What is modal logic

This book develops a new view of logic as a theory of information-driven agency and intelligent interaction between many agents - with conversation, argumentation and games as guiding examples. It provides one uniform account of dynamic logics for acts of inference, observation, questions and communication, that can handle both update of knowledge and revision of beliefs. It then extends the dynamic style of analysis to include changing preferences and goals, temporal processes, group action and strategic interaction in games. Throughout, the book develops a mathematical theory unifying all these systems, and positioning them at the interface of logic, philosophy, computer science and game theory. A series of further chapters explores repercussions of the 'dynamic stance' for these areas, as well as cognitive science.

/pdf/logical-dynamics-of-information-and-interaction-3fy0u23au4.pdf

Logical Dynamics of Information and Interaction

We present the architecture and technologies underpinning the OBDA system Ontop and taking full advantage of storing data in relational databases. We discuss the theoretical foundations of Ontop: the tree-witness query rewriting, $\mathcal{T}$ -mappings and optimisations based on database integrity constraints and SQL features. We analyse the performance of Ontop in a series of experiments and demonstrate that, for standard ontologies, queries and data stored in relational databases, Ontop is fast, efficient and produces SQL rewritings of high quality.

/pdf/ontology-based-data-access-ontop-of-databases-hxhum6zhw9.pdf

Ontology-Based Data Access: Ontop of Databases

We survey results about static analysis of pattern-based queries over XML documents. These queries are analogs of conjunctive queries, their unions and Boolean combinations, in which tree patterns play the role of atomic formulae. As in the relational case, they can be viewed as both queries and incomplete documents, and thus static analysis problems can also be viewed as finding certain answers of queries over such documents. We look at satisfiability of patterns under schemas, containment of queries for various features of XML used in queries, finding certain answers, and applications of pattern-based queries in reasoning about schema mappings for data exchange.

/pdf/reasoning-about-pattern-based-xml-queries-4pijxg98zk.pdf

Reasoning about pattern-based XML queries

We present an extension of the ontology-based data access platform Ontop that supports answering SPARQL queries under the OWL 2 QL direct semantics entailment regime for data instances stored in relational databases. On the theoretical side, we show how any input SPARQL query, OWL 2 QL ontology and R2RML mappings can be rewritten to an equivalent SQL query solely over the data. On the practical side, we present initial experimental results demonstrating that by applying the Ontop technologiesthe tree-witness query rewriting, $\mathcal{T}$ -mappings compiling R2RML mappings with ontology hierarchies, and $\mathcal{T}$ -mapping optimisations using SQL expressivity and database integrity constraintsthe system produces scalable SQL queries.

/pdf/answering-sparql-queries-over-databases-under-owl-2-ql-55xyeox5br.pdf

Answering SPARQL Queries over Databases under OWL 2 QL Entailment Regime

Current methods for solving games embody a form of "procedural rationality" that invites logical analysis in its own right. This paper is a brief case study of Backward Induction for extensive games, replacing earlier static logical definitions by stepwise dynamic ones. We consider a number of analysis from recent years that look different conceptually, and find that they are all mathematically equivalent. This shows how an abstract logical perspective can bring out basic invariant structure in games. We then generalize this to an exploration of fixed-point logics on finite trees that best fit game-theoretic equilibria. We end with some open questions that suggest a broader program for merging current computational logics with notions and results from game theory. This paper is largely a program for opening up an area: an extended version of the technical results will be found in the forthcoming dissertation [26].

/pdf/game-solution-epistemic-dynamics-and-fixed-point-logics-2rgb97p7u5.pdf

Game Solution, Epistemic Dynamics and Fixed-Point Logics

The term naive evaluation refers to evaluating queries over incomplete databases as if nulls were usual data values, that is, to using the standard database query evaluation engine. Since the semantics of query answering over incomplete databases is that of certain answers, we would like to know when naive evaluation computes them, that is, when certain answers can be found without inventing new specialized algorithms. For relational databases it is well known that unions of conjunctive queries possess this desirable property, and results on preservation of formulae under homomorphisms tell us that, within relational calculus, this class cannot be extended under the open-world assumption. Our goal here is twofold. First, we develop a general framework that allows us to determine, for a given semantics of incompleteness, classes of queries for which naive evaluation computes certain answers. Second, we apply this approach to a variety of semantics, showing that for many classes of queries beyond unions of conjunctive queries, naive evaluation makes perfect sense under assumptions different from open world. Our key observations are: (1) naive evaluation is equivalent to monotonicity of queries with respect to a semantics-induced ordering, and (2) for most reasonable semantics of incompleteness, such monotonicity is captured by preservation under various types of homomorphisms. Using these results we find classes of queries for which naive evaluation works, for example, positive first-order formulae for the closed-world semantics. Even more, we introduce a general relation-based framework for defining semantics of incompleteness, show how it can be used to capture many known semantics and to introduce new ones, and describe classes of first-order queries for which naive evaluation works under such semantics.

/pdf/naive-evaluation-of-queries-over-incomplete-databases-2gv3zlhkmd.pdf

Naïve Evaluation of Queries over Incomplete Databases

We 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 Πp2 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.

/pdf/containment-of-pattern-based-queries-over-data-trees-2f7decp1rg.pdf

Containment of pattern-based queries over data trees

Previous studies of incomplete XML documents have identified three main sources of incompleteness -- in structural information, data values, and labeling -- and addressed data complexity of answering analogs of unions of conjunctive queries under the open world assumption. It is known that structural incompleteness leads to intractability, while incompleteness in data values and labeling still permits efficient computation of certain answers.The goal of this paper is to provide a complete picture of the complexity of query answering over incomplete XML documents. We look at more expressive languages, at other semantic assumptions, and at both data and combined complexity of query answering, to see whether some well-behaving tractable classes have been missed. To incorporate non-positive features into query languages, we look at gentle ways of introducing negation via inequalities and/or Boolean combinations of positive queries, as well as the analog of relational calculus. We also look at the closed world assumption which, due to the hierarchical structure of XML, has two variations. For all combinations of languages and semantics of incompleteness we determine data and combined complexity of computing certain answers. We show that structural incompleteness leads to intractability under all assumptions, while by dropping it we can recover efficient evaluation algorithms for some queries that go beyond those previously studied.

/pdf/on-the-complexity-of-query-answering-over-incomplete-xml-2nz4tsx4ks.pdf

Amélie Gheerbrant

Papers

Reasoning about pattern-based XML queries

Game Solution, Epistemic Dynamics and Fixed-Point Logics

Naïve Evaluation of Queries over Incomplete Databases

Containment of pattern-based queries over data trees

On the complexity of query answering over incomplete XML documents