When humans evaluate the validity of a logical conclusion, they naturally consider its meaning and its context, allowing them to focus on relevant information and to avoid unnecessary inferences. For example, when asked to prove that all hammocks are also beds, they will certainly not draw conclusions about vehicles or weapons. In contrast, automated theorem provers typically do not account for the contextual meaning of a conclusion when selecting inference steps. Existing heuristics for selecting the clause for the next inference step usually ignore the meaning of symbol names, overlooking valuable contextual information. As a result, in the example above, clauses with symbol names such as weapon or vehicle could well be found in the processed clauses. However, since these clauses are not required for the actual proof, they are not helpful to the prover and tend to distract from the actual proof task. In this paper, we present an approach that uses natural language processing techniques to align the selection of the clause for the next inference step with the meaning of the proof goal. Our implementation and experimental results show that this method not only increases the number of successful proofs but also reduces the number of clauses processed during proof search.

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Context-Aware Clause Selection Using Symbol Name Meanings in Theorem Proving

  • Claudia Schon

摘要

When humans evaluate the validity of a logical conclusion, they naturally consider its meaning and its context, allowing them to focus on relevant information and to avoid unnecessary inferences. For example, when asked to prove that all hammocks are also beds, they will certainly not draw conclusions about vehicles or weapons. In contrast, automated theorem provers typically do not account for the contextual meaning of a conclusion when selecting inference steps. Existing heuristics for selecting the clause for the next inference step usually ignore the meaning of symbol names, overlooking valuable contextual information. As a result, in the example above, clauses with symbol names such as weapon or vehicle could well be found in the processed clauses. However, since these clauses are not required for the actual proof, they are not helpful to the prover and tend to distract from the actual proof task. In this paper, we present an approach that uses natural language processing techniques to align the selection of the clause for the next inference step with the meaning of the proof goal. Our implementation and experimental results show that this method not only increases the number of successful proofs but also reduces the number of clauses processed during proof search.