The Four Color Conjecture is a well-known coloring problem of graphs. Since its advent, there are a lot of solvers. One of the early pioneers was Percy John Heawood, who has proved the Five Color Theorem. In addition,...The Four Color Conjecture is a well-known coloring problem of graphs. Since its advent, there are a lot of solvers. One of the early pioneers was Percy John Heawood, who has proved the Five Color Theorem. In addition, Kempe first demonstrated an important conclusion about planar graph: in any map, there must be a country with five or fewer neighbors. Kempe’s proof proposed two important concepts—“configuration” and “reducibility”, which laid the foundation for further solving the Four Color Problem. The Four Color Problem had previously been proved by use of computer. Based on Kempe’s concepts of “configuration” and “reducibility”, this paper attempts to provide a non-computer proof of the Four Color Problem through rigorous logical analysis.展开更多
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
基于扩展规则的方法是一种定理证明方法.在IER(improved extension rule)扩展规则算法的基础上,提出了IMOM(improved maximum occurrences on clauses of maximumsize)和IBOHM(improved BOHM)启发式策略,并将两种启发式策略用于IER算法...基于扩展规则的方法是一种定理证明方法.在IER(improved extension rule)扩展规则算法的基础上,提出了IMOM(improved maximum occurrences on clauses of maximumsize)和IBOHM(improved BOHM)启发式策略,并将两种启发式策略用于IER算法中,有指导性地选择限定搜索空间的子句,设计并实现了算法IMOMH_IER和IBOHMH_IER.实验结果表明,由于这两种启发式策略能够选择较为合适的搜索空间,可以尽快地判定出原问题是否可满足,故其速度平均能够达到原有算法DR(directional resolution)和IER的10～200倍.展开更多
文摘The Four Color Conjecture is a well-known coloring problem of graphs. Since its advent, there are a lot of solvers. One of the early pioneers was Percy John Heawood, who has proved the Five Color Theorem. In addition, Kempe first demonstrated an important conclusion about planar graph: in any map, there must be a country with five or fewer neighbors. Kempe’s proof proposed two important concepts—“configuration” and “reducibility”, which laid the foundation for further solving the Four Color Problem. The Four Color Problem had previously been proved by use of computer. Based on Kempe’s concepts of “configuration” and “reducibility”, this paper attempts to provide a non-computer proof of the Four Color Problem through rigorous logical analysis.
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.
文摘基于扩展规则的方法是一种定理证明方法.在IER(improved extension rule)扩展规则算法的基础上,提出了IMOM(improved maximum occurrences on clauses of maximumsize)和IBOHM(improved BOHM)启发式策略,并将两种启发式策略用于IER算法中,有指导性地选择限定搜索空间的子句,设计并实现了算法IMOMH_IER和IBOHMH_IER.实验结果表明,由于这两种启发式策略能够选择较为合适的搜索空间,可以尽快地判定出原问题是否可满足,故其速度平均能够达到原有算法DR(directional resolution)和IER的10～200倍.
