Related papers: PBNF-transform as a formulation of Propositional C…
The "2-variable general-$\lambda$-matrix polynomials (2VG$\lambda$MP)" is a new family of matrix polynomials, introduced and studied in this article. These matrix polynomials are constructed using umbral and symbolic methods. We delve into…
Probabilistic circuits compute multilinear polynomials that represent multivariate probability distributions. They are tractable models that support efficient marginal inference. However, various polynomial semantics have been considered in…
Probabilistic neurosymbolic learning seeks to integrate neural networks with symbolic programming. Many state-of-the-art systems rely on a reduction to the Probabilistic Weighted Model Counting Problem (PWMC), which requires computing a…
Permissive-Nominal Logic (PNL) is an extension of first-order predicate logic in which term-formers can bind names in their arguments. This allows for direct axiomatisations with binders, such as of the lambda-binder of the lambda-calculus…
Addressing machines have been introduced as a formalism to construct models of the pure, untyped lambda-calculus. We extend the syntax of their programs by adding instructions for executing arithmetic operations on natural numbers, and…
In this paper, we derive formal general formulas for noncommutative exponentiation and the exponential function, while also revisiting an unrecognized, and yet powerful theorem. These tools are subsequently applied to derive counterparts…
Given a parametric polynomial ideal I, the algorithm DISPGB, introduced by the author in 2002, builds up a binary tree describing a dichotomic discussion of the different reduced Groebner bases depending on the values of the parameters,…
In this paper we present an algorithmic procedure that transforms, if possible, a given system of ordinary or partial differential equations with radical dependencies in the unknown function and its derivatives into a system with polynomial…
We construct biorthogonal polynomials for a measure over the complex plane which consists in the exponential of a potential V(z,z*) and in a set of external sources at the numerator and at the denominator. We use the pseudonorm of these…
The relevance of polynomial formula classes to deductive efficiency motivated their search, and currently, a great number of such classes is known. Nonetheless, they have been exclusively sought in the setting of clausal form and…
In this paper, we consider iterative propositional calculi, which are finite sets of propositional formulas together with the rules of modus ponens and weak substitution (when formula being substituted must be already inferred). We…
The research on conditional planning rejects the assumptions that there is no uncertainty or incompleteness of knowledge with respect to the state and changes of the system the plans operate on. Without these assumptions the sequences of…
The paper introduces a generalization for known probabilistic models such as log-linear and graphical models, called here multiplicative models. These models, that express probabilities via product of parameters are shown to capture…
When studying families in the moduli space of dynamical systems, choosing an appropriate representative function for a conjugacy class can be a delicate task. The most delicate questions surround rationality of the conjugacy class compared…
Four recursive constructions of permutation polynomials over $\gf(q^2)$ with those over $\gf(q)$ are developed and applied to a few famous classes of permutation polynomials. They produce infinitely many new permutation polynomials over…
We compute two parametric determinants in which rows and columns are indexed by compositions, where in one determinant the entries are products of binomial coefficients, while in the other the entries are products of powers. These results…
In this research, the Bernoulli polynomials are introduced. The properties of these polynomials are employed to construct the operational matrices of integration together with the derivative and product. These properties are then utilized…
For a polynomial with palindromic coefficients, unimodality is equivalent to having a nonnegative $g$-vector. A sufficient condition for unimodality is having a nonnegative $\gamma$-vector, though one can have negative entries in the…
In this paper we discuss the permutational property of polynomials of the form $f(L(x))+k(L(x))\cdot M(x)\in \mathbb F_{q^n}[x]$ over the finite field $\mathbb F_{q^n}$, where $L, M\in \mathbb F_q[x]$ are $q$-linearized polynomials. The…
We present Probabilistic Decision Model and Notation (pDMN), a probabilistic extension of Decision Model and Notation (DMN). DMN is a modeling notation for deterministic decision logic, which intends to be user-friendly and low in…