Related papers: On Categories of Nested Conditions
We show that the class of representable substitution algebras is characterized by a set of universal first order sentences. In addition, it is shown that a necessary and sufficient condition for a substitution algebra to be representable is…
A nested coordinate system is a reassigning of independent variables to take advantage of geometric or symmetry properties of a particular application. Polar, cylindrical and spherical coordinate systems are primary examples of such a…
We present a new probabilistic modelling framework based on the recent notion of normal factor graph (NFG). We show that the proposed NFG models and their transformations unify some existing models such as factor graphs, convolutional…
Game semantics describe the interactive behavior of proofs by interpreting formulas as games on which proofs induce strategies. Such a semantics is introduced here for capturing dependencies induced by quantifications in first-order…
We describe a basic correspondence between linear algebraic structures within vector embeddings in artificial neural networks and conditional independence constraints on the probability distributions modeled by these networks. Our framework…
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 cartesian structure possessed by relations, spans, profunctors, and other such morphisms is elegantly expressed by universal properties in double categories. Though cartesian double categories were inspired in part by the older program…
In recent work, the authors developed a simple method of constructing topological spaces from certain well-behaved partially ordered sets -- those coming from sequences of relations between finite sets. This method associates a given poset…
We present a metagrammatical formalism, {\em generic rules}, to give a default interpretation to grammar rules. Our formalism introduces a process of {\em dynamic binding} interfacing the level of pure grammatical knowledge representation…
We consider an array of random variables, taking values in a complete and separable metric space, that exhibits a kind of symmetry which we call row exchangeability. Given such an array, a natural model for Bayesian nonparametric inference…
The constraints arising from DAG models with latent variables can be naturally represented by means of acyclic directed mixed graphs (ADMGs). Such graphs contain directed and bidirected arrows, and contain no directed cycles. DAGs with…
Nested space-filling designs are nested designs with attractive low-dimensional stratification. Such designs are gaining popularity in statistics, applied mathematics and engineering. Their applications include multi-fidelity computer…
Representing a proof tree by a combinator term that reduces to the tree lets subtle forms of duplication within the tree materialize as duplicated subterms of the combinator term. In a DAG representation of the combinator term these…
We extend the theory of initial conflicts in the framework of M-adhesive categories to transformation rules with ACs. We first show that for rules with ACs, conflicts are in general neither inherited from a bigger context any more, nor is…
This paper extends the class of ordinal regression models with a structured interpretation of the problem by applying a novel treatment of encoded labels. The net effect of this is to transform the underlying problem from an ordinal…
Injecting structure into neural networks enables learning functions that satisfy invariances with respect to subsets of inputs. For instance, when learning generative models using neural networks, it is advantageous to encode the…
A notion of stratification is introduced for any compactly generated triangulated category T endowed with an action of a graded commutative noetherian ring R. The utility of this notion is demonstrated by establishing diverse consequences…
This paper addresses the following verification task: Given a graph transformation system and a class of initial graphs, can we guarantee (non-)reachability of a given other class of graphs that characterizes bad or erroneous states? Both…
Variables are a crucial element in logic and are also addressed in institution theory, an effort to axiomatize logic. In institution theory, we typically use extensions (signature morphisms) obtained from variables instead of introducing…
In recent work, we introduced a new semantics for conditionals, covering a large class of what we call preconditionals. In this paper, we undertake an axiomatic study of preconditionals and subclasses of preconditionals. We then prove that…