Processes of opinion formation rooted in social dynamics can significantly contribute to the polarization of social, political, and democratic interaction. Opinion dynamic models are essential for understanding the impact of specific social factors on the acceptance or rejection of opinions. This extended paper builds upon the conference presentation documented in [1] , introducing improvements and new opinion models that explore biases and collective human behaviors. It presents a framework based on concurrent set relations that formalizes, simulates, and analyzes social interaction systems with dynamic opinion models. Within this framework, standard models for social learning are realized as specific instances. Implemented in the Maude system as a fully executable rewrite theory, the framework enables a detailed examination of how agents' opinions can be influenced within a system. The authors report on new formalization of several and existing social learning models, exploring their relationships with different concurrency models. New experimentation involving reachability analysis, probabilistic simulation, and statistical model checking has been conducted. These experiments are crucial for validating significant properties related to dynamic opinion models in Maude, offering new insights into the mechanisms of opinion shaping in social interaction.

P is a domain-specific language designed for specifying asynchronous, event-driven systems. Its computational model is based on actors, i.e., on communicating state machines. This paper presents a formal semantics of P using rewriting logic, extending the language's verification capabilities. Implemented in Maude, a rewriting logic language, this semantics enables automated analysis of P programs, including reachability analysis, LTL model checking, and statistical model checking. Through illustrative examples, this paper demonstrates how this formalization significantly enhances P 's verification capacities in practical scenarios.

Session types are a well-established approach to communication correctness in message-passing processes. Widely studied from a process calculi perspective, here we pursue an unexplored strand and investigate the use of the Maude system for implementing session-typed process languages and reasoning about session-typed process specifications. We present four technical contributions. First, we develop and implement in Maude an executable specification of the operational semantics of a session-typed π-calculus by Vasconcelos. Second, we also develop an executable specification of its associated algorithmic type checking, and describe how both specifications can be integrated. Third, we show that our executable specification can be coupled with reachability and model checking tools in Maude to detect well-typed but deadlocked processes. Finally, we demonstrate the robustness of our approach by adapting it to a higher-order session π-calculus, in which exchanged values include names but also abstractions (functions from names to processes). All in all, our contributions define a promising new approach to the (semi)automated analysis of communication correctness in message-passing concurrency.