4,128 research outputs found
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
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
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
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
Learning-Assisted Automated Reasoning with Flyspeck
The considerable mathematical knowledge encoded by the Flyspeck project is
combined with external automated theorem provers (ATPs) and machine-learning
premise selection methods trained on the proofs, producing an AI system capable
of answering a wide range of mathematical queries automatically. The
performance of this architecture is evaluated in a bootstrapping scenario
emulating the development of Flyspeck from axioms to the last theorem, each
time using only the previous theorems and proofs. It is shown that 39% of the
14185 theorems could be proved in a push-button mode (without any high-level
advice and user interaction) in 30 seconds of real time on a fourteen-CPU
workstation. The necessary work involves: (i) an implementation of sound
translations of the HOL Light logic to ATP formalisms: untyped first-order,
polymorphic typed first-order, and typed higher-order, (ii) export of the
dependency information from HOL Light and ATP proofs for the machine learners,
and (iii) choice of suitable representations and methods for learning from
previous proofs, and their integration as advisors with HOL Light. This work is
described and discussed here, and an initial analysis of the body of proofs
that were found fully automatically is provided
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