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ENGL

2007

2007

Abstract—In any formal theory, a proof is a sequence of well formed formulas (wﬀ). Here, we consider the digraph whose nodes are proofs and the edges are pairs of proofs such that the second proof is obtained from the ﬁrst proof by the application of an inference rule. A path is thus a proof extension, and the corresponding shortest path problem consists of ﬁnding the minimum number of inference rules applications in order to extend a proof from another given proof. A slight modiﬁcation is considered by introducing a probability associated to each inference rule from a current proof. Also a corresponding version of the Longest Common Subsequence problem is stated: Given two proofs, ﬁnd the longest common subproof. The dual problem is to ﬁnd the Shortest Common Superproof. We discuss these problems with respect to the decidability of the given formal theory. Our main purpose is to point similarities among the LCS problem, rather important in areas as Bioinformatics, and th...

Related Content

Added |
13 Dec 2010 |

Updated |
13 Dec 2010 |

Type |
Journal |

Year |
2007 |

Where |
ENGL |

Authors |
Guillermo Morales-Luna |

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