Abstract
Connection calculi allow for very compact implementations of goal-directed proof search. We give an overview of our work related to connection tableaux calculi: first, we show optimised functional implementations of connection tableaux proof search, including a consistent Skolemisation procedure for machine learning. Then, we show two guidance methods based on machine learning, namely reordering of proof steps with Naive Bayesian probabilities, and expansion of a proof search tree with Monte Carlo Tree Search.
Highlights
Connection calculi enable goal-directed proof search in a variety of logics
We have presented our framework for integrating machine learning in connection tableaux
We showed that the number of solved problems can be increased by up to 58.8%, on one dataset beating even E in automatic mode
Summary
Connection calculi enable goal-directed proof search in a variety of logics. Connections were considered among others for classical first-order logic [49], for higher-order logic [3] and for linear logic [23]. We have used connection provers from the leanCoP family as a basis for experiments with machine learning 5) and proof certification [41] For these applications, we implemented connection provers in functional instead of logic programming languages. In this paper we develop an integration of internal guidance based on machine learning and Monte Carlo methods in connection-style proof search. – We implement proof search based on clausal and nonclausal connection tableaux calculi in functional programming languages, improving performance upon previous Prologbased implementations, see Sect. The techniques added over the conference versions include: consistent Skolemisation applicable for nonclausal proof search and efficient functional-style implementation of proof search in clausal and nonclausal connection calculi.
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