2016 ◽  
Vol 58 (2) ◽  
pp. 253-291 ◽  
Author(s):  
M. Ganesalingam ◽  
W. T. Gowers

Author(s):  
Martin Suda

AbstractWe re-examine the topic of machine-learned clause selection guidance in saturation-based theorem provers. The central idea, recently popularized by the ENIGMA system, is to learn a classifier for recognizing clauses that appeared in previously discovered proofs. In subsequent runs, clauses classified positively are prioritized for selection. We propose several improvements to this approach and experimentally confirm their viability. For the demonstration, we use a recursive neural network to classify clauses based on their derivation history and the presence or absence of automatically supplied theory axioms therein. The automatic theorem prover Vampire guided by the network achieves a 41 % improvement on a relevant subset of SMT-LIB in a real time evaluation.


2012 ◽  
Vol 50 (1) ◽  
pp. 99-117 ◽  
Author(s):  
James P. Bridge ◽  
Lawrence Charles Paulson

10.29007/q4pt ◽  
2020 ◽  
Author(s):  
Martin Suda

The Sumo INference Engine (SInE) is a well-established premise selection algorithm for first-order theorem provers, routinely used, especially on large theory problems. The main idea of SInE is to start from the goal formula and to iteratively add other formulas to those already added that are related by sharing signature symbols. This implicitly defines a certain heuristical distance of the individual formulas and symbols from the goal.In this paper, we show how this distance can be successfully used for other purposes than just premise selection. In particular, biasing clause selection to postpone introduction of input clauses further from the goal helps to solve more problems. Moreover, a precedence which respects such goal distance of symbols gives rise to a goal sensitive simplification ordering. We implemented both ideas in the automatic theorem prover Vampire and present their experimental evaluation on the TPTP benchmark.


Brooks has criticized traditional approaches to artificial intelligence as too inefficient. In particular, he has singled out techniques involving search as inadequate to achieve the fast reaction times required by robots and other AI products that need to work in the real world. Instead he proposes the subsumption architecture as an overall organizing principle. This consists of layers of behavioural modules, each of which is capable of carrying out a complete (usually simple) task. He has employed this architecture to build a series of simple mobile robots, but he claims that it is appropriate for all AI products. Brooks’s proposal is usually seen as an example of nouvelle AI, in contrast to good old-fashioned AI (GOFAl). Automatic theorem proving is the archetypal example of GOFAl. The resolution theorem proving technique once served as the engine of AI. Of all areas of AI it seems the most difficult to implement using Brooks’s ideas. It would thus serve as a keen test of Brooks’s proposal to explore to what extent the task of theorem proving can be achieved by a subsumption architecture. Tactics are programs for guiding a theorem prover. They were introduced as an efficient alternative to search-based techniques. In this paper I compare recent work on tactic-based theorem proving with Brooks’s proposals and show that, surprisingly, there is a similarity between them. It thus seems that the distinction between nouvelle AI and GOFAl is not so great as is sometimes claimed. However, this exercise also identifies some criticisms of Brooks’s proposal.


10.29007/wm8b ◽  
2018 ◽  
Author(s):  
Jasmin Christian Blanchette

This paper presents an algorithm that redirects proofs by contradiction. The input is a refutation graph, as produced by an automatic theorem prover (e.g., E, SPASS, Vampire, Z3); the output is a direct proof expressed in natural deduction extended with case analyses and nested subproofs. The algorithm is implemented in Isabelle’s Sledgehammer, where it enhances the legibility of machine-generated proofs.


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