Perturbed utility functions—the sum of expected utility and a nonlinear perturbation function—provide a simple and tractable way to model various sorts of stochastic choice. We provide two easily understood conditions each of which characterizes this representation: One condition generalizes the acyclicity condition used in revealed preference theory, and the other generalizes Luce’s IIA condit...

The absence of a finite axiomatization of the first-order theory of datatypes and codatatypes represents a challenge for automatic theorem provers. We propose two approaches to reason by saturation in this theory: one is a conservative theory extension with a finite number of axioms; the other is an extension of the superposition calculus, in conjunction with axioms. Both techniques are refutat...

We characterize a class of collective choice rules such that collective preference relations are consistent. Consistency is a weakening of transitivity and a strengthening of acyclicity requiring that there be no cycles with at least one strict preference, which excludes the possibility of a “money pump.” The properties of collective choice rules used in our characterization are unrestricted do...

In real-world phenomena which involve mutual influence or causal effects between interconnected units, equilibrium states are typically represented with cycles in graphical models. An expressive class of models, relational can represent and reason about complex dynamic systems exhibiting such feedback loops. Existing cyclic discovery algorithms for learning models from observational data assume...

The N -Koszul algebras are N -homogeneous algebras satisfying a homological property. These algebras are characterised by their Koszul complex: an N -homogeneous algebra is N -Koszul if and only if its Koszul complex is acyclic. Methods based on computational approaches were used to prove N -Koszulness: an algebra admitting a side-confluent presentation is N -Koszul if and only if the extra-con...

In this paper, we propose an algorithm for maintaining a concurrent directed graph (for shared memory architecture) that is concurrently being updated by threads adding/deleting vertices and edges. The update methods of the algorithm are deadlock-free while the contains methods are waitfree. To the the best of our knowledge, this is the first work to propose a concurrent data structure for an a...

Self-reference in semantics, which leads to well-known paradoxes, is a thoroughly researched subject. The phenomenon can appear also in decision theoretic situations. There is a structural analogy between the two and, more interestingly, an analogy between principles concerning truth and those concerning rationality. The former can serve as a guide for clarifying the latter. Both the analogies ...

A type of directed multigraph called aW -digraph is introduced to model the structure of certain representations of Hecke algebras, including those constructed by Lusztig and Vogan from involutions in a Weyl group. Building on results of Lusztig, a complete characterization of W -digraphs is given in terms of subdigraphs for dihedral parabolic subgroups. In addition, results are obtained relati...

In this work, we consider function-free existential rules extended with nonmonotonic negation under a stable model semantics. We present new acyclicity and stratification conditions that identify a large class of rule sets having finite, unique stable models, and we show how the addition of constraints on the input facts can further extend this class. Checking these conditions is computationall...

This paper provides a brief introduction to the use and usefulness of Suzumura consistency, a coherence requirement for binary relations that weakens transitivity. The property is introduced by Suzumura (1976b) in the context of collective choice but, as demonstrated in some recent contributions, its applicability reaches beyond the boundaries of social-choice theory. In addition to a summary o...