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

Asymptotic Entanglement and Lindblad Dynamics: a Perturbative Approach

We consider an open bipartite quantum system with dissipative Lindblad type dynamics. In order to study the entanglement of the stationary states, we develop a perturbative approach and apply it to the physically significant case when a purely dissipative perturbation is added to the unperturbed generator which by itself would produce reversible unitary dynamics.Comment: 15 page

Decidability of the Monadic Shallow Linear First-Order Fragment with Straight Dismatching Constraints

The monadic shallow linear Horn fragment is well-known to be decidable and has many application, e.g., in security protocol analysis, tree automata, or abstraction refinement. It was a long standing open problem how to extend the fragment to the non-Horn case, preserving decidability, that would, e.g., enable to express non-determinism in protocols. We prove decidability of the non-Horn monadic shallow linear fragment via ordered resolution further extended with dismatching constraints and discuss some applications of the new decidable fragment.Comment: 29 pages, long version of CADE-26 pape

Petrological Constraints on the Recycling of Mafic Crystal Mushes and Intrusion of Braided Sills in the Torres del Paine Mafic Complex (Patagonia)

Cumulate and crystal mush disruption and reactivation are difficult to recognize in coarse-grained, shallow plutonic rocks. Mafic minerals included in hornblende and zoned plagioclase provide snapshots of early crystallization and cumulate formation, but are difficult to interpret in terms of the dynamics of magma ascent and possible links between silicic and mafic rock emplacement. This study presents the field relations, the microtextures and the mineral chemistry of the Miocene mafic sill complex of the Torres del Paine intrusive complex (Patagonia, Chile) and its subvertical feeder zone. We summarize a number of observations that occur in structurally different, shallow, plutonic rocks, as follows. (1) The mafic sill complex was built up by a succession of braided sills of shoshonitic and high-K calc-alkaline porphyritic hornblende-gabbro and fine-grained monzodiorite sills. Local diapiric structures and felsic magma accumulation between sills indicate limited separation of intercumulus liquid from the mafic sills. Anhedral hornblende cores, with olivine + clinopyroxene ± plagioclase ± apatite inclusions, crystallized at temperatures >900°C and pressures of ∼300 to ∼400 MPa. The corresponding rims and monzodiorite matrix crystallized at 950°C) than estimated from the composition of the granite minimum. We show that hornblende-plagioclase thermobarometry is a useful monitor for the determination of the segregation conditions of granitic magmas from gabbroic crystal mushes, and for monitoring the evolution of shallow crustal magmatic crystallization, decompression and coolin

Stable isotopic disequilibrium in high-T metamorphic systems

A principal use of stable isotopes in metamorphic rocks is as thermometers, or as tests for isotopic equilibrium where metamorphic temperatures are known. Applications are often complicated when apparent isotopic temperatures are discordant and disagree with petrologic temperatures, indicating a failure of isotopic systems to record and/or preserve equilibrium, peak-T fractionations. In low-T, fluid-hosted environments such features often clearly reflect open system exchange. However, in high-T metamorphic environments a slow cooling history can be sufficient to produce such features by retrograde, closed system exchange between coexisting minerals

Petrological Constraints on the Recycling of Mafic Crystal Mushes and Intrusion of Braided Sills in the Torres del Paine Mafic Complex (Patagonia)

Cumulate and crystal mush disruption and reactivation are difficult to recognize in coarse-grained, shallow plutonic rocks. Mafic minerals included in hornblende and zoned plagioclase provide snapshots of early crystallization and cumulate formation, but are difficult to interpret in terms of the dynamics of magma ascent and possible links between silicic and mafic rock emplacement. This study presents the field relations, the microtextures and the mineral chemistry of the Miocene mafic sill complex of the Torres del Paine intrusive complex (Patagonia, Chile) and its subvertical feeder zone. We summarize a number of observations that occur in structurally different, shallow, plutonic rocks, as follows. (1) The mafic sill complex was built up by a succession of braided sills of shoshonitic and high-K calc-alkaline porphyritic hornblende-gabbro and fine-grained monzodiorite sills. Local diapiric structures and felsic magma accumulation between sills indicate limited separation of intercumulus liquid from the mafic sills. Anhedral hornblende cores, with olivine + clinopyroxene ± plagioclase ± apatite inclusions, crystallized at temperatures >900°C and pressures of ∼300 to ∼400 MPa. The corresponding rims and monzodiorite matrix crystallized at <830°C, ∼70 MPa. This abrupt compositional variation suggests stability and instability of hornblende during recycling of the mafic roots of the complex and subsequent decompression. (2) The near lack of intercumulus crystals in the subvertical feeder zone layered gabbronorite and pyroxene–hornblende gabbronorite stocks testifies that melt is more efficiently extracted than in sills, resulting in a cumulate signature in the feeding system. Granitic liquids were extracted at a higher temperature (T >950°C) than estimated from the composition of the granite minimum. We show that hornblende–plagioclase thermobarometry is a useful monitor for the determination of the segregation conditions of granitic magmas from gabbroic crystal mushes, and for monitoring the evolution of shallow crustal magmatic crystallization, decompression and cooling

Time and duration of chondrule formation: Constraints from 26Al-26Mg ages of individual chondrules

Chondrules from unequilibrated ordinary and carbonaceous chondrites belong to the oldest and most primitive materials from the early solar system and record chemical and isotopic signatures relating to their formation and evolution. These signatures allow tracing protoplanetary disk processes that eventually led to the formation of planetary building blocks and rocky planets. 26Al-26Mg ages based on mineral-mesostasis isochrons of 31 porphyritic ferromagnesian chondrules, that belong mainly to type-II, constrain the time of chondrule melting prior to incorporation into the respective chondrite parent bodies. For this study chondrules from the unequilibrated L, L(LL) and LL ordinary chondrites (UOCs) NWA 5206, NWA 8276, MET 96503, MET 00452, MET 00526, NWA 7936 and QUE 97008 were selected, which are of petrologic types 3.00-3.15 and were thus least metamorphosed after formation. Magnesium and Al isotopes were measured in-situ by Secondary Ion Mass Spectrometry (SIMS) using a CAMECA 1280 ims. 26Mg excess from in-situ decay of 26Al correlating with 27Al/24Mg has been detected in the mesostasis of all but one chondrule. The initial Al isotopic compositions (26Al/27Al)0 and 26Mg/24Mg ratios (d26Mg*0) deduced from internal mineral isochron regressions range from (9.5 ± 2.8) × 10-6 to (3.1 ± 1.2) × 10-6 and -0.020 ± 0.028‰ to 0.011 ± 0.039‰, respectively. The corresponding chondrule ages (∆tCAI), calculated relative to calcium-aluminum-rich inclusions (CAIs) using the canonical 26Al/27Al = (5.23 ± 0.13) × 10-5, are between 1.76_(-0.27)^(+0.36) and 2.92_(-0.34)^(+0.51) Ma and date the melt formation and thus primary chondrule formation from dust-like precursors or reprocessing of older chondrules. The age range agrees with those acquired with different short-lived chronometers and with published 26Al-26Mg ages, the majority of which were obtained for chondrules from the Bishunpur and Semarkona meteorites, although no chondrule with (26Al/27Al)0 > 10-5 was found. Chondrules in single chondrite samples or between different chondrite groups show no distinct age distributions. The initial 26Al/27Al of the oldest chondrules in the L(LL)/LL and L chondrite samples are identical within their 1σ uncertainties and yield a mean age of 1.99_(-0.08)^(+0.08) Ma and 1.81_(-0.10)^(+0.11) Ma, respectively. The oldest chondrules from six of the seven studied samples record a mean age of 1.94_(-0.06)^(+0.07) Ma. Since heating events in the protoplanetary disk could have partially reset the Al-Mg systematics in pre-existing chondrules and this would have shifted recorded 26Al-26Mg ages toward younger dates, the oldest mean age of 1.81_(-0.10)^(+0.11) Ma recorded in L chondrite chondrules is interpreted to date the rapid and punctuated onset of chondrule formation. The density distribution of chondrule ages from this study, which comprises the largest single dataset of OC chondrule ages, combined with published ages for chondrules from ordinary and carbonaceous chondrites reveals major age peaks for OC chondrules at 2.0 and 2.3 Ma. Chondrules in ordinary and carbonaceous chondrites formed almost contemporaneously (with a possible distinction between CC groups) in two chemically distinct reservoirs, probably in density-enriched regions at the edges of Jupiter’s orbit. The young formation ages of chondrules suggest that they do not represent precursors but rather by-products of planetesimal accretion

A Detailed Geochemical Study of a Shallow Arc-related Laccolith; the Torres del Paine Mafic Complex (Patagonia)

The shallow crustal Torres del Paine Intrusive Complex in southern Patagonia offers an opportunity to understand the chemical evolution and timing of crystallization processes in shallow plutonic rocks. It is characterized by hornblende-gabbros, gabbronorites, monzodiorites and granitic plutonic rocks. The exceptional exposure of the intrusion permits the identification of two structurally and petrographically different zones. Layered gabbronorite, olivine-bearing pyroxene-hornblende gabbronorite and monzodiorite forming vertical sheets and stocks in the west are referred to here as the feeder zone. These mafic rocks are in vertical contact with younger granitic rocks on their eastern border. The eastern part is a laccolith complex. It is characterized by three major units (I, II, III) of granitic rocks of over 1000 m vertical thickness; these are underlain in places by a sequence of hornblende-gabbro sills intermingled with evolved monzodiorite granite. Chilled, crenulated margins as well as flame structures between gabbroic rocks and monzodiorites suggest that the mafic sill complex remained partially molten during most of its construction. Bulk-rock major and trace element data indicate that the Paine mafic rocks follow a high-K calc-alkaline to shoshonitic differentiation trend. The parental magmas were basaltic trachyandesite liquids, with variable H2O and alkali contents. The majority of the feeder zone gabbronorites have high Al2O3 contents and positive Eu and Sr anomalies, consistent with accumulation of plagioclase and efficient extraction of intercumulus melt. The mafic sill complex largely lacks these cumulate signatures. Comparisons of the intercumulus groundmass in the hornblende-gabbros with intra-sill dioritic stocks and pods reveal similar rare earth element patterns and trace element ratios indicating incomplete extraction of evolved interstitial liquids. The Sr, Nd and Pb isotopic compositions of the mafic and granitic rocks exhibit ranges of 87Sr/86Sr of 0·704-0·708, εNd +3·8 to −1·2, 206Pb/204Pb 18·61-18·77, 207Pb/204Pb 15·67-15·67 and 208Pb/204Pb 38·56-38·77. Crystal fractionation and assimilation-fractional crystallization modelling, combined with high-precision U-Pb dating of zircons, indicates that the western feeder zone gabbronorites are linked to the uppermost Paine granite (granite I), whereas the mafic sill complex is younger and not directly related to the voluminous granite units II and III. These results are interpreted to indicate that crystal-liquid separation is facilitated in subvertical, dynamic feeder systems whereas subhorizontal sill complexes are inefficient in separating large volumes of mafic cumulates and complementary felsic rock

Crystal Size Distribution of Periclase in Contact Metamorphic Dolomite Marbles from the Southern Adamello Massif, Italy

Crystal size distributions (CSD) of periclase in contact metamorphic dolomite marbles are presented for two profiles near the Cima Uzza summit in the southern Adamello Massif (Italy). The database was combined with geochemical and petrological information to deduce the controls on the periclase-forming reaction. The contact metamorphic dolomite marbles are exposed at the contact of mafic intrusive rocks and are partially surrounded by them. Brucite is retrograde and pseudomorphs spherical periclase crystals. Prograde periclase growth is the consequence of limited infiltration of water-rich fluid at T near 605°C. Stable isotope data show depletion in 13C and 18O over a narrow region (∼40 cm) near the magmatic contact, whereas the periclase-forming reaction front extends up to 4 m from the contact. CSD analyses along the two profiles show that the median grain size of the periclase crystals does not change, but that there is a progressively greater distribution of grain sizes, including a greater proportion of larger grains, with increasing distance from the contact. A qualitative model, based on the textural and geochemical data, attributes these variations in grain size to changing reaction affinities along a kinetically dispersed infiltration front. This study highlights the need to invoke disequilibrium processes for metamorphic mineral growth and expands the use of CSDs to systems of mineral formation driven by fluid infiltratio