Abstract

Abstract
Dynamic Epistemic Logic (DEL) is used in the analysis of a wide class of application scenarios involving multi-agents systems with local perceptions of information and knowledge. In its classical form, the knowledge of epistemic states is represented by sets of propositions. However, the complexity of the current systems, requires other richer structures, than sets of propositions, to represent knowledge on their epistemic states. Algebras, graphs or distributions are examples of useful structures for this end. Based on this observation, we introduced a parametric method to build dynamic epistemic logics on-demand, taking as parameter the specific knowledge representation framework (e.g., propositional, equational or even a modal logic) that better fits the problems in hand. In order to use the built logics in practices, tools support is needed. Based on this, we extended our previous method with a parametric construction of complete proof calculi. The complexity of the model checking and satisfiability problems for the achieved logics are provided. © 2021, IFIP International Federation for Information Processing.

Abstract
This work introduces a new fuzzy epistemic logic with public announcement with fuzzyness on both transitions and propositions. The interpretation of the connectives is done over the Godel algebra and the interpretation of public announcements in this logic generalises the traditional update one. The core idea is that, the effect of a public announcement is reflected on the transitions degrees of the models. The update takes in account not only the truth degree of the announcement, at a target state, but also the degree of the transitions reaching that state. We prove the soundness of all axioms of the multi-agent epistemic logic with public announcements with respect to this graded semantics. Finally, we introduce the notion of bisimulation and prove the modal invariance property for our logic.

Abstract
We propose E-down arrow((D) over right arrow)-logic as a formal foundation for the specification and development of event-based systems with data states. The framework is presented as an institution in the sense of Goguen and Burstall and the logic itself is parametrised by an underlying institution (D) over right arrow whose structures are used to model data states. E-down arrow((D) over right arrow)-logic is intended to cover a broad range of abstraction levels from abstract requirements specifications up to constructive specifications. It uses modal diamond and box operators over complex actions adopted from dynamic logic. Atomic actions are pairs e/psi where e is an event and psi a state transition predicate capturing the allowed reactions to the event. Towrite concrete specifications of recursive process structureswe integrate (control) state variables and binders of hybrid logic. The semantic interpretation relies on event/data transition systems. For the presentation of constructive specifications we propose operational event/data specifications allowing for familiar, diagrammatic representations by state transition graphs. We show that E-down arrow((D) over right arrow)-logic is powerful enough to characterise the semantics of an operational specification by a single E-down arrow((D) over right arrow)-sentence. Thus the whole (formal) development process for event/data-based systems relies on E-down arrow((D) over right arrow)-logic and its semantics as a common basis. It is supported by a variety of implementation constructors which can express, among others, event refinement and parallel composition. Due to the genericity of the approach, it is also possible to change a data state institution during system development when needed. All steps of our formal treatment are illustrated by a running example.

Abstract
Fuzzy programming languages, such as the Fuzzy Arden Syntax (FAS), are used to describe behaviours which evolve in a fuzzy way and thus cannot be characterized neither by a Boolean outcome nor by a probability distribution. This paper introduces a semantics for FAS, focusing on the weighted parallel interpretation of its conditional statement. The proposed construction is based on the notion of a fuzzy multirelation which associates with each state in a program a fuzzy set of weighted possible evolutions. The latter is parametric on a residuated lattice which models the underlying semantic 'truth space'. Finally, a family of dynamic logics, equally parametric on the residuated lattice, is introduced to reason about FAS programs.

Abstract
This paper explores a strict relation between two core notions of the semantics of programs and of fuzzy logics: Kleene Algebras and (pseudo) uninorms. It shows that every Kleene algebra induces a pseudo uninorm, and that some pseudo uninorms induce Kleene algebras. This connection establishes a new perspective on the theory of Kleene algebras and provides a way to build (new) Kleene algebras. The latter aspect is potentially useful as a source of formalism to capture and model programs acting with fuzzy behaviours and domains. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.