Christoph Weidenbach

System Description: Spass Version 3.0

An electrophotographic copying system is disclosed wherein the DC charging and DC transfer corotrons are powered with an unfiltered full wave rectified voltage derived from a 110 volt, 60 hertz line source. The DC corotrons are regulated along with AC corotrons used for detack and erase operations. The regulation is achieved by a feedback loop coupled to only one of the corotrons.

SPASS - Version 0.49

This article describes SPASS, Version 0.49, as it was entered in the system competition at CADE-13. SPASS is an automated theorem prover for full first-order logic with equality. It is based on the superposition calculus originally developed by Bachmair and Ganzinger, extended by the sort techniques due to Weidenbach and an inference rule for case analysis.

Superposition modulo linear arithmetic SUP(LA)

The hierarchical superposition based theorem proving calculus of Bachmair, Ganzinger, and Waldmann enables the hierarchic combination of a theory with full first-order logic. If a clause set of the combination enjoys a sufficient completeness criterion, the calculus is even complete. We instantiate the calculus for the theory of linear arithmetic. In particular, we develop new effective versions for the standard superposition redundancy criteria taking the linear arithmetic theory into account. The resulting calculus is implemented in SPASS(LA) and extends the state of the art in proving properties of first-order formulas over linear arithmetic.

More SPASS with Isabelle : Superposition with Hard Sorts and Configurable Simplification

Sledgehammer for Isabelle/HOL integrates automatic theorem provers to discharge interactive proof obligations. This paper considers a tighter integration of the superposition prover SPASS to increase Sledgehammer’s success rate. The main enhancements are native support for hard sorts (simple types) in SPASS, simplification that honors the orientation of Isabelle simp rules, and a pair of clause-selection strategies targeted at large lemma libraries. The usefulness of this integration is confirmed by an evaluation on a vast benchmark suite and by a case study featuring a formalization of language-based security.

Towards verification of the pastry protocol using TLA

Pastry is an algorithm that provides a scalable distributed hash table over an underlying P2P network. Several implementations of Pastry are available and have been applied in practice, but no attempt has so far been made to formally describe the algorithm or to verify its properties. Since Pastry combines rather complex data structures, asynchronous communication, concurrency, resilience to churn and fault tolerance, it makes an interesting target for verification. We have modeled Pastrys core routing algorithms and communication protocol in the specification language TLA+. In order to validate the model and to search for bugs we employed the TLA+ model checker tlc to analyze several qualitative properties. We obtained non-trivial insights in the behavior of Pastry through the model checking analysis. Furthermore, we started to verify Pastry using the very same model and the interactive theorem prover tlaps for TLA+. A first result is the reduction of global Pastry correctness properties to invariants of the underlying data structures.

On the saturation of YAGO

YAGO is an automatically generated ontology out of Wikipedia and WordNet. It is eventually represented in a proprietary flat text file format and a core comprises 10 million facts and formulas. We present a translation of YAGO into the Bernays-Schonfinkel Horn class with equality. A new variant of the superposition calculus is sound, complete and terminating for this class. Together with extended term indexing data structures the new calculus is implemented in Spass-YAGO. YAGO can be finitely saturated by Spass-YAGO in about 1 hour. We have found 49 inconsistencies in the original generated ontology which we have fixed. Spass-YAGO can then prove non-trivial conjectures with respect to the resulting saturated and consistent clause set of about 1.4 GB in less than one second.

A PLTL-prover based on labelled superposition with partial model guidance

Labelled superposition (LPSup) is a new calculus for PLTL. One of its distinguishing features, in comparison to other resolution-based approaches, is its ability to construct partial models on the fly. We use this observation to design a new decision procedure for the logic, where the models are effectively used to guide the search. On a representative set of benchmarks, our implementation is then shown to considerably advance the state of the art.

Superposition as a Decision Procedure for Timed Automata

The success of superposition-based theorem proving in first-order logic relies in particular on the fact that the superposition calculus can be turned into a decision procedure for various decidable fragments of first-order logic and has been successfully used to identify new decidable classes. In this paper, we extend this story to the hierarchic combination of linear arithmetic and first-order superposition. We show that decidability of reachability in timed automata can be obtained by instantiation of an abstract termination result for SUP(LA), the hierarchic combination of linear arithmetic and first-order superposition.

Unification in sort theories and its applications

In this article we investigate the properties of unification in sort theories. A sort is represented by a set of monadic predicates, called sort symbols. Sorts are attached to variables restricting their respective domain to the intersection of the denotations of the sort symbols. A sort theory consists of a set of declarations that are atoms starting with a sort symbol. Two terms are unifiable with respect to some sort theory, if they are unifiable in the standard sense and the assignments of the unifier do respect the declarations in the sort theory. Therefore, the new sorted unification algorithm is formed by standard unification augmented by extra rules that consider the information in the sort theory. We prove the new sorted unification algorithm to be correct and complete and establish complexity results for several different, syntactically characterized sort theories. The notions of a sort and a sort theory are developed in such a way that sort symbols are used like ordinary monadic predicate symbols. To this end, sorts may denote empty sets, and the sort theory is not a static part of the signature. It may dynamically change during a deduction process. The applicability of the approach is demonstrated for the resolution and the tableau calculus.

Superposition for fixed domains

Superposition is an established decision procedure for a variety of first-order logic theories represented by sets of clauses. A satisfiable theory, saturated by superposition, implicitly defines a minimal term-generated model for the theory. Proving universal properties with respect to a saturated theory directly leads to a modification of the minimal models term-generated domain, as new Skolem functions are introduced. For many applications, this is not desired. Therefore, we propose the first superposition calculus that can explicitly represent existentially quantified variables and can thus compute with respect to a given domain. This calculus is sound and refutationally complete in the limit for a first-order fixed domain semantics. For saturated Horn theories and classes of positive formulas, we can even employ the calculus to prove properties of the minimal model itself, going beyond the scope of known superposition-based approaches.