We give a geometric condition that characterizes the differential nets having a finitary interpretation in finiteness spaces: visible acyclicity. This is based on visible paths, an extension to differential nets of a class of paths we introduced in the framework of linear logic nets. The characterization is then carried out as follows: the differential nets having no visible cycles are exactly ...

We investigate absorption, i.e., almost sure convergence to an absorbing state, in time-varying (non-homogeneous) discrete-time Markov chains with finite state space. consider systems that can switch among a set of transition matrices, which we call the modes. Our analysis is focused on two properties: 1) under any switching, and 2) desired states via proper switching policy. derive necessary s...

For a nite undirected graph G = (V;E) and a subset A V , the vertexswitching of G by A is de ned as the graph G A = (V;E 0 ), which is obtained from G by removing all edges between A and its complement A and adding as edges all nonedges between A and A. A switching class [G] determined by G consists of all vertex-switchings G A for subsets A V . We prove that the trees of a switching class [G] ...

Given an input structure, a relational Bayesian network returns a Bayesian network over ground atoms. In this paper, we analyze the problem of checking the consistency of a relational Bayesian network for a given class of input structures. This consistency is defined as the acyclicity of the output Bayesian network. We employ first-order logic to encode both the input structure and the structur...

This paper investigates obviously strategyproof (OSP) implementation of the popular top trading cycles (TTC) and deferred acceptance (DA) mechanisms. Introduced by Li (2016), obvious strategyproofness requires not only that truthful reporting be a dominant strategy, but also that this be obvious to agents who may have limited abilities of contingent reasoning. We characterize the full class of ...

The rationalizability of a choice function by means of a transitive relation has been analyzed thoroughly in the literature. However, not much seems to be known when transitivity is weakened to quasi-transitivity or acyclicity. We describe the logical relationships between the different notions of rationalizability involving, for example, the transitivity, quasi-transitivity, or acyclicity of t...

Acyclicity is shown to be a modular property of orthogonal first-order term rewriting systems (TRSs), which answers a question raised by Klop. Here, a rewrite system → is acyclic if it doesn’t allow non-empty cycles, where a cycle on t is a reduction sequence of the form t t. We assume knowledge of modularity, standardisation, tracing, and externality in term rewriting. To be specific, we freel...