551 research outputs found
Hierarchic Superposition Revisited
Many applications of automated deduction require reasoning in first-order logic modulo background theories, in particular some form of integer arithmetic. A major unsolved research challenge is to design theorem provers that are "reasonably complete" even in the presence of free function symbols ranging into a background theory sort. The hierarchic superposition calculus of Bachmair, Ganzinger, and Waldmann already supports such symbols, but, as we demonstrate, not optimally. This paper aims to rectify the situation by introducing a novel form of clause abstraction, a core component in the hierarchic superposition calculus for transforming clauses into a form needed for internal operation. We argue for the benefits of the resulting calculus and provide two new completeness results: one for the fragment where all background-sorted terms are ground and another one for a special case of linear (integer or rational) arithmetic as a background theory
Superposition and chaining for totally ordered divisible abelian groups
We present a calculus for first-order theorem proving in the presence of the axioms of totally ordered divisible abelian groups. The calculus extends previous superposition or chaining calculi for divisible torsion-free abelian groups and dense total orderings without endpoints. As its predecessors, it is refutationally complete and requires neither explicit inferences with the theory axioms nor variable overlaps. It offers thus an efficient way of treating equalities and inequalities between additive terms over, e.g., the rational numbers within a first-order theorem prover
Quantum dynamics of the Neel vector in the antiferromagnetic molecular wheel CsFe8
The inelastic neutron scattering (INS) spectrum is studied for the
antiferromagnetic molecular wheel CsFe8, in the temperature range 2 - 60 K, and
for transfer energies up 3.6 meV. A qualitative analysis shows that the
observed peaks correspond to the transitions between the L-band states, from
the ground state up to the S = 5 multiplet. For a quantitative analysis, the
wheel is described by a microscopic spin Hamiltonian (SH), which includes the
nearest-neighbor Heisenberg exchange interactions and uniaxial easy-axis
single-ion anisotropy, characterized by the constants J and D, respectively.
For a best-fit determination of J and D, the L band is modeled by an effective
SH, and the effective SH concept extended such as to facilitate an accurate
calculation of INS scattering intensities, overcoming difficulties with the
dimension of the Hilbert space. The low-energy magnetism in CsFe8 is
excellently described by the generic SH used. The two lowest states are
characterized by a tunneling of the Neel vector, as found previously, while the
higher-lying states are well described as rotational modes of the Neel vector.Comment: 12 pages, 10 figures, REVTEX4, to appear in PR
Cancellative superposition decides the theory of divisible torsion-free abelian groups
In divisible torsion-free abelian groups, the efficiency of the cancellative superposition calculus can be greatly increased by combining it with a variable elimination algorithm that transforms every clause into an equivalent clause without unshielded variables. We show that the resulting calculus is a decision procedure for the theory of divisible torsion-free abelian groups
Ferromagnetic coupling and magnetic anisotropy in molecular Ni(II) squares
We investigated the magnetic properties of two isostructural Ni(II) metal
complexes [Ni4Lb8] and [Ni4Lc8]. In each molecule the four Ni(II) centers form
almost perfect regular squares. Magnetic coupling and anisotropy of single
crystals were examined by magnetization measurements and in particular by
high-field torque magnetometry at low temperatures. The data were analyzed in
terms of an effective spin Hamiltonian appropriate for Ni(II) centers. For both
compounds, we found a weak intramolecular ferromagnetic coupling of the four
Ni(II) spins and sizable single-ion anisotropies of the easy-axis type. The
coupling strengths are roughly identical for both compounds, whereas the
zero-field-splitting parameters are significantly different. Possible reasons
for this observation are discussed.Comment: 7 pages, 7 figure
Superposition for Lambda-Free Higher-Order Logic
We introduce refutationally complete superposition calculi for intentional and extensional clausal -free higher-order logic, two formalisms that allow partial application and applied variables. The calculi are parameterized by a term order that need not be fully monotonic, making it possible to employ the -free higher-order lexicographic path and Knuth-Bendix orders. We implemented the calculi in the Zipperposition prover and evaluated them on Isabelle/HOL and TPTP benchmarks. They appear promising as a stepping stone towards complete, highly efficient automatic theorem provers for full higher-order logic
Exchange-coupling constants, spin density map, and Q dependence of the inelastic neutron scattering intensity in single-molecule magnets
The Q dependence of the inelastic neutron scattering (INS) intensity of
transitions within the ground-state spin multiplet of single-molecule magnets
(SMMs) is considered. For these transitions, the Q dependence is related to the
spin density map in the ground state, which in turn is governed by the
Heisenberg exchange interactions in the cluster. This provides the possibility
to infer the exchange-coupling constants from the Q dependence of the INS
transitions within the spin ground state. The potential of this strategy is
explored for the M = +-10 -> +- 9 transition within the S = 10 multiplet of the
molecule Mn12 as an example. The Q dependence is calculated for powder as well
as single-crystal Mn12 samples for various exchange-coupling situations
discussed in the literature. The results are compared to literature data on a
powder sample of Mn12 and to measurements on an oriented array of about 500
single-crystals of Mn12. The calculated Q dependence exhibits significant
variation with the exchange-coupling constants, in particular for a
single-crystal sample, but the experimental findings did not permit an
unambiguous determination. However, although challenging, suitable experiments
are within the reach of today's instruments.Comment: 11 pages, 6 figures, REVTEX4, to appear in PR
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