorphism between propositions and types, and proofs and programs. To support our method, a proof development system called PowerEpsilon has been developed, and the synthesis of a decision procedure for validity of first-order propositional logic is discussed to show the power of the system.展开更多
该文利用大语言模型(large language models,LLMs)与形式化验证技术实现线性数据结构定理的自动证明,并提出通过引入引理来提高线性数据结构定理证明效率的方法.首先,利用LLMs生成定理的非形式化证明及形式化证明草图;然后,基于非形式...该文利用大语言模型(large language models,LLMs)与形式化验证技术实现线性数据结构定理的自动证明,并提出通过引入引理来提高线性数据结构定理证明效率的方法.首先,利用LLMs生成定理的非形式化证明及形式化证明草图;然后,基于非形式化证明构造相关引理进行形式化验证以确保引理的正确性;最后,通过引入引理,辅助定理形式化验证,降低现有自动定理证明工具在处理形式化证明草图时的难度,提高自动证明效率.实验结果显示线性数据结构定理的证明成功率从54.55%提升至68.18%,这充分表明引理在定理证明过程中发挥了关键作用.展开更多
文摘We present a method for using type theory to solve decision making problem. Our method is based on the view that decision making is a special kind of theorem proving activity. An isomorphism between problems and types, and solutions and programs has been established to support this view which is much similar to the Curry-Howard isomorphism between propositions and types, and proofs and programs. To support our method, a proof development system called PowerEpsilon has been developed, and the synthesis of a decision procedure for validity of first-order propositional logic is discussed to show the power of the system.
文摘该文利用大语言模型(large language models,LLMs)与形式化验证技术实现线性数据结构定理的自动证明,并提出通过引入引理来提高线性数据结构定理证明效率的方法.首先,利用LLMs生成定理的非形式化证明及形式化证明草图;然后,基于非形式化证明构造相关引理进行形式化验证以确保引理的正确性;最后,通过引入引理,辅助定理形式化验证,降低现有自动定理证明工具在处理形式化证明草图时的难度,提高自动证明效率.实验结果显示线性数据结构定理的证明成功率从54.55%提升至68.18%,这充分表明引理在定理证明过程中发挥了关键作用.
