Complete Axiomatizations of Fragments of Monadic Second-Order Logic on Finite Trees

We consider a specific class of tree structures that can represent basic structures in linguistics and computer science such as XML documents, parse trees, and treebanks, namely, finite node-labeled sibling-ordered trees. We present axiomatizations of the monadic second-order logic (MSO), monadic transitive closure logic (FO(TC1)) and monadic least fixed-point logic (FO(LFP1)) theories of this class of structures. These logics can express important properties such as reachability. Using model-theoretic techniques, we show by a uniform argument that these axiomatizations are complete, i.e., each formula that is valid on all finite trees is provable using our axioms. As a backdrop to our positive results, on arbitrary structures, the logics that we study are known to be non-recursively axiomatizable

A new Chinese-language textbook of ancient Greek with a historical outline of teaching Greek and Latin in China

In this paper we present the project of a new Chinese-language textbook of ancient Greek. This textbook is intended for students majoring in philosophy. In the first part of the paper, we provide an introduction to the historical circumstances inwhich ancient Greek literature and philosophy were originally introduced to China. We draw an outline of the cultural significance of the studies of ancient Greek in China, especially from the beginning of the 20th century. This helps explains the reasons why studies of ancient Greek were tightly connected to those of ancient Greek philosophy — and hence shed light on the intended focus of our textbook. In the second part of the paper, we present the textbook properly speaking: its intended audience and general structure, and an overview of the linguistic diff erence between ancient Greek and modern Chinese. This overview will reveal the types of issues faced by native Chinese speakers when learning ancient Greek and show that in some cases, such as the verbal aspect, Chinese has better resources to translate Greek sentences than English. We provide the example of a sample chapter to make the discussion more material and also to illustrate how the specific resources of Chinese language allow the translator to render the uses of subjunctive in ancient Greek.In this paper we present the project of a new Chinese-language textbook of ancient Greek. This textbook is intended for students majoring in philosophy. In the first part of the paper, we provide an introduction to the historical circumstances inwhich ancient Greek literature and philosophy were originally introduced to China. We draw an outline of the cultural significance of the studies of ancient Greek in China, especially from the beginning of the 20th century. This helps explains the reasons why studies of ancient Greek were tightly connected to those of ancient Greek philosophy — and hence shed light on the intended focus of our textbook. In the second part of the paper, we present the textbook properly speaking: its intended audience and general structure, and an overview of the linguistic diff erence between ancient Greek and modern Chinese. This overview will reveal the types of issues faced by native Chinese speakers when learning ancient Greek and show that in some cases, such as the verbal aspect, Chinese has better resources to translate Greek sentences than English. We provide the example of a sample chapter to make the discussion more material and also to illustrate how the specific resources of Chinese language allow the translator to render the uses of subjunctive in ancient Greek

Containment of Pattern-Based Queries over Data Trees

International audienceWe study static analysis, in particular the containment problem, for analogs of conjunctive queries over XML documents. The problem has been studied for queries based on arbitrary patterns, not necessarily following the tree structure of documents. However, many applications force the syntactic shape of queries to be tree-like, as they are based on proper tree patterns. This renders previous results, crucially based on having non-tree-like features, inapplicable. Thus, we investigate static analysis of queries based on proper tree patterns. We go beyond simple navigational conjunctive queries in two ways: we look at unions and Boolean combinations of such queries as well and, crucially, all our queries handle data stored in documents, i.e., we deal with containment over data trees. We start by giving a general \Pi^p_2 upper bound on the containment of conjunctive queries and Boolean combinations for patterns that involve all types of navigation through documents. We then show matching hardness for conjunctive queries with all navigation, or their Boolean combinations with the simplest form of navigation. After that we look at cases when containment can be witnessed by homomorphisms of analogs of tableaux. These include conjunctive queries and their unions over child and next-sibling axes; however, we show that not all cases of containment can be witnessed by homomorphisms. We look at extending tree patterns used in queries in three possible ways: with wildcard, with schema information, and with data value comparisons. The first one is relatively harmless, the second one tends to increase complexity by an exponential, and the last one quickly leads to undecidability

Querying Incomplete Data : Complexity and Tractability via Datalog and First-Order Rewritings

To answer database queries over incomplete data the gold standard is finding certain answers: those that are true regardless of how incomplete data is interpreted. Such answers can be found efficiently for conjunctive queries and their unions, even in the presence of constraints. With negation added, the problem becomes intractable however. We concentrate on the complexity of certain answers under constraints, and on effficiently answering queries outside the usual classes of (unions) of conjunctive queries by means of rewriting as Datalog and first-order queries. We first notice that there are three different ways in which query answering can be cast as a decision problem. We complete the existing picture and provide precise complexity bounds on all versions of the decision problem, for certain and best answers. We then study a well-behaved class of queries that extends unions of conjunctive queries with a mild form of negation. We show that for them, certain answers can be expressed in Datalog with negation, even in the presence of functional dependencies, thus making them tractable in data complexity. We show that in general Datalog cannot be replaced by first-order logic, but without constraints such a rewriting can be done in first-order. The paper is under consideration in Theory and Practice of Logic Programming (TPLP).Comment: Under consideration in Theory and Practice of Logic Programming (TPLP

Certain Answers of Extensions of Conjunctive Queries by Datalog and First-Order Rewriting

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Mallé en son exil ou la parole caméra. Entretien de Denis Gheerbrant par Corinne Fortier

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