Related papers: Independence and abstract multiplication
The notion of monotonic independence, introduced by N. Muraki, is considered in a more general frame, similar to the construction of operator-valued free probability. The paper presents constructions for maps with similar properties to the…
In this paper we investigate the links between instantiated argumentation systems and the axioms for non-monotonic reasoning described in [9] with the aim of characterising the nature of argument based reasoning. In doing so, we consider…
The Expansion property considered by researchers in Social Choice is shown to correspond to a logical property of nonmonotonic consequence relations that is the {\em pure}, i.e., not involving connectives, version of a previously known weak…
The independence polynomial of a hypergraph is the generating function for its independent (vertex) sets with respect to their cardinality. This article aims to discuss several recurrence relations for the independence polynomial using some…
This paper investigates the independence polynomials arising from iterated strong products of cycle graphs, examining their algebraic symmetries and combinatorial structures. Leveraging modular arithmetic and Galois theory, we establish…
Path independence is arguably one of the most important choice rule properties in economic theory. We show that a choice rule is path independent if and only if it is rationalizable by a utility function satisfying ordinal concavity, a…
We introduce a logic for reasoning about evidence that essentially views evidence as a function from prior beliefs (before making an observation) to posterior beliefs (after making the observation). We provide a sound and complete…
Over the past few decades, non-monotonic reasoning has developed to be one of the most important topics in computational logic and artificial intelligence. Different ways to introduce non-monotonic aspects to classical logic have been…
In this paper we prove that three of the main propositional logics of dependence (including propositional dependence logic and inquisitive logic), none of which is structural, are structurally complete with respect to a class of…
Separation logic is a recent extension of Hoare logic for reasoning about programs with references to shared mutable data structures. In this paper, we provide a new interpretation of the logic for a programming language with higher types.…
We introduce and study algebraic dynamical systems generated by triangular systems of rational functions. We obtain several results about the degree growth and linear independence of iterates as well as about possible lengths of…
Possibility theory offers a framework where both Lehmann's "preferential inference" and the more productive (but less cautious) "rational closure inference" can be represented. However, there are situations where the second inference does…
We consider the first-order theory of random variables with the probabilistic independence relation, which concerns statements consisting of random variables, the probabilistic independence symbol, logical operators, and existential and…
We prove a generalization of Maehara's lemma to show that the extensions of classical and intuitionistic first-order logic with a special type of geometric axioms, called singular geometric axioms, have Craig's interpolation property. As a…
We review a few results concerning interpolation of monotone functions on infinite lattices, emphasizing the role of set-theoretic considerations. We also discuss a few open problems.
A set of real $n$th roots that is pairwise linearly independent over the rationals must also be linearly independent. We show how this result may be extended to more general fields.
We associate in a canonical way a substitution to any abstract numeration system built on a regular language. In relationship with the growth order of the letters, we define the notion of two independent substitutions. Our main result is…
Interactive theorem provers based on dependent type theory have the flexibility to support both constructive and classical reasoning. Constructive reasoning is supported natively by dependent type theory and classical reasoning is typically…
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…
This paper aims at comparing two coupling approaches as basic layers for building clustering criteria, suited for modularizing and clustering very large networks. We briefly use "optimal transport theory" as a starting point, and a way as…