Comparing Approaches To Resolution Based Higher-Order Theorem Proving

Benzmüller, Christoph

doi:10.1023/a:1020840027781

Cited by 10 publications

(8 citation statements)

References 29 publications

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“…In contrast to the experiments with LEO alone, we used only the EXT-INPUT strategy for our experiments with the LEO-BLIKSEM and LEO-VAMPIRE. 5 Each of column eight (LEO-BLIKSEM) and nine (LEO-VAMPIRE) in Table 5 presents the number of clauses generated by LEO (Cl.) together with the time (Time), and in addition, the number of first-order clauses (FOcl) sent to, the time (FOtm) used by, and the number of clauses generated (GnCl) by BLIKSEM and VAMPIRE, respectively.…”

Section: Resultsmentioning

confidence: 99%

“…However, during I/O operations (i.e., writing input files and reading output files of the provers) the threads were locked and could only be killed once the operation was completed. While these operations generally only took milliseconds, for particular large files this could take longer, which accounts for 5 In a small empirical study we identified EXT-INPUT as the most successful strategy for LEO-BLIKSEM and LEO-VAMPIRE. Table 5 Experimental data for the benchmark test problems given in Table 2 TPTPProblem .89…”

Section: Resultsmentioning

confidence: 99%

“…Moreover, first-order systems often use a case tailored problem representation (e.g., by avoiding some base axioms of the addressed theory), while the higher-order prover has a harder task of dealing with a general (not specifically tailored) representation that does not make any assumptions about which parts of the theory are or are not needed for the concrete problem at hand. We use λ-abstraction as well as the extensionality treatment inherent in LEO's calculus [5]. This enables a theoretically 4 Henkin-complete proof system for set theory.…”

Section: Equivclasses(r) = Equivclasses(q) ∨ Disjoint(equivclasses(r)mentioning

confidence: 99%

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Combined reasoning by automated cooperation

Benzmüller

Sorge

Jamnik

et al. 2008

Journal of Applied Logic

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Different reasoning systems have different strengths and weaknesses, and often it is useful to combine these systems to gain as much as possible from their strengths and retain as little as possible from their weaknesses. Of particular interest is the integration of first-order and higher-order techniques. First-order reasoning systems, on the one hand, have reached considerable strength in some niches, but in many areas of mathematics they still cannot reliably solve relatively simple problems, for example, when reasoning about sets, relations, or functions. Higher-order reasoning systems, on the other hand, can solve problems of this kind automatically. But the complexity inherent in their calculi prevents them from solving a whole range of problems. However, while many problems cannot be solved by any one system alone, they can be solved by a combination of these systems.We present a general agent-based methodology for integrating different reasoning systems. It provides a generic integration framework which facilitates the cooperation between diverse reasoners, but can also be refined to enable more efficient, specialist integrations. We empirically evaluate its usefulness, effectiveness and efficiency by case studies involving the integration of firstorder and higher-order automated theorem provers, computer algebra systems, and model generators.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Equivclasses(r) = Equivclasses(q) ∨ Disjoint(equivclasses(r)mentioning

confidence: 99%

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Combined reasoning by automated cooperation

Benzmüller

Sorge

Jamnik

et al. 2008

Journal of Applied Logic

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“…Another challenge is that unification modulo Boolean extensionality subsumes theorem proving: proving a proposition ϕ is the same as unifying ϕ and modulo Boolean extensionality. More information on these challenges is provided by Benzmüller et al (2009) andBenzmüller (2002).…”

Section: Equality Extensionality and Choicementioning

confidence: 99%

Automation of Higher-Order Logic

Benzmüller¹,

Miller²

2014

Handbook of the History of Logic

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“…Leo-II is written in OCaml and implements a RUE calculus [12] which relies on a 'Boolean aware' (or, more generally, 'theory aware' [3]) extensional preunification engine. Leo-II accepts problems encoded in the CNF (clausal first-order form) and FOF (first-order form) languages from the TPTP [15], but its principal input language is THF0, core typed higher-order form [16].…”

Section: System Overviewmentioning

confidence: 99%