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**1 - 3**of**3**### Formalization of Agents and Multi-Agent Systems. The Special Case of Category Theory

, 1996

"... This working paper lists some ideas on how to apply category theory to agents, and multi-agent systems. It focuses more on the distributivity and compositionality of agents, as well as on the emergence of sociality and properties, than on the intelligence or on the ability of agents to reason. It pr ..."

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This working paper lists some ideas on how to apply category theory to agents, and multi-agent systems. It focuses more on the distributivity and compositionality of agents, as well as on the emergence of sociality and properties, than on the intelligence or on the ability of agents to reason. It presents some categorical notions, and explains informally how they can be connected with agents and multi-agent systems. Contents 1 Introduction 4 2 Agents and Multi-Agent Systems 5 2.1 Definitions and Primitives of Agents . . . . . . . . . . . . . . . . 5 2.2 Definitions and Primitives of Multi-agent systems . . . . . . . . . 6 2.3 Agent Theories . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.4 Multi-Agent Systems Theories . . . . . . . . . . . . . . . . . . . . 8 3 Category Theory 9 3.1 Category Theory in Computer Science . . . . . . . . . . . . . . . 9 3.2 Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 4 Ideas for Formalization of Agents an...

### On the folding of Algebraic Nets

, 1994

"... A folding in General Net theory is morphism that is surjective on places and transitions. Foldings can be used to relate CE-systems to "high-level system". In this paper we study the problem of relating Petri Nets to non-strict High-level Nets. We give a construction that given a morphism ..."

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A folding in General Net theory is morphism that is surjective on places and transitions. Foldings can be used to relate CE-systems to "high-level system". In this paper we study the problem of relating Petri Nets to non-strict High-level Nets. We give a construction that given a morphism of Petri Nets produces an Algebraic Net that characterises the folding in a canonical way. We also prove that the construction is functorial. Then we show how the construction can be made to work on Algebraic Nets directly. Finally we discuss an application of the construction.

### Constantine Tsinakis

"... Abstract. The starting point of the present study is the interpretation of intuitionistic linear logic in Petri nets proposed by U. Engberg and G. Winskel. We show that several categories of order algebras provide equivalent interpretations of this logic, and identify the category of the so called s ..."

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Abstract. The starting point of the present study is the interpretation of intuitionistic linear logic in Petri nets proposed by U. Engberg and G. Winskel. We show that several categories of order algebras provide equivalent interpretations of this logic, and identify the category of the so called strongly coherent quantales arising in these interpretations. The equivalence of the interpretations is intimately related to the categorical facts that the aforementioned categories are connected with each other via adjunctions, and the compositions of the connecting functors with co-domain the category of strongly coherent quantales are dense. In particular, each quantale canonically induces a Petri net, and this