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Strategies for Focusing Structure-Based Theorem Proving

Summary: Strategies for Focusing Structure-Based
Theorem Proving
Eyal Amir 1 Sheila McIlraith 2
Stanford University, Computer Science Department, Gates Building 2A, Stanford,
CA 94305-9020, USA
Motivated by the problem of query answering over multiple structured common-
sense theories, we exploit graph-based techniques to improve the e∆ciency of the-
orem proving for structured theories. Theories are organized into subtheories that
are minimally connected by the literals they share. We present message-passing al-
gorithms that reason over these theories while minimizing the number of inferences
done within each subtheory and the number of messages sent between subtheo-
ries. We do so using consequence nding, specializing our algorithms for the case
of rst-order resolution, and for batch and concurrent theorem proving. We pro-
vide an algorithm that restricts the interaction between subtheories by exploiting
the polarity of literals. We attempt to minimize the reasoning within each individ-
ual partition by exploiting existing algorithms for focused incremental and general
consequence nding. Finally, we propose an algorithm that compiles each subtheory
into one in a reduced sublanguage. We have proven the soundness and completeness
of our algorithms.


Source: Amir, Eyal - Department of Computer Science, University of Illinois at Urbana-Champaign


Collections: Computer Technologies and Information Sciences