12 research outputs found
The Modal Logic of Stepwise Removal
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
() and its corresponding removal modality, we analyze its
expressive power and prove a bisimulation characterization theorem. We then
provide a complete Hilbert-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 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
Mapping Health Literacy Research in the European Union: A Bibliometric Analysis
Background: To examine and compare the research productivity on selected fields related to health literacy of the curren
Probing the Quantitative-Qualitative Divide in Probabilistic Reasoning
This paper explores the space of (propositional) probabilistic logical
languages, ranging from a purely `qualitative' comparative language to a highly
`quantitative' language involving arbitrary polynomials over probability terms.
While talk of qualitative vs. quantitative may be suggestive, we identify a
robust and meaningful boundary in the space by distinguishing systems that
encode (at most) additive reasoning from those that encode additive and
multiplicative reasoning. The latter includes not only languages with explicit
multiplication but also languages expressing notions of dependence and
conditionality. We show that the distinction tracks a divide in computational
complexity: additive systems remain complete for , while
multiplicative systems are robustly complete for . We also
address axiomatic questions, offering several new completeness results as well
as a proof of non-finite-axiomatizability for comparative probability.
Repercussions of our results for conceptual and empirical questions are
addressed, and open problems are discussed