Progress in the Development of Automated Theorem Proving for Higher-Order Logic

Sutcliffe, Geoff; Benzmüller, Christoph; Brown, Chad E.; Theiss, Frank

doi:10.1007/978-3-642-02959-2_8

Cited by 21 publications

(27 citation statements)

References 29 publications

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“…It would have been harder to integrate them into a prover based on superposition, because in these provers, selection is not symmetrical between positive and negative literals. We tested it using the encoding in deduction modulo of the problems of higher-order logic of the TPTP [25]. As can be expected, performances compared to the provers dedicated to higher-order logic such as TPS (http://gtps.math.cmu.edu/tps.html) is quite poor, but they are promising (about a third of the problems solved by TPS can be solved by the modified iprover).…”

Section: Implementation Issuesmentioning

confidence: 93%

Embedding Deduction Modulo into a Prover

Burel¹

2010

Computer Science Logic

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Abstract. Deduction modulo consists in presenting a theory through rewrite rules to support automatic and interactive proof search. It induces proof search methods based on narrowing, such as the polarized resolution modulo. We show how to combine this method with more traditional ordering restrictions. Interestingly, no compatibility between the rewriting and the ordering is requested to ensure completeness. We also show that some simplification rules, such as strict subsumption eliminations and demodulations, preserve completeness. For this purpose, we use a new framework based on a proof ordering. These results show that polarized resolution modulo can be integrated into existing provers, where these restrictions and simplifications are present. We also discuss how this integration can actually be done by diverting the main algorithm of state-of-the-art provers.Whatever their applications, proofs are rarely searched for without context: mathematical proofs rely on set theory, or Euclidean geometry, or arithmetic, etc.; proofs of program correctness are done using e.g. pointer arithmetic and/or theories defining data structures (chained lists, trees, . . . ); concerning security, theories are used for instance to model properties of encryption algorithms. It is therefore essential to have theoretical foundations and practical methods that handle theories conveniently and efficiently. For this purpose, there are two directions: to develop methods that are really specific to a particular theory; or to develop a generic framework that can handle all theories. The first option is appealing for efficiency reasons: for instance, combining a SAT solver with the Simplex method leads to very powerful SMT solvers for linear arithmetic. However, developing methods for new theories is hard. Even the combination of such specific methods is not trivial, although there have been a lot of interesting results in that direction in the recent years. In this paper, we are more interested in the second option: having a generic way to handle theories efficiently. A naive way to do so would be to use an axiomatization of the theory, but in general, this approach would be really inefficient for automated proving. Somehow, we need to present the theory so as to take advantage of its properties.A first idea is to use the consistency of the theory. When proving a goal in a consistent theory by refutation, resolving the clauses of the theory is useless, since it will not bring out a contradiction. This idea defines the set-of-support

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Section: Implementation Issuesmentioning

confidence: 93%

Embedding Deduction Modulo into a Prover

Burel¹

2010

Computer Science Logic

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“…Additionally, four theorem proving ATP systems and two model finders have been produced, and are available in SystemOnTPTP. The addition of THF to the TPTP World has had an immediate impact on progress in the development of automated reasoning in higher-order logic [22].…”

Section: Current Developments In the Tptp Worldmentioning

confidence: 99%

The TPTP World – Infrastructure for Automated Reasoning

Sutcliffe

2010

Logic for Programming, Artificial Intelligence, and Reasoning

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Abstract. The TPTP World is a well known and established infrastructure that supports research, development, and deployment of Automated Theorem Proving (ATP) systems for classical logics. The data, standards, and services provided by the TPTP World have made it increasingly easy to build, test, and apply ATP technology. This paper reviews the core features of the TPTP World, describes key service components of the TPTP World, presents some successful applications, and gives an overview of the most recent developments.

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“…LEO-II's competition performance is hard to predict for different reasons: this is the first higher-order CASC competition ever held, the THF TPTP library [SBBT09] grew very fast over the last year (faster than the first-order TPTP at any point) and many novel problems have recently entered the THF TPTP, LEO-II version 1.0 has substantially changed compared to the previous versions, and the performance of the competitor systems is hard to predict since they appear to be improving fast. An exciting and very motivating situation!…”

Section: Expected Competition Performancementioning

confidence: 99%

The CADE ATP System Competition — CASC

Sutcliffe

2016

AI Magazine

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The CADE ATP System Computer (CASC) evaluates the performance of sound, fully automatic, classical logic, ATP systems. The evaluation is in terms of the number of problems solved, the number of acceptable proofs and models produced, and the average runtime for problems solved, in the context of a bounded number of eligible problems chosen from the TPTP problem library, and a specified time limit for each solution attempt. The CADE-22 ATP System Competition (CASC-22) was held on 5th August 2009. The design of the competition and it's rules, and information regarding the competing systems, are provided in this report.

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Progress in the Development of Automated Theorem Proving for Higher-Order Logic

Cited by 21 publications

References 29 publications

Embedding Deduction Modulo into a Prover

Embedding Deduction Modulo into a Prover

The TPTP World – Infrastructure for Automated Reasoning

The CADE ATP System Competition — CASC

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