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The dot-depth hierarchy is a classification of star-free languages. It is related to the quantifier alternation hierarchy of first-order logic over finite words. We consider fragments of languages with dot-depth 1/2 and dot-depth 1 obtained…
The article continues the study of the genus of regular languages that the authors introduced in a 2012 paper. Generalizing a previous result, we produce a new family of regular languages on a two-letter alphabet having arbitrary high…
When we work with information from multiple sources, the formalism each employs to handle uncertainty may not be uniform. In order to be able to combine these knowledge bases of different formats, we need to first establish a common basis…
We study the question of whether a given regular language of finite trees can be defined in first-order logic. We develop an algebraic approach to address this question and we use it to derive several necessary and sufficient conditions for…
The notion of class is ubiquitous in computer science and is central in many formalisms for the representation of structured knowledge used both in knowledge representation and in databases. In this paper we study the basic issues…
We determine, by hierarchy, dependencies between higher order linear symmetries which occur when generating them using recursion operators. Thus, we deduce a formula which gives the number of independent generalized symmetries (basis) of…
This paper presents matching logic, a first-order logic (FOL) variant for specifying and reasoning about structure by means of patterns and pattern matching. Its sentences, the patterns, are constructed using variables, symbols, connectives…
Logical reasoning about program data often requires dealing with heap structures as well as scalar data types. Recent advances in Satisfiability Modular Theory (SMT) already offer efficient procedures for dealing with scalars, yet they lack…
We consider two-variable first-order logic on finite words with a fixed number of quantifier alternations. We show that all languages with a neutral letter definable using the order and finite-degree predicates are also definable with the…
Nominal Logic is a version of first-order logic with equality, name-binding, renaming via name-swapping and freshness of names. Contrarily to higher-order logic, bindable names, called atoms, and instantiable variables are considered as…
Separation Logic is an effective Program Logic for proving programs that involve pointers. Reasoning with pointers becomes difficult especially when there is aliasing arising due to several pointers to a given cell location. In this paper,…
Superposition is an established decision procedure for a variety of first-order logic theories represented by sets of clauses. A satisfiable theory, saturated by superposition, implicitly defines a minimal term-generated model for the…
Previous results on proving confluence for Constraint Handling Rules are extended in two ways in order to allow a larger and more realistic class of CHR programs to be considered confluent. Firstly, we introduce the relaxed notion of…
In this paper, we continue the research on the power of contextual grammars with selection languages from subfamilies of the family of regular languages. In the past, two independent hierarchies have been obtained for external and internal…
Discovering pattern sets or global patterns is an attractive issue from the pattern mining community in order to provide useful information. By combining local patterns satisfying a joint meaning, this approach produces patterns of higher…
We consider the quantifier alternation hierarchy within two-variable first-order logic FO^2[<,suc] over finite words with linear order and binary successor predicate. We give a single identity of omega-terms for each level of this…
We study first-order logic (FO) over the structure consisting of finite words over some alphabet $A$, together with the (non-contiguous) subword ordering. In terms of decidability of quantifier alternation fragments, this logic is…
This paper explores the space of (propositional) probabilistic logical languages, ranging from a purely `qualitative' comparative language to a highly `quantitative' language involving arbitrary polynomials over probability terms. While…
Hierarchy is a common and effective way of organizing data and representing their relationships at different levels of abstraction. However, hierarchical data dependencies cause difficulties in the estimation of "separable" models that can…
The principle behind algebraic language theory for various kinds of structures, such as words or trees, is to use a compositional function from the structures into a finite set. To talk about compositionality, one needs some way of…