Related papers: A Compositional Query Algebra for Second-Order Log…
A quantitative model of concurrent interaction is introduced. The basic objects are linear combinations of partial order relations, acted upon by a group of permutations that represents potential non-determinism in synchronisation. This…
Answering logical queries over incomplete knowledge bases is challenging because: 1) it calls for implicit link prediction, and 2) brute force answering of existential first-order logic queries is exponential in the number of existential…
This paper proposes an alternative to standard first-order logic that seeks greater naturalness, generality, and semantic self-containment. The system removes the first-order restriction, avoids type hierarchies, and dispenses with external…
Algorithmic meta-theorems state that problems definable in a fixed logic can be solved efficiently on structures with certain properties. An example is Courcelle's Theorem, which states that all problems expressible in monadic second-order…
This paper presents State Algebra, a novel framework designed to represent and manipulate propositional logic using algebraic methods. The framework is structured as a hierarchy of three representations: Set, Coordinate, and Row…
Imprecise probability is concerned with uncertainty about which probability distributions to use. It has applications in robust statistics and machine learning. We look at programming language models for imprecise probability. Our…
An algebra is finitely related (or has finite degree) if its term functions are determined by some finite set of finitary relations. Nilpotent monoids built from words, via Rees quotients of free monoids, have been used to exhibit many…
An FOL-program consists of a background theory in a decidable fragment of first-order logic and a collection of rules possibly containing first-order formulas. The formalism stems from recent approaches to tight integrations of ASP with…
We explain how the simplicial higher-order unstable homotopy operations defined in [BBS2] may be composed and inserted one in another, thus forming a coherent if complicated algebraic structure.
This paper is about Kripke structures that are inside a relational database and queried with a modal language. At first the modal language that is used is introduced, followed by a definition of the database and relational algebra. Based on…
Tableaux originate as a decision method for a logical language. They can also be extended to obtain a structure that spells out all the information in a set of sentences in terms of truth value assignments to atomic formulas that appear in…
Spatial conjunction is a powerful construct for reasoning about dynamically allocated data structures, as well as concurrent, distributed and mobile computation. While researchers have identified many uses of spatial conjunction, its…
When reasoning about formal objects whose structures involve binding, it is often necessary to analyze expressions relative to a context that associates types, values, and other related attributes with variables that appear free in the…
This thesis investigates the central role of homomorphism problems (structure-preserving maps) in two complementary domains: database querying over finite, graph-shaped data, and constraint solving over (potentially infinite) structures.…
Databases are widespread, yet extracting relevant data can be difficult. Without substantial domain knowledge, multivariate search queries often return sparse or uninformative results. This paper introduces an approach for searching…
We extend the two-variable logic on data words with guarded regular binary predicates of the form $\widetilde{L}(x,y)$ that is true if positions $x$ and $y$ are in the same class and the factor strictly between $x$ and $y$ is in the regular…
Query containment and query answering are two important computational tasks in databases. While query answering amounts to compute the result of a query over a database, query containment is the problem of checking whether for every…
We study Monadic Second-Order Logic (MSO) over finite words, extended with (non-uniform arbitrary) monadic predicates. We show that it defines a class of languages that has algebraic, automata-theoretic and machine-independent…
The position we advocate in this paper is that relational algebra can provide a unified language for both representing and computing with statistical-relational objects, much as linear algebra does for traditional single-table machine…
Uncertainty arises naturally inmany application domains due to, e.g., data entry errors and ambiguity in data cleaning. Prior work in incomplete and probabilistic databases has investigated the semantics and efficient evaluation of ranking…