We investigate the modal logic of stepwise removal of objects, both for its intrinsic interest as a logic of quantification without replacement, and as a pilot study to better understand the complexity jumps between dynamic epistemic logics of model transformations and logics of freely chosen graph changes that get registered in a growing memory. After introducing this logic (MLSR) and its corresponding removal modality, we analyze its expressive power and prove a bisimulation characterization theorem. We then provide a complete Hillbert-style (...) axiomatization for the logic of stepwise removal in a hybrid language enriched with nominals and public announcement operators. Next, we show that model-checking for MLSR is PSPACE-complete, while its satisfiability problem is undecidable. Lastly, we consider an issue of fine-structure: the expressive power gained by adding the stepwise removal modality to fragments of first-order logic. (shrink)

We propose a general framework for dynamic epistemic logics. It consists of a generic language for DELs and a class of structures, called model transition systems, that describe model transformations in a static way. An MTS can be viewed as a two-layered Kripke model and consequently inherits standard concepts such as bisimulation and bounded morphism from the ordinary Kripke models. In the second half of this article we add the global operator to the language, which enables us to define the (...) notions of a canonical MTS and canonicity of a DEL formula for a property of MTSs. Using these notions, we clarify correspondences between axioms of DELs and properties of MTSs. (shrink)

We discuss a simple logic to describe one of our favourite games from childhood, hide and seek, and show how a simple addition of an equality constant to describe the winning condition of the seeker makes our logic undecidable. There are certain decidable fragments of first-order logic which behave in a similar fashion with respect to such a language extension, and we add a new modal variant to that class. We discuss the relative expressive power of the proposed logic in (...) comparison to the standard modal counterparts. We prove that the model checking problem for the resulting logic is \(\textsf{P}\) -complete. In addition, by exploring the connection with related product logics, we gain more insight towards having a better understanding of the subtleties of the proposed framework. (shrink)

Formal learning theory formalizes the process of inferring a general result from examples, as in the case of inferring grammars from sentences when learning a language. In this work, we develop a general framework—the supervised learning game—to investigate the interaction between Teacher and Learner. In particular, our proposal highlights several interesting features of the agents: on the one hand, Learner may make mistakes in the learning process, and she may also ignore the potential relation between different hypotheses; on the other (...) hand, Teacher is able to correct Learner’s mistakes, eliminate potential mistakes and point out the facts ignored by Learner. To reason about strategies in this game, we develop a modal logic of supervised learning and study its properties. Broadly, this work takes a small step towards studying the interaction between graph games, logics and formal learning theory. (shrink)

In this article, we present a modal logic that extends the basic modal logic ML with two dynamic operators: copy, which replicates the current model, labelling each copy with a different prop...