SAT-Inspired Higher-Order Eliminations

We generalize several propositional preprocessing techniques to higher-order logic, building on existing first-order generalizations. These techniques eliminate literals, clauses, or predicate symbols from the problem, with the aim of making it more amenable to automatic proof search. We also introduce a new technique, which we call quasipure literal elimination, that strictly subsumes pure literal elimination. The new techniques are implemented in the Zipperposition theorem prover. Our evaluation shows that they sometimes help prove problems originating from Isabelle formalizations and the TPTP library.Comment: 23 pages, 1 figur

Cumulant expansion in the Holstein model: Spectral functions and mobility

We examine the range of validity of the second-order cumulant expansion (CE) for the calculation of spectral functions, quasiparticle properties, and mobility of the Holstein polaron. We devise an efficient numerical implementation that allows us to make comparisons in a broad interval of temperature, electron-phonon coupling, and phonon frequency. For a benchmark, we use the dynamical mean-field theory (DMFT) which gives, as we have recently shown, rather accurate spectral functions in the whole parameter space even in low dimension. We find that in one dimension the CE resolves well both the quasiparticle and the first satellite peak in a regime of intermediate coupling. At high temperatures, the charge mobility assumes a power law $\mu\propto T^{-2}$ in the limit of weak coupling and $\mu\propto T^{-3/2}$ for stronger coupling. We find that, for stronger coupling, the CE gives slightly better results than the self-consistent Migdal approximation (SCMA), while the one-shot Migdal approximation is appropriate only for a very weak electron-phonon interaction. We also analyze the atomic limit and the spectral sum rules. We derive an analytical expression for the moments in CE and find that they are exact up to the fourth order, as opposed to the SCMA where they are exact to the third order. Finally, we analyze the results in higher dimensions.Comment: 22 pages, 14 figures + supp.mat. 12 pages, 9 figure

SAT-Inspired Eliminations for Superposition

International audienceOptimized SAT solvers not only preprocess the clause set, they also transform it during solving as inprocessing. Some preprocessing techniques have been generalized to firstorder logic with equality. In this paper, we port inprocessing techniques to work with superposition, and we strengthen preprocessing. Specifically, we look into elimination of hidden literals, variables (predicates), and blocked clauses. Our evaluation using the Zipperposition prover confirms that the new techniques usefully supplement the existing superposition machinery

Seventeen Provers under the Hammer

International audienceOne of the main success stories of automatic theorem provers has been their integration into proof assistants. Such integrations, or "hammers," increase proof automation and hence user productivity. In this paper, we use Isabelle/HOL's Sledgehammer tool to find out how useful modern provers are at proving formulas in higher-order logic. Our evaluation follows in the steps of Böhme and Nipkow's Judgment Day study from 2010, but instead of three provers we use 17, including SMT solvers and higher-order provers. Our work offers an alternative yardstick for comparing modern provers, next to the benchmarks and competitions emerging from the TPTP World and SMT-LIB

Sportske aktivnosti kod djece s autizmom

Autizam je kompleksan i sveobuhvatan razvojni poremećaj, te kao takav predstavlja veliki izazov za stručnjake i osobe koje se odluče baviti ovom problematikom. Potrebno je da terapeut, koji radi s djecom s autizmom, bude upoznat i educiran o specifičnim metodama rada, te o smjernicama koje mu omogućuju provedbu procesa tjelesnog vježbanja. Djeca s autizmom imaju puno veći rizik da postanu pretila i obole od većeg broja bolesti, stoga je važno da stručnjaci znaju odabrati i individualno prilagoditi tjelesne aktivnosti njihovim potrebama i mogućnostima, te se držati smjernica koje omogućuju kvalitetan i uspješan rad. Autizam je razvojni poremećaj koji se karakterizira poteškoćama u socijalnoj interakciji i komunikaciji s okolinom stoga sport ima važnu ulogu i pozitivan utjecaj na socijalnu interakciju. Prilagođene tjelesne aktivnosti predstavljaju važan čimbenik zdravlja i kvalitete života svakog pojedinca, pa tako i djece s autizmom. Pravilno dozirane i kvalitetno provedene prilagođene aktivnosti utječu na pravilan i skladan psiho-fizički razvoj djeteta, i na prilagodbu u različitim životnim situacijama, kao što su stjecanje prijatelja i kvalitetno provođenje slobodnog vremena. U rad s djecom s autizmom trebao bi biti uključen multidisciplinarni tim stručnjaka koji bi se sastojao od kinezio-terapeuta, edukacijskog rehabilitatora, fizioterapeuta, radnog terapeuta i liječnika kako bi pridonijeli poboljšanju zdravstvenog stanja djeteta

Sportske aktivnosti kod djece s autizmom

Autizam je kompleksan i sveobuhvatan razvojni poremećaj, te kao takav predstavlja veliki izazov za stručnjake i osobe koje se odluče baviti ovom problematikom. Potrebno je da terapeut, koji radi s djecom s autizmom, bude upoznat i educiran o specifičnim metodama rada, te o smjernicama koje mu omogućuju provedbu procesa tjelesnog vježbanja. Djeca s autizmom imaju puno veći rizik da postanu pretila i obole od većeg broja bolesti, stoga je važno da stručnjaci znaju odabrati i individualno prilagoditi tjelesne aktivnosti njihovim potrebama i mogućnostima, te se držati smjernica koje omogućuju kvalitetan i uspješan rad. Autizam je razvojni poremećaj koji se karakterizira poteškoćama u socijalnoj interakciji i komunikaciji s okolinom stoga sport ima važnu ulogu i pozitivan utjecaj na socijalnu interakciju. Prilagođene tjelesne aktivnosti predstavljaju važan čimbenik zdravlja i kvalitete života svakog pojedinca, pa tako i djece s autizmom. Pravilno dozirane i kvalitetno provedene prilagođene aktivnosti utječu na pravilan i skladan psiho-fizički razvoj djeteta, i na prilagodbu u različitim životnim situacijama, kao što su stjecanje prijatelja i kvalitetno provođenje slobodnog vremena. U rad s djecom s autizmom trebao bi biti uključen multidisciplinarni tim stručnjaka koji bi se sastojao od kinezio-terapeuta, edukacijskog rehabilitatora, fizioterapeuta, radnog terapeuta i liječnika kako bi pridonijeli poboljšanju zdravstvenog stanja djeteta

Extending a High-Performance Prover to Higher-Order Logic

International audienceAbstract Most users of proof assistants want more proof automation. Some proof assistants discharge goals by translating them to first-order logic and invoking an efficient prover on them, but much is lost in translation. Instead, we propose to extend first-order provers with native support for higher-order features. Building on our extension of E to $$\lambda$$ -free higher-order logic, we extend E to full higher-order logic. The result is the strongest prover on benchmarks exported from a proof assistant

SAT-Inspired Eliminations for Superposition

Optimized SAT solvers not only preprocess the clause set, they also transform it during solving as inprocessing. Some preprocessing techniques have been generalized to first-order logic with equality. In this article, we port inprocessing techniques to work with superposition, a leading first-order proof calculus, and we strengthen known preprocessing techniques. Specifically, we look into elimination of hidden literals, variables (predicates), and blocked clauses. Our evaluation using the Zipperposition prover confirms that the new techniques usefully supplement the existing superposition machinery

Superposition for Higher-Order Logic

We recently designed two calculi as stepping stones towards superposition for full higher-order logic: Boolean-free λ-superposition and superposition for first-order logic with interpreted Booleans. Stepping on these stones, we finally reach a sound and refutationally complete calculus for higher-order logic with polymorphism, extensionality, Hilbert choice, and Henkin semantics. In addition to the complexity of combining the calculus’s two predecessors, new challenges arise from the interplay between λ-terms and Booleans. Our implementation in Zipperposition outperforms all other higher-order theorem provers and is on a par with an earlier, pragmatic prototype of Booleans in Zipperposition