Traditionally, an agent's beliefs would come from what the agent can see, hear, or sense. In the modern world, beliefs are often based on the data available to the agents. In this work, we investigate a dynamic logic of such beliefs that incorporates public announcements of data. The main technical contribution is a sound and complete axiomatisation of the interplay between data-informed beliefs and data announcement modalities. We also describe a non-trivial polynomial model checking algorithm for this logical system.

In our daily lives and industrial settings, we often encounter dynamic problems that require reasoning over time and metric constraints. These include tasks such as scheduling, routing, and production sequencing. Dynamic logics have traditionally addressed these needs but often lack the flexibility and integration required for comprehensive problem modeling. This research aims to extend Answer Set Programming (ASP), a powerful declarative problem-solving approach, to handle dynamic domains effectively. By integrating concepts from dynamic, temporal, and metric logics into ASP, we seek to develop robust systems capable of modeling complex dynamic problems and performing efficient reasoning tasks, thereby enhancing ASPs applicability in industrial contexts.

Planning and reasoning about actions and processes, in addition to reasoning about propositions, are important issues in recent logical and computer science studies. The widespread use of actions in everyday life such as IoT, semantic web services, etc., and the limitations and issues in the action formalisms are two factors that lead us to study how actions are represented. Since 2007, there have been some ideas to integrate Description Logic (DL) and action formalisms for representing both static and dynamic knowledge. Meanwhile, time is an important factor in dynamic situations, and actions change states over time. In this study, on the one hand, we examined related logical structures such as extensions of description logics (DLs), temporal formalisms, and action formalisms. On the other hand, we analyzed possible tools for designing and developing the Knowledge and Action Base (KAB). For representation and reasoning about actions, we embedded actions into DLs (such as Dynamic-ALC and its extensions). We propose a terminable algorithm for action projection, planning, checking the satisfiability, consistency, realizability, and executability, and also querying from KAB. Actions in this framework were modeled with SPIN and added to state space. This framework has also been implemented as a plugin for the Prot\'eg\'e ontology editor. During the last two decades, various algorithms have been presented, but due to the high computational complexity, we face many problems in implementing dynamic ontologies. In addition, an algorithm to detect the inconsistency of actions' effects was not explicitly stated. In the proposed strategy, the interactions of actions with other parts of modeled knowledge, and a method to check consistency between the effects of actions are presented. With this framework, the ramification problem can be well handled in future works.

We examine several belief change operations in the light of Dynamic Logic of Propositional Assignments DL-PA. We show that we can encode in a systematic way update operations (such as Winslett's Possible Models Approach') and revision operations (such as Dalal's) as particular DL-PA programs. Every DL-PA formula being equivalent to a boolean formula, we obtain syntactical counterparts for all these belief change operations.

We propose a new formalization of legal competences, and in particular for the Hohfeldian categories of power and immunity, through a deontic reinterpretation of dynamic epistemic logic. We argue that this logic explicitly captures the norm-changing character of legal competences while providing a sophisticated reduction of the latter to static normative positions. The logic is completely axiomatizable, and we apply it to a concrete case in German contract law to illustrate that it can capture the distinction between legal ability and legal permissibility.

In the literature there different kind of timed logical fram eworks exist, where time is specified directly using hybrid logics (cf., e.g., [2]), temporal epistemic lo gic (cf., e.g., [4]) or simply by using Linear Temporal Logic. We propose a temporal module which can be ado pted to "temporalize" many logical framework. This module is in practice a particular kind of fu nction that assigns a "timing" to atoms. We have exploited this T function in two different settings. The first one is the formalization of the reasoning on the formation of beliefs and the interaction wi th background knowledge in non-omniscient agents' memory.

Remember that time and space are a priori conditions of human perception in Kant's philosophy. On the one hand, time is inherent to action and change; on the other, action and change are possible because of the passage of time. According to McDermott, "Dealing with time correctly would change everything in an AI program" (McDermott 1982, p. 101). It should not be surprising then that temporal reasoning has always been a very important topic in many fields of AI, particularly areas dealing with change, causality, and action (planning, diagnosis, natural language understanding, and so on). AI developments based on temporal reasoning lead to general theories about time and action, such as McDermott's (1982) temporal logic, Vilain's (1982) theory of time, and Allen's (1984) theory of action and time. Work on the application of these results has taken place in fields such as planning and medical knowledge-based systems. However, action and change are not an exclusive interest of AI.

There are however, a variety of different approaches that claim to capture the true nature of this concept. One reason for this diversity lies in the fact that abductive reasoning occurs in a multitude of contexts. It concerns cases that cover the simplest selection of already existing hypotheses to the generation of new concepts in science. It also concerns cases where the observation is puzzling because it is novel versus cases in which the surprise concerns an anomalous observation. For example, if we wake up, and the lawn is wet, we might explain this observation by assuming that it must have rained or that the sprinklers have been on.

I begin by considering examples of practical reasoning. In the remainder of the paper, I try to say something about what Example 8. Playing soccer. Soccer is like table tennis, but a logical approach that begins to do justice to the subject with the added dimension of teamwork and the need to might be like. This task was selected as a benchmark problem in robotics, and has been extensively Example 1. Ordering a meal at a restaurant. Here, the problem is deciding what to eat and drink. Typing an email message, Even if the only relevant factors are price and preferences composing it as you go along, starts perhaps with a general about food, the number of possible combinations is very idea of what to say.

This first part covers mathematical that teachers will find useful.