24 research outputs found
Automated Reasoning and Presentation Support for Formalizing Mathematics in Mizar
This paper presents a combination of several automated reasoning and proof
presentation tools with the Mizar system for formalization of mathematics. The
combination forms an online service called MizAR, similar to the SystemOnTPTP
service for first-order automated reasoning. The main differences to
SystemOnTPTP are the use of the Mizar language that is oriented towards human
mathematicians (rather than the pure first-order logic used in SystemOnTPTP),
and setting the service in the context of the large Mizar Mathematical Library
of previous theorems,definitions, and proofs (rather than the isolated problems
that are solved in SystemOnTPTP). These differences poses new challenges and
new opportunities for automated reasoning and for proof presentation tools.
This paper describes the overall structure of MizAR, and presents the automated
reasoning systems and proof presentation tools that are combined to make MizAR
a useful mathematical service.Comment: To appear in 10th International Conference on. Artificial
Intelligence and Symbolic Computation AISC 201
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Track A Basic Science
Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/138319/1/jia218438.pd
Learning Search Control Knowledge for Equational Theorem Proving
One of the major problems in clausal theorem proving is the control of the proof search. In the presence of equality, this problem is particularly hard, since nearly all state-of-the-art systems perform the proof search by saturating a mostly unstructured set of clauses. We describe an approach that enables a superposition-based prover to pick good clauses for generating inferences based on experiences from previous successful proof searches for other problems. Information about good and bad search decisions (useful and superfluous clauses) is automatically collected from search protocols and represented in the form of annotated clause patterns. At run time, new clauses are compared with stored patterns and evaluated according to the associated information found. We describe our implementation of the system. Experimental results demonstrate that a learned heuristic significantly outperforms the conventional base strategy, especially in domains where enough training examples are available
PTTP+GLiDeS: Guiding Linear Deductions with Semantics
This paper describes PTTP+GLiDeS, a PTTP style prover augmented with a semantic pruning mechanism, GLiDeS. PTTP+GLiDeS combines modified versions of Stickel's PTTP style prover [6] and the model generator MACE [4]