Related papers: Ellipses and Lambda Definability

Lifted probabilistic inference algorithms exploit regularities in the structure of graphical models to perform inference more efficiently. More specifically, they identify groups of interchangeable variables and perform inference once per…

This paper describes a 2-D graphics algorithm that uses shifts and adds to precisely plot a series of points on an ellipse of any shape and orientation. The algorithm can also plot an elliptic arc that starts and ends at arbitrary angles.…

In this paper, we extend the enumerative study of planar hypermaps with an alternating boundary introduced in an earlier work of Bouttier and the second author. In that article, an explicit rational parametrization was obtained for the…

The notion of topological entropy can be conceptualized in terms of the number of forward trajectories that are distinguishable at resolution $\varepsilon$ within $T$ time units. It can then be formally defined as a limit of a limit…

This technical report presents a general framework for parsing a variety of grammar formalisms. We develop a grammar formalism, called an Abstract Grammar, which is general enough to represent grammars at many levels of the hierarchy,…

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…

In this work we provide alternative formulations of the concepts of lambda theory and extensional theory without introducing the notion of substitution and the sets of all, free and bound variables occurring in a term. We also clarify the…

Recent work on vector-based compositional natural language semantics has proposed the use of density matrices to model lexical ambiguity and (graded) entailment (e.g. Piedeleu et al 2015, Bankova et al 2019, Sadrzadeh et al 2018). Ambiguous…

Fixed points are a recurring theme in computer science and are often constructed as limits of suitably seeded fixed point iterations. We present the algebra of iterative constructions (AIC) -- a purely algebraic approach to reasoning about…

In this paper, we present an explicit substitution calculus which distinguishes between ordinary bound variables and meta-variables. Its typing discipline is derived from contextual modal type theory. We first present a dependently typed…

The management of uncertainty in expert systems has usually been left to ad hoc representations and rules of combinations lacking either a sound theory or clear semantics. The objective of this paper is to establish a theoretical basis for…

Two are the main objectives of this article: first, we introduce a method for determining and analyzing constrained local extrema that provides a different alternative to all previous works on the topic, by eliminating Lagrange multipliers…

We shall generalize the notion of a Laver table to algebras which may have many generators, several fundamental operations, fundamental operations of arity higher than 2, and to algebras where only some of the operations are…

In this document we achieve exact and asymptotic enumeration of words, compositions over a finite group, and/or integer compositions characterized by local restrictions and, separately, subsequence pattern avoidance. We also count…

Sentences with gapping, such as Paul likes coffee and Mary tea, lack an overt predicate to indicate the relation between two or more arguments. Surface syntax representations of such sentences are often produced poorly by parsers, and even…

Recently, several methods have leveraged deep generative modeling to produce example-based explanations of image classifiers. Despite producing visually stunning results, these methods are largely disconnected from classical explainability…

This paper investigates the problem of extending measure theory to non-separable structures, from generalized descriptive set theory to a broader class of spaces beyond this framework. While various notions, such as the ideal of measure…

We study the problem of enumerating Tarski fixed points on finite lattices. We derive query complexity lower bounds for finding three or more Tarski fixed points of isotone maps and the subclasses of increasing and decreasing isotone maps.…

Extending the lambda-calculus with a construct for sharing, such as let expressions, enables a special representation of terms: iterated applications are decomposed by introducing sharing points in between any two of them, reducing to the…

Lattice rounding in Euclidean space can be viewed as finding the nearest point in the orbit of an action by a discrete group, relative to the norm inherited from the ambient space. Using this point of view, we initiate the study of…