Related papers: Random Models and the Guarded Fragment

Over the past two decades several fragments of first-order logic have been identified and shown to have good computational and algorithmic properties, to a great extent as a result of appropriately describing the image of the standard…

The Triguarded Fragment (TGF) is among the most expressive decidable fragments of first-order logic, subsuming both its two-variable and guarded fragments without equality. We show that the TGF has the finite model property (providing a…

Hilbert's Entscheidungsproblem has given rise to a broad and productive line of research in mathematical logic, where the classification process of decidable classes of first-order sentences represent only one of the remarkable results.…

An important class of decidable first-order logic fragments are those satisfying a guardedness condition, such as the guarded fragment (GF). Usually, decidability for these logics is closely linked to the tree-like model property - the fact…

We define the adjacent fragment AF of first-order logic, obtained by restricting the sequences of variables occurring as arguments in atomic formulas. The adjacent fragment generalizes (after a routine renaming) two-variable logic as well…

Recently, symbolic structures were proposed as finite representations of potentially infinite first-order structures, where Linear Integer Arithmetic terms and formulas define the domain and interpretations of a structure. We generalize…

The Guarded Fragment (GF) is a well-established decidable fragment of first-order logic. We study an extension of GF with nested equivalence relations, namely a family of distinguished binary predicates $E_1, E_2, \dots$ interpreted as…

We present a new technique for proving logarithmic upper bounds for diameters of evolving random graph models, which is based on defining a coupling between random graphs and variants of random recursive trees. The advantage of the…

During the last decades, a lot of effort was put into identifying decidable fragments of first-order logic. Such efforts gave birth, among the others, to the two-variable fragment and the guarded fragment, depending on the type of…

We consider extensions of the two-variable guarded fragment, GF2, where distinguished binary predicates that occur only in guards are required to be interpreted in a special way (as transitive relations, equivalence relations, pre-orders or…

Many representation schemes combining first-order logic and probability have been proposed in recent years. Progress in unifying logical and probabilistic inference has been slower. Existing methods are mainly variants of lifted variable…

Quantitative logic reasons about the degree to which formulas are satisfied. This paper studies the fundamental reasoning principles of higher-order quantitative logic and their application to reasoning about probabilistic programs and…

We study the Guarded Fragment with Regular Guards (RGF), which combines the expressive power of the Guarded Fragment (GF) with Propositional Dynamic Logic with Intersection and Converse (ICPDL). Our logic generalizes, in a uniform way, many…

We study the problem of bounding the posterior distribution of discrete probabilistic programs with unbounded support, loops, and conditioning. Loops pose the main difficulty in this setting: even if exact Bayesian inference is possible,…

This note contains some material promised in our earlier papers on submodel preservation and the guarded fragment, along with some information on the current status of the problems mentioned in these papers. Section 1 contains an early…

We call a first-order formula one-dimensional if its every maximal block of existential (universal) quantifiers leaves at most one variable free. We consider the one-dimensional restrictions of the guarded fragment, GF, and the tri-guarded…

We establish non-asymptotic bounds on the finite-sample behavior of generalized first-order iterative algorithms -- including gradient-based optimization methods and approximate message passing (AMP) -- with Gaussian data matrices and…

We consider an extension of the unary negation fragment of first-order logic in which arbitrarily many binary symbols may be required to be interpreted as equivalence relations. We show that this extension has the finite model property.…

Continuous first-order logic is used to apply model-theoretic analysis to analytic structures (e.g. Hilbert spaces, Banach spaces, probability spaces, etc.). Classical computable model theory is used to examine the algorithmic structure of…

In this paper, we study the sampling problem for first-order logic proposed recently by Wang et al. -- how to efficiently sample a model of a given first-order sentence on a finite domain? We extend their result for the…