Invited Lectures.- Tableau Algorithms for Description Logics.- Modality and Databases.- Local Symmetries in Propositional Logic.- Comparison.- Design and Results of TANCS-2000 Non-classical (Modal) Systems Comparison.- Consistency Testing: The RACE Experience.- Benchmark Analysis with FaCT.- MSPASS: Modal Reasoning by Translation and First-Order Resolution.- TANCS-2000 Results for DLP.- Evaluating *SAT on TANCS 2000 Benchmarks.- Research Papers.- A Labelled Tableau Calculus for Nonmonotonic (Cumulative) Consequence Relations.- A Tableau System for Godel-Dummett Logic Based on a Hypersequent Calculus.- An Analytic Calculus for Quantified Propositional Godel Logic.- A Tableau Method for Inconsistency-Adaptive Logics.- A Tableau Calculus for Integrating First-Order and Elementary Set Theory Reasoning.- Hypertableau and Path-Hypertableau Calculi for some Families of Intermediate Logics.- Variants of First-Order Modal Logics.- Complexity of Simple Dependent Bimodal Logics.- Properties of Embeddings from Int to S4.- Term-Modal Logics.- A Subset-Matching Size-Bounded Cache for Satisfiability in Modal Logics.- Dual Intuitionistic Logic Revisited.- Model Sets in a Nonconstructive Logic of Partial Terms with Definite Descriptions.- Search Space Compression in Connection Tableau Calculi Using Disjunctive Constraints.- Matrix-Based Inductive Theorem Proving.- Monotonic Preorders for Free Variable Tableaux.- The Mosaic Method for Temporal Logics.- Sequent-Like Tableau Systems with the Analytic Superformula Property for the Modal Logics KB, KDB, K5, KD5.- A Tableau Calculus for Equilibrium Entailment.- Towards Tableau-Based Decision Procedures for Non-Well-Founded Fragments of Set Theory.- Tableau Calculus for Only Knowing and Knowing At Most.- A Tableau-Like Representation Framework for Efficient Proof Reconstruction.- The Semantic Tableaux Version of the Second Incompleteness Theorem Extends Almost to Robinson's Arithmetic Q.- System Descriptions.- Redundancy-Free Lemmatization in the Automated Model-Elimination Theorem Prover AI-SETHEO.- E-SETHEO: An Automated3 Theorem Prover.

Automated Reasoning with Analytic Tableaux and Related Methods: International Conference, TABLEAUX 2000 St Andrews, Scotland, UK, July 3-7, 2000 Proceedings

We study the query answering using views (QAV) problem for tree pattern queries. Given a query and a view, the QAV problem is traditionally formulated in two ways: (i) find an equivalent rewriting of the query using only the view, or (ii) find a maximal contained rewriting using only the view. The former is appropriate for classical query optimization and was recently studied by Xu and Ozsoyoglu for tree pattern queries (TP). However, for information integration, we cannot rely on equivalent rewriting and must instead use maximal contained rewriting as shown by Halevy. Motivated by this, we study maximal contained rewriting for TP, a core subset of XPath, both in the absence and presence of a schema. In the absence of a schema, we show there are queries whose maximal contained rewriting (MCR) can only be expressed as the union of exponentially many TPs. We characterize the existence of a maximal contained rewriting and give a polynomial time algorithm for testing the existence of an MCR. We also give an algorithm for generating the MCR when one exists. We then consider QAV in the presence of a schema. We characterize the existence of a maximal contained rewriting when the schema contains no recursion or union types, and show that it consists of at most one TP. We give an efficient polynomial time algorithm for generating the maximal contained rewriting whenever it exists. Finally, we discuss QAV in the presence of recursive schemas.

/pdf/answering-tree-pattern-queries-using-views-xbvgrvmt4b.pdf

Answering tree pattern queries using views

That one-quarter of Medicare spending in the United States occurs in the last year of life is commonly interpreted as waste. But this interpretation presumes knowledge of who will die and when. Here we analyze how spending is distributed by predicted mortality, based on a machine-learning model of annual mortality risk built using Medicare claims. Death is highly unpredictable. Less than 5% of spending is accounted for by individuals with predicted mortality above 50%. The simple fact that we spend more on the sick—both on those who recover and those who die—accounts for 30 to 50% of the concentration of spending on the dead. Our results suggest that spending on the ex post dead does not necessarily mean that we spend on the ex ante “hopeless.”

/pdf/predictive-modeling-of-u-s-health-care-spending-in-late-life-2787a7zajb.pdf

Predictive modeling of U.S. health care spending in late life.

Separation logic (SL) is a widely used formalism for verifying heap manipulating programs. Existing SL solvers focus on decidable fragments for list-like structures. More complex data structures such as trees are typically unsupported in implementations, or handled by incomplete heuristics. While complete decision procedures for reasoning about trees have been proposed, these procedures suffer from high complexity, or make global assumptions about the heap that contradict the separation logic philosophy of local reasoning. In this paper, we present a fragment of classical first-order logic for local reasoning about tree-like data structures. The logic is decidable in NP and the decision procedure allows for combinations with other decidable first-order theories for reasoning about data. Such extensions are essential for proving functional correctness properties. We have implemented our decision procedure and, building on earlier work on translating SL proof obligations into classical logic, integrated it into an SL-based verification tool. We successfully used the tool to verify functional correctness of tree-based data structure implementations.

/pdf/automating-separation-logic-with-trees-and-data-1zy24sagtj.pdf

Automating Separation Logic with Trees and Data

The discrete cosine transform (DCT), introduced by Ahmed, Natarajan and Rao, has been used in many applications of digital signal processing, data compression and information hiding. There are four types of the discrete cosine transform. In simulating the discrete cosine transform, we propose a generalized discrete cosine transform with three parameters, and prove its orthogonality for some new cases. A new type of discrete cosine transform is proposed and its orthogonality is proved. Finally, we propose a generalized discrete W transform with three parameters, and prove its orthogonality for some new cases. Keywords: Discrete Fourier transform, discrete sine transform, discrete cosine transform, discrete W transform Nigerian Journal of Technological Research , vol7(1) 2012

On discrete cosine transform

We present an algorithm to solve XPath decision problems under regular tree type constraints and show its use to statically type-check XPath queries. To this end, we prove the decidability of a logic with converse for finite ordered trees whose time complexity is a simple exponential of the size of a formula. The logic corresponds to the alternation free modal μ-calculus without greatest fixpoint, restricted to finite trees, and where formulas are cycle-free.Our proof method is based on two auxiliary results. First, XML regular tree types and XPath expressions have a linear translation to cycle-free formulas. Second, the least and greatest fixpoints are equivalent for finite trees, hence the logic is closed under negation.Building on these results, we describe a practical, effective system for solving the satisfiability of a formula. The system has been experimented with some decision problems such as XPath emptiness, containment, overlap, and coverage, with or without type constraints. The benefit of the approach is that our system can be effectively used in static analyzers for programming languages manipulating both XPath expressions and XML type annotations (as input and output types).

/pdf/efficient-static-analysis-of-xml-paths-and-types-2e9m3wfvoj.pdf

Efficient static analysis of XML paths and types

The problem of SPARQL query containment is defined as determining if the result of one query is included in the result of another for any RDF graph. Query containment is important in many areas, including information integration, query optimization, and reasoning about Entity-Relationship diagrams. We encode this problem into an expressive logic called μ-calculus: where RDF graphs become transition systems, queries and schema axioms become formulas. Thus, the containment problem is reduced to formula satisfiability test. Beyond the logic's expressive power, satisfiability solvers are available for it. Hence, this study allows to exploit these advantages.

/pdf/sparql-query-containment-under-rdfs-entailment-regime-299400mofc.pdf

SPARQL query containment under RDFS entailment regime

SPARQL query containment under schema axioms is the problem of determining whether, for any RDF graph satisfying a given set of schema axioms, the answers to a query are contained in the answers of another query. This problem has major applications for verification and optimization of queries. In order to solve it, we rely on the µ-calculus. Firstly, we provide a mapping from RDF graphs into transition systems. Secondly, SPARQL queries and RDFS and SHI axioms are encoded into µ-calculus formulas. This allows us to reduce query containment and equivalence to satisfiability in the µ-calculus. Finally, we prove a double exponential upper bound for containment under SHI schema axioms.

/pdf/sparql-query-containment-under-shi-axioms-2adfv6257d.pdf

SPARQL query containment under SHI axioms

Developing and maintaining cascading style sheets (CSS) is an important issue to web developers as they suffer from the lack of rigorous methods. Most existing means rely on validators that check syntactic rules, and on runtime debuggers that check the behavior of a CSS style sheet on a particular document instance. However, the aim of most style sheets is to be applied to an entire set of documents, usually defined by some schema. To this end, a CSS style sheet is usually written w.r.t. a given schema. While usual debugging tools help reducing the number of bugs, they do not ultimately allow to prove properties over the whole set of documents to which the style sheet is intended to be applied. We propose a novel approach to fill this lack. We introduce ideas borrowed from the fields of logic and compile-time verification for the analysis of CSS style sheets. We present an original tool based on recent advances in tree logics. The tool is capable of statically detecting a wide range of errors (such as empty CSS selectors and semantically equivalent selectors), as well as proving properties related to sets of documents (such as coverage of styling information), in the presence or absence of schema information. This new tool can be used in addition to existing runtime debuggers to ensure a higher level of quality of CSS style sheets.

https://hal.inria.fr/hal-00643075/document

On the analysis of cascading style sheets

This work describes the theoretical and practical foundations of a system for the static analysis of XML processing languages. The system relies on a fixpoint modal logic with converse where models are finite trees. This calculus is expressive enough to capture regular tree types along with multi-directional navigation in trees. The decidability of the logic is proved in time 2^O(n) where n is the size of the input formula. XPath expressions and XML schemas are linearly translated into the logic. Based on these embeddings, several problems of major importance in XML applications are reduced to logical satisfiability. The focus is then given to a sound and complete algorithm for deciding the logic, along with crucial implementation techniques for building an effective solver. Practical experiments using a full system implementation are presented. The system appears efficient in practice for several realistic scenarios. The main application of this work is a new class of static analyzers for programs manipulating XML data. Such analyzers allow to ensure at compile-time valuable properties such as type-safety and optimizations, for safer and more efficient XML processing.

https://tel.archives-ouvertes.fr/docs/00/98/88/62/PDF/geneves-phd.pdf

Pierre Genevès

Papers

Efficient static analysis of XML paths and types

SPARQL query containment under RDFS entailment regime

SPARQL query containment under SHI axioms

On the analysis of cascading style sheets

Logics for XML