Asteroids provide fundamental clues to the formation and evolution of planetesimals. Collisional models based on the depletion of the primordial main belt of asteroids predict 10-15 craters >400 km should have formed on Ceres, the largest object between Mars and Jupiter, over the last 4.55 Gyr. Likewise, an extrapolation from the asteroid Vesta would require at least 6-7 such basins. However, C...

Cut-elimination is the most prominent form of proof transformation in logic. The elimination of cuts in formal proofs corresponds to the removal of intermediate statements (lemmas) in mathematical proofs. The cut-elimination method CERES (cut-elimination by resolution) works by extracting a set of clauses from a proof with cuts. Any resolution refutation of this set then serves as a skeleton of...

Introduction: We consider Ceres as a prototype for planetary evolution [1]. From thermal modeling by McCord and Sotin [2, 3, 4], Ceres was inferred to have differentiated into a rocky core of hydrated silicates, and an icy outer shell. Thomas et al. [5] confirmed such a model from direct observation of Ceres’s shape from Hubble Space Telescope observations, and pervious occultation measurements...

The axiomatization of arithmetical properties in theorem proving creates many straightforward inference steps. In analyzing mathematical proofs with the CERES (Cut-Elimination by Resolution) system, it is convenient to hide these inferences. The central topic of the thesis is the extension of the CERES method to allow reasoning modulo equational theories. For this, the inference systems of Sequ...

We have investigated the possibility of main belt asteroids being trapped in the 1:1 resonance with other asteroids. Using contemporary mass estimates for the large asteroids (1) Ceres, (2) Pallas and (4) Vesta, it is found that four asteroids are temporarily trapped in such resonances with Ceres and Vesta during numerical integrations spanning 2 × 106 yr. In particular, the asteroid (1372) Har...

This work defines an extension CERES of the first-order cut-elimination method CERES to the subclass of sequent calculus proofs in second-order logic using quantifier-free comprehension. This extension is motivated by the fact that cut-elimination can be used as a tool to extract information from real mathematical proofs, and often a crucial part of such proofs is the definition of sets by form...

We consider the full Solar System including (1) Ceres and some of the main asteroids, (2) Pallas, (4) Vesta, (7) Iris, and (324) Bamberga. We show that close encounters among these small bodies induce strong chaotic behavior in their orbits and in those of many asteroids that are much more chaotic than previously thought. Even if space missions will allow very precise measurements of the positi...

Prior to the arrival of the Dawn spacecraft at Ceres, the dwarf planet was anticipated to be ice-rich. Searches for morphological features related to ice have been ongoing during Dawn's mission at Ceres. Here we report the identification of pitted terrains associated with fresh Cerean impact craters. The Cerean pitted terrains exhibit strong morphological similarities to pitted materials previo...