A Coalgebraic View on Reachability

Coalgebras for an endofunctor provide a category-theoretic framework for modeling a wide range of state-based systems of various types. We provide an iterative construction of the reachable part of a given pointed coalgebra that is inspired by and resembles the standard breadth-first search procedure to compute the reachable part of a graph. We also study coalgebras in Kleisli categories: for a functor extending a functor on the base category, we show that the reachable part of a given pointed coalgebra can be computed in that base category

Fixed Points Theorems for Non-Transitive Relations

In this paper, we develop an Isabelle/HOL library of order-theoretic fixed-point theorems. We keep our formalization as general as possible: we reprove several well-known results about complete orders, often with only antisymmetry or attractivity, a mild condition implied by either antisymmetry or transitivity. In particular, we generalize various theorems ensuring the existence of a quasi-fixed point of monotone maps over complete relations, and show that the set of (quasi-)fixed points is itself complete. This result generalizes and strengthens theorems of Knaster-Tarski, Bourbaki-Witt, Kleene, Markowsky, Pataraia, Mashburn, Bhatta-George, and Stouti-Maaden

Negotiation protocols and dynamic social networks

International audienceMulti-agent system make it possible to investigate systems with complex interaction protocols and limited information sharing. Our objective in this paper is to emphasize the impact of exchange protocols in social networks. The presented MAS considers a loan-granting scenario where each agent can borrow/lend money to its neighbors and/or consume it. We define six interaction protocols, ranging from fixed equilibrium rate loans to double-free auctions, and we study their impact on the network structure and the global welfare of the economy. Further, the agent fitness is investigated in relation with its connectivity (number of neighbors) and eccentricity (longest path to the other agents)

Economy-driven Shaping of Social Networks and Emerging Class Behaviors

International audienceIn this paper, we propose an agent-based analysis of a cumulative social-network game. Agents grant loans to their neighbours to maximize their intertemporal utility function. With a complete graph, we show that interest rates converge toward the theoretical equilibrium, even if ther is no centralized walrasian auctioneer and no preference transmition between agents. With a dynamic network, we explain why the network can't stabilize with a rational strategy. We introduce death and show that, even if the rational strategy is individually the best, the situation where three different strategies coexist is better for the global welfare

A Categorical Framework for Program Semantics and Semantic Abstraction

Categorical semantics of type theories are often characterized as structure-preserving functors. This is because in category theory both the syntax and the domain of interpretation are uniformly treated as structured categories, so that we can express interpretations as structure-preserving functors between them. This mathematical characterization of semantics makes it convenient to manipulate and to reason about relationships between interpretations. Motivated by this success of functorial semantics, we address the question of finding a functorial analogue in abstract interpretation, a general framework for comparing semantics, so that we can bring similar benefits of functorial semantics to semantic abstractions used in abstract interpretation. Major differences concern the notion of interpretation that is being considered. Indeed, conventional semantics are value-based whereas abstract interpretation typically deals with more complex properties. In this paper, we propose a functorial approach to abstract interpretation and study associated fundamental concepts therein. In our approach, interpretations are expressed as oplax functors in the category of posets, and abstraction relations between interpretations are expressed as lax natural transformations representing concretizations. We present examples of these formal concepts from monadic semantics of programming languages and discuss soundness.Comment: MFPS 202