Related papers: A logical implication between two conjectures on m…

We introduce and investigate a family of consequence relations with the goal of capturing certain important patterns of data-driven inference. The inspiring idea for our framework is the fact that data may reject, possibly to some degree,…

We prove completeness of preferential conditional logic with respect to convexity over finite sets of points in the Euclidean plane. A conditional is defined to be true in a finite set of points if all extreme points of the set interpreting…

Many questions in number theory concern the nonvanishing of determinants of square matrices of logarithms (complex or p-adic) of algebraic numbers. We present a new conjecture that states that if such a matrix has vanishing determinant,…

In this paper, we study a general Syracuse problem. We give some necessary conditions concerning the existence of eventual non trivial cycles. Some properties based on linear logarithmic forms are established. New general conjectures are…

This paper presents and discusses several methods for reasoning from inconsistent knowledge bases. A so-called argumentative-consequence relation taking into account the existence of consistent arguments in favor of a conclusion and the…

The well known Andrews-Curtis Conjecture [2] is still open. In this paper, we establish its finite version by describing precisely the connected components of the Andrews-Curtis graphs of finite groups. This finite version has independent…

This short note, in part of expository nature, points out several new or recent consequences of a quite nice decomposition for positive semi-definite matrices.

We give an elementary proof of a Caratheodory-type result on the invertibility of a sum of matrices, due first to Facchini and Barioli. The proof yields a polynomial identity, expressing the determinant of a large sum of matrices in terms…

The notion of non-deterministic logical matrix (where connectives are interpreted as multi-functions) preserves many good properties of traditional semantics based on logical matrices (where connectives are interpreted as functions) whilst…

We characterize 2-dimensional complexes associated canonically with basis graphs of matroids as simply connected triangle-square complexes satisfying some local conditions. This proves a version of a (disproved) conjecture by Stephen Maurer…

The material conditional has long been charged with paradox. Defined truth-functionally, it renders true any conditional whose antecedent is false or consequent true -- hence, seemingly absurd statements such as `If unicorns exist, then…

Let $\overline{bt}(n)$ denote the number of overcubic partition triples of $n$. Nayaka, Dharmendra and Kumar proved some congruences modulo 8, 16 and 32 for $\overline{bt}(n)$. Recently, Saikia and Sarma established some congruences modulo…

Let A,B be matrices in SL(2,R) having trace greater than or equal to 2. Assume the pair A,B is coherently oriented, that is, can be conjugated to a pair having nonnegative entries. Assume also that either A,B^(-1) is coherently oriented as…

We established two-sided Curto-Herrero conjecture for pairs of matrices, where the first matrix has a simple spectrum. Namely, it is shown that these pairs are separated by ranks of non-commutative polynomials in matrices. Moreover, we…

In the context of continuous first-order logic, special attention is often given to theories that are somehow continuous in an 'essential' way. A common feature of such theories is that they do not interpret any infinite discrete…

The infinitary propositional logic of here-and-there is important for the theory of answer set programming in view of its relation to strongly equivalent transformations of logic programs. We know a formal system axiomatizing this logic…

In this short paper we will show, via elementary arguments, the equivalence of the Twin Prime Conjecture to a problem which might be simpler to prove. Some conclusions are drawn, and it is shown that proving the Twin Prime Conjecture is…

We prove a strengthened form of a conjecture of Sun on a determinant attached to a binary quadratic form. Let $n>3$ and let $c,d\in\Z$. If $n$ is composite, then \[ \det\big[(i^2+cij+dj^2)^{n-2}\big]_{0\leq i,j\leq n-1}\equiv 0\pmod {n^2}…

It is well-known that Choice and Regularity are independent of each other but have important common consequences of logical character (reflection principles, representations of classes by sets, etc.). We explain this phenomenon by isolating…

Bi-intuitionistic logic is the conservative extension of intuitionistic logic with a connective dual to implication. It is sometimes presented as a symmetric constructive subsystem of classical logic. In this paper, we compare three sequent…