Tableaux Modulo Theories Using Superdeduction

We propose a method that allows us to develop tableaux modulo theories using the principles of superdeduction, among which the theory is used to enrich the deduction system with new deduction rules. This method is presented in the framework of the Zenon automated theorem prover, and is applied to the set theory of the B method. This allows us to provide another prover to Atelier B, which can be used to verify B proof rules in particular. We also propose some benchmarks, in which this prover is able to automatically verify a part of the rules coming from the database maintained by Siemens IC-MOL. Finally, we describe another extension of Zenon with superdeduction, which is able to deal with any first order theory, and provide a benchmark coming from the TPTP library, which contains a large set of first order problems.Comment: arXiv admin note: substantial text overlap with arXiv:1501.0117

On the Expressivity and Applicability of Model Representation Formalisms

A number of first-order calculi employ an explicit model representation formalism for automated reasoning and for detecting satisfiability. Many of these formalisms can represent infinite Herbrand models. The first-order fragment of monadic, shallow, linear, Horn (MSLH) clauses, is such a formalism used in the approximation refinement calculus. Our first result is a finite model property for MSLH clause sets. Therefore, MSLH clause sets cannot represent models of clause sets with inherently infinite models. Through a translation to tree automata, we further show that this limitation also applies to the linear fragments of implicit generalizations, which is the formalism used in the model-evolution calculus, to atoms with disequality constraints, the formalisms used in the non-redundant clause learning calculus (NRCL), and to atoms with membership constraints, a formalism used for example in decision procedures for algebraic data types. Although these formalisms cannot represent models of clause sets with inherently infinite models, through an additional approximation step they can. This is our second main result. For clause sets including the definition of an equivalence relation with the help of an additional, novel approximation, called reflexive relation splitting, the approximation refinement calculus can automatically show satisfiability through the MSLH clause set formalism.Comment: 15 page

On the Expressivity and Applicability of Model Representation Formalisms

A number of first-order calculi employ an explicit model representation formalism for automated reasoning and for detecting satisfiability. Many of these formalisms can represent infinite Herbrand models. The first-order fragment of monadic, shallow, linear, Horn (MSLH) clauses, is such a formalism used in the approximation refinement calculus. Our first result is a finite model property for MSLH clause sets. Therefore, MSLH clause sets cannot represent models of clause sets with inherently infinite models. Through a translation to tree automata, we further show that this limitation also applies to the linear fragments of implicit generalizations, which is the formalism used in the model-evolution calculus, to atoms with disequality constraints, the formalisms used in the non-redundant clause learning calculus (NRCL), and to atoms with membership constraints, a formalism used for example in decision procedures for algebraic data types. Although these formalisms cannot represent models of clause sets with inherently infinite models, through an additional approximation step they can. This is our second main result. For clause sets including the definition of an equivalence relation with the help of an additional, novel approximation, called reflexive relation splitting, the approximation refinement calculus can automatically show satisfiability through the MSLH clause set formalism

12th International Workshop on Termination (WST 2012) : WST 2012, February 19–23, 2012, Obergurgl, Austria / ed. by Georg Moser

This volume contains the proceedings of the 12th International Workshop on Termination (WST 2012), to be held February 19–23, 2012 in Obergurgl, Austria. The goal of the Workshop on Termination is to be a venue for presentation and discussion of all topics in and around termination. In this way, the workshop tries to bridge the gaps between different communities interested and active in research in and around termination. The 12th International Workshop on Termination in Obergurgl continues the successful workshops held in St. Andrews (1993), La Bresse (1995), Ede (1997), Dagstuhl (1999), Utrecht (2001), Valencia (2003), Aachen (2004), Seattle (2006), Paris (2007), Leipzig (2009), and Edinburgh (2010). The 12th International Workshop on Termination did welcome contributions on all aspects of termination and complexity analysis. Contributions from the imperative, constraint, functional, and logic programming communities, and papers investigating applications of complexity or termination (for example in program transformation or theorem proving) were particularly welcome. We did receive 18 submissions which all were accepted. Each paper was assigned two reviewers. In addition to these 18 contributed talks, WST 2012, hosts three invited talks by Alexander Krauss, Martin Hofmann, and Fausto Spoto

What Java Developers Know About Compatibility, And Why This Matters

Real-world programs are neither monolithic nor static -- they are constructed using platform and third party libraries, and both programs and libraries continuously evolve in response to change pressure. In case of the Java language, rules defined in the Java Language and Java Virtual Machine Specifications define when library evolution is safe. These rules distinguish between three types of compatibility - binary, source and behavioural. We claim that some of these rules are counter intuitive and not well-understood by many developers. We present the results of a survey where we quizzed developers about their understanding of the various types of compatibility. 414 developers responded to our survey. We find that while most programmers are familiar with the rules of source compatibility, they generally lack knowledge about the rules of binary and behavioural compatibility. This can be problematic when organisations switch from integration builds to technologies that require dynamic linking, such as OSGi. We have assessed the gravity of the problem by studying how often linkage-related problems are referenced in issue tracking systems, and find that they are common

GO faster ChEBI with Reasonable Biochemistry

Chemical Entities of Biological Interest (ChEBI) is a database and ontology that represents biochemical knowledge about small molecules. Recent changes to the ontology have created new opportunities for automated reasoning with description logic, that have not previously been fully exploited in Chemistry. These changes open up the possibility of building an improved chemical semantic web, by making more use of necessary and sufficient conditions, allowing reasoning about chemical structure, highlighting ambiguous inconsistencies and improving alignment with the Gene Ontology (GO). This paper briefly discusses some of the problems with reasoning over the current version of ChEBI, to tackle these issues, and their potential solutions