A theorem proving procedure is described which combines the approach of locking resolution with that of rewriting systems. Indeed, both the binary resolution and a complete restr ict ion of paramodulation are embodied by an extension of the rewriting operation called superposition. Experimental results are reported and compared with l i terature automated proofs.

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,...

If one takes seriously the postulate of quantum mechanics in which physical states are rays in the standard Hilbert space of the theory, one is naturally lead to a geometric formulation of the theory. Within this formulation of quantum mechanics, the resulting description is very elegant from the geometrical viewpoint, since it allows to cast the main postulates of the theory in terms of two ge...

The typical mathematical language systematically exploits notational and logical abuses whose resolution requires not just the knowledge of domain specific notation and conventions, but not trivial skills in the given mathematical discipline. A large part of this background knowledge is expressed in form of equalities and isomorphisms, allowing mathematicians to freely move between different in...

High dimensional superposition models characterize observations using parameters which can be written as a sum of multiple component parameters, each with its own structure, e.g., sum of low rank and sparse matrices, sum of sparse and rotated sparse vectors, etc. In this paper, we consider general superposition models which allow sum of any number of component parameters, and each component str...

We present a new calculus for first-order theorem proving with equality, ME+Sup, which generalizes both the Superposition calculus and the Model Evolution calculus (with equality) by integrating their inference rules and redundancy criteria in a non-trivial way. The main motivation is to combine the advantageous features of both—rather complementary—calculi in a single framework. For instance, ...

introduction radiotherapy with small fields is used widely in newly developed techniques. additionally, dose calculation accuracy of treatment planning systems in small fields plays a crucial role in treatment outcome. in the present study, dose calculation accuracy of two commercial treatment planning systems was evaluated against monte carlo method. materials and methods siemens once or linea...

We present a systematic quantitative analysis of power-law force relaxation and investigate logarithmic superposition of force response in relaxed porcine airway smooth muscle (ASM) strips in vitro. The term logarithmic superposition describes linear superposition on a logarithmic scale, which is equivalent to multiplication on a linear scale. Additionally, we examine whether the dynamic respon...

In the context of a strongly local Dirichlet space we show that if a function mapping the real line to itself (and fixing the origin) operates by composition on the left to map the Dirichlet space into itself, then the function is necessarily locally Lipschitz continuous. If, in addition, the Dirichlet space contains unbounded elements, then the function must be globally Lipschitz continuous. T...

We discuss a space of Young measures in connection with some variational problems. We use it to present a proof of the Theorem of Tonelli on the existence of minimizing curves. We generalize a recent result of Ambrosio, Gigli and Savaré on the decomposition of the weak solutions of the transport equation. We also prove, in the context of Mather theory, the equality between Closed measures and H...