Related papers: The Logic of Counting Query Answers

We consider the problem of answering queries about formulas of first-order logic based on background knowledge partially represented explicitly as other formulas, and partially represented as examples independently drawn from a fixed…

We study the complexity of the model checking problem, for fixed model A, over certain fragments L of first-order logic. These are sometimes known as the expression complexities of L. We obtain various complexity classification theorems for…

We investigate the quantifier alternation hierarchy in first-order logic on finite words. Levels in this hierarchy are defined by counting the number of quantifier alternations in formulas. We prove that one can decide membership of a…

We describe an approach to modelling and reasoning about data-centric business processes and present a form of general model checking. Our technique extends existing approaches, which explore systems only from concrete initial states.…

First-order model counting (FOMC) is the problem of counting the number of models of a sentence in first-order logic. Since lifted inference techniques rely on reductions to variants of FOMC, the design of scalable methods for FOMC has…

We study the reactive synthesis problem for distributed systems with an unbounded number of participants interacting with an uncontrollable environment. Executions of those systems are modeled by data words, and specifications are given as…

One of the major open problems in automata and logic is the following: is there an algorithm which inputs a regular tree language and decides if the language can be defined in first-order logic? The goal of this paper is to present this…

We formalize an existing computability-theoretic method of presenting first-order structures whose domains have the cardinality of the continuum. Work using these methods until now has emphasized their topological properties. We shift the…

Matching logic is a logical framework for specifying and reasoning about programs using pattern matching semantics. A pattern is made up of a number of structural components and constraints. Structural components are syntactically matched,…

This paper gives a thorough overview of what is known about first-order logic with counting quantifiers and with arithmetic predicates. As a main theorem we show that Presburger arithmetic is closed under unary counting quantifiers.…

First-order logic is known to have limited expressive power over finite structures. It enjoys in particular the locality property, which states that first-order formulae cannot have a global view of a structure. This limitation ensures on…

A logic calculus is presented that is a conservative extension of linear logic. The motivation beneath this work concerns lazy evaluation, true concurrency and interferences in proof search. The calculus includes two new connectives to deal…

Blocked clauses provide the basis for powerful reasoning techniques used in SAT, QBF, and DQBF solving. Their definition, which relies on a simple syntactic criterion, guarantees that they are both redundant and easy to find. In this paper,…

This paper defines the (first-order) conflict resolution calculus: an extension of the resolution calculus inspired by techniques used in modern SAT-solvers. The resolution inference is restricted to (first-order) unit-propagation and the…

The theory of finite term algebras provides a natural framework to describe the semantics of functional languages. The ability to efficiently reason about term algebras is essential to automate program analysis and verification for…

The primary goal of this paper is to present a unified way to transform the syntax of a logic system into certain initial algebraic structure so that it can be studied algebraically. The algebraic structures which one may choose for this…

In this note, we give a linear-size translation from formulas of first-order logic into equations of the calculus of relations preserving validity and finite validity. Our translation also gives a linear-size conservative reduction from…

In this note we describe a new method of counting the number of unordered factorizations of a natural number by means of a generating function and a recurrence relation arising from it, which improves an earlier result in this direction.

We consider an extension of first-order logic with a recursion operator that corresponds to allowing formulas to refer to themselves. We investigate the obtained language under two different systems of semantics, thereby obtaining two…

We lay the foundations for a database-inspired approach to interpreting and understanding neural network models by querying them using declarative languages. Towards this end we study different query languages, based on first-order logic,…