Related papers: On projective systems of rational difference equat…

In visual cognition, illusions help elucidate certain intriguing latent perceptual functions of the human vision system, and their proper mathematical modeling and computational simulation are therefore deeply beneficial to both biological…

Logical relations are one of the most powerful techniques in the theory of programming languages, and have been used extensively for proving properties of a variety of higher-order calculi. However, there are properties that cannot be…

We give a complete description of the qualitative behavior of the second-order rational difference equation #166. We also establish the boundedness character for the rational system in the plane #(8,30).

We present a new system S for handling uncertainty in a quantified modal logic (first-order modal logic). The system is based on both probability theory and proof theory. The system is derived from Chisholm's epistemology. We concretize…

In this study, a recursive solution technique in conjunction with generalized integrating factors is presented and applied to address first and second order linear differential equations. This approach demonstrates practical utility in…

This paper presents the development of a software tool that enables the translation of first-order predicate logic with at most three variables into relation algebra. The tool was developed using the Z3 theorem prover, leveraging its…

We study the problem of learning probabilistic first-order logical rules for knowledge base reasoning. This learning problem is difficult because it requires learning the parameters in a continuous space as well as the structure in a…

Logic languages based on the theory of rational, possibly infinite, trees have much appeal in that rational trees allow for faster unification (due to the safe omission of the occurs-check) and increased expressivity (cyclic terms can…

Humans learn complex latent structures from their environments (e.g., natural language, mathematics, music, social hierarchies). In cognitive science and cognitive neuroscience, models that infer higher-order structures from sensory or…

A new class of Semantic Numeration Systems, namely, positive rational Semantic Numeration Systems is introduced. For cardinal semantic operators, differences in the formation of carry (common carry) and remainders are defined. The…

After introducing the concept of commutativity for continuous-time linear time-varying systems, the related literature and the results obtained so far are presented. For a simple introduction of the commutativity of discrete-time linear…

First-order probabilistic models combine representational power of first-order logic with graphical models. There is an ongoing effort to design lifted inference algorithms for first-order probabilistic models. We analyze lifted inference…

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…

A superposition rule is a particular type of map that enables one to express the general solution of certain systems of first-order ordinary differential equations, the so-called Lie systems, out of generic families of particular solutions…

This paper discusses predictive inference and feature selection for generalized linear models with scarce but high-dimensional data. We argue that in many cases one can benefit from a decision theoretically justified two-stage approach:…

We develop a well-posedness theory for second order systems in bounded domains where boundary phenomena like glancing and surface waves play an important role. Attempts have previously been made to write a second order system consisting of…

It was recently conjectured that every component of a discrete-time rational dynamical system is a solution to an algebraic difference equation that is linear in its highest-shift term (a quasi-linear equation). We prove that the conjecture…

Projection-based reduced order models are effective at approximating parameter-dependent differential equations that are parametrically separable. When parametric separability is not satisfied, which occurs in both linear and nonlinear…

We select policies for large Markov Decision Processes (MDPs) with compact first-order representations. We find policies that generalize well as the number of objects in the domain grows, potentially without bound. Existing…

In this study, explicit differential equations representing commutative pairs of some well-known second-order linear time-varying systems have been derived. The commutativity of these systems are investigated by considering 30 second-order…