We deene a superposition calculus specialized for abelian groups represented as integer modules, and show its refutational completeness. This allows to substantially reduce the number of inferences compared to a standard superposition prover which applies the axioms directly. Speciically, equational literals are simpliied, so that only the maximal term of the sums is on the left-hand side. Only...

The most efficient techniques that have been developed to date for equality handling in first-order theorem proving are based on superposition calculi. Superposition is a refinement of paramodulation in that various ordering constraints are imposed on inferences. For practical purposes, a key aspect of superposition is its compatibility with powerful simplification techniques. In this paper we ...

The fast-flying day-active hawkmoth Macroglossum stellatarum (Lepidoptera: Sphingidae) has a remarkable refracting superposition eye that departs radically from the classical principles of Exnerian superposition optics. Unlike its classical counterparts, this superposition eye is highly aspherical and contains extensive gradients of resolution and sensitivity. While such features are well known...

The most e cient techniques that have been developed to date for equality handling in rst-order theorem proving are based on superposition calculi. Superposition is a re nement of paramodulation in that various ordering constraints are imposed on inferences. For practical purposes, a key aspect of superposition is its compatibility with powerful simpli cation techniques. In this paper we solve ...

Two apparently different approaches to automating deduction are mentioned in the title; they are the subject of a debate on “big engines vs. little engines of proof”. The contributions in this thesis advocate that these two strands of research can interplay in subtle and sometimes unexpected ways, such that mutual pervasion can lead to intriguing results: Firstly, superposition can be run on to...

Optical imaging and lithography, the processes in which spatial patterns are resolved or transferred onto a detector or substrate via photons, cannot produce spatial features that are much smaller than the wavelength of light. This limitation has its roots in classical diffraction [1], which had been considered as a fundamental limit to all such imaging systems. Most notably, computer chip manu...

3dSS is a web-based interactive computing server, primarily designed to aid researchers, to superpose two or several 3D protein structures. In addition, the server can be effectively used to find the invariant and common water molecules present in the superposed homologous protein structures. The molecular visualization tool RASMOL is interfaced with the server to visualize the superposed 3D st...

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This thesis is about the Hierarchic Superposition calculus SUP(T) and its application to reasoning in hierarchic combinations FOL(T) of the free first-order logic FOL with a background theory T where the hierarchic calculus is refutationally complete or serves as a decision procedure. Particular hierarchic combinations covered in the thesis are the combinations of FOL and linear and non-linear ...