67,701 research outputs found
Abstract Canonical Inference
An abstract framework of canonical inference is used to explore how different
proof orderings induce different variants of saturation and completeness.
Notions like completion, paramodulation, saturation, redundancy elimination,
and rewrite-system reduction are connected to proof orderings. Fairness of
deductive mechanisms is defined in terms of proof orderings, distinguishing
between (ordinary) "fairness," which yields completeness, and "uniform
fairness," which yields saturation.Comment: 28 pages, no figures, to appear in ACM Trans. on Computational Logi
A Labelled Analytic Theorem Proving Environment for Categorial Grammar
We present a system for the investigation of computational properties of
categorial grammar parsing based on a labelled analytic tableaux theorem
prover. This proof method allows us to take a modular approach, in which the
basic grammar can be kept constant, while a range of categorial calculi can be
captured by assigning different properties to the labelling algebra. The
theorem proving strategy is particularly well suited to the treatment of
categorial grammar, because it allows us to distribute the computational cost
between the algorithm which deals with the grammatical types and the algebraic
checker which constrains the derivation.Comment: 11 pages, LaTeX2e, uses examples.sty and a4wide.st
On Automated Lemma Generation for Separation Logic with Inductive Definitions
Separation Logic with inductive definitions is a well-known approach for
deductive verification of programs that manipulate dynamic data structures.
Deciding verification conditions in this context is usually based on
user-provided lemmas relating the inductive definitions. We propose a novel
approach for generating these lemmas automatically which is based on simple
syntactic criteria and deterministic strategies for applying them. Our approach
focuses on iterative programs, although it can be applied to recursive programs
as well, and specifications that describe not only the shape of the data
structures, but also their content or their size. Empirically, we find that our
approach is powerful enough to deal with sophisticated benchmarks, e.g.,
iterative procedures for searching, inserting, or deleting elements in sorted
lists, binary search tress, red-black trees, and AVL trees, in a very efficient
way
Towards an Intelligent Tutor for Mathematical Proofs
Computer-supported learning is an increasingly important form of study since
it allows for independent learning and individualized instruction. In this
paper, we discuss a novel approach to developing an intelligent tutoring system
for teaching textbook-style mathematical proofs. We characterize the
particularities of the domain and discuss common ITS design models. Our
approach is motivated by phenomena found in a corpus of tutorial dialogs that
were collected in a Wizard-of-Oz experiment. We show how an intelligent tutor
for textbook-style mathematical proofs can be built on top of an adapted
assertion-level proof assistant by reusing representations and proof search
strategies originally developed for automated and interactive theorem proving.
The resulting prototype was successfully evaluated on a corpus of tutorial
dialogs and yields good results.Comment: In Proceedings THedu'11, arXiv:1202.453
Deduction modulo theory
This paper is a survey on Deduction modulo theor
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
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