Each year, the NMR workshop brings together researchers from the field of nonmonotonic reasoning to present their work and discuss their research. This series of online talks on nonmonotonic reasoning aims to continue and extend the exchange in the 11 months between the workshops.
The series consists of regular online talks followed by a Q&A/discussion phase. The aim of the series is to offer a platform for the presentation of new and developing ideas in NMR. We encourage both the presentation of preliminary and ongoing work as well as mature results.
The scope of the series is nonmonotonic reasoning and all its subtopics, e.g., belief revision, uncertain reasoning, argumentation, and answer set programming.
The talks are given online via Zoom and are announced on the Planet KR mailing list. While there is no strict time limit, we aim for approximatly 40 minutes for each talk (followed by questions and discussion).
Adding non-monotonic capabilities to Description Logics (DLs) has been one of the greatest dreams of the DL community. This is testified by a thriving family of formalisms, among which we have circumscribed DLs. One of the biggest challenges of introducing non-monotonic features to DLs is the increase in computational complexity and circumscription is no exception. Nevertheless, circumscribed DLs remain a flexible and powerful framework that can be used as a host language for other non-monotonic DLs, e.g., DLs with defeasible inclusions or the more recent Equilibrium Description Logics.
This talk aims to give an overview of the recent advancements in DLs with circumscription and other related formalisms based on forms of predicate minimization. In particular, we will see an alternative approach to circumscription, namely pointwise circumscription, which aims to mitigate the computational complexity of standard circumscription.
Conditional logics, as introduced by David Lewis in 1973, enrich the language of classical propositional logic with a two-places modal operator, the conditional, suitable to represent fine-grained notions of conditionality. The proof theory of conditional logics relies on proof-theoretic techniques similar to those employed to define proof systems for modal logics: either the language of sequent calculus is enriched, giving rise to labelled calculi, or additional structural connectives are employed, thus defining various kinds of structured sequents (e.g., nested sequents). In this talk I will present sequent calculi for conditional logics belonging both to the labelled and to the structured approach.
After introducing conditional logics and their semantics, that I will define in terms of neighborhood models, I will present a labelled sequent calculus, modularly capturing a large family of systems, and a nested-style sequent calculus, featuring a structural connective representing neighborhoods of the model. I will then compare the properties of the two proof systems, discussing their strengths and weaknesses.
This talk is based on joint work with: Bjoern Lellmann, Sara Negri, Nicola Olivetti and Gian Luca Pozzato.
In this talk, we will discuss the role of conditionals in Explainable AI. I will focus on two classes of conditionals that align well with my research interests, namely probabilistic conditionals and counterfactual conditionals. The literature is currently mostly driven by ideas from machine learning and may benefit from insights about non-monotonic and quantitative reasoning to improve analytical guarantees of explanations and to design better-informed algorithms.
The role of probabilistic conditionals in Explainable AI emerged from rule-based explanations. While rule-based explanations have a long tradition in machine learning, recently an interesting direction evolved that applies propositional-logical reasoning technology to infer provably correct rules from machine learning models. While deterministic rules are interesting, they are unlikely to explain much of what a machine learning model learned because rules usually come with exceptions. This strand of work has already been expanded to probabilistic rules but mostly makes use of classical logical workarounds or purely numerical ideas. I will give an introduction to the area and discuss how some ideas from the literature on reasoning about (probabilistic) conditionals can enrich the current Landscape.
Another interesting direction in Explainable AI are counterfactual explanations. Here, explanations take the form of counterfactual conditionals of the form “If it had not been for X, then the decision would not have been Y”. For example, in a loan application scenario, such a counterfactual explanation may explain the reasons for a denied application to an applicant. For example, the conditional could take the form “If your debt-to-income ratio would be lower, then your application would not have been rejected.” An obvious problem here is that there is typically not a unique explanation. This causes multiple problems. I will again introduce the area and discuss some ideas how methods for reasoning about conditionals may be helpful to balance completeness and the number of counterfactual explanations, and to improve the robustness of counterfactual explainers.This talk presents a broad view on inductive reasoning by embedding it in theories of epistemic states, conditionals, and belief revision. More precisely, we consider nonmonotonic inductive reasoning as a specific case of belief revision on epistemic states which include conditionals as a basic means for representing beliefs. We present a general framework for inductive reasoning from conditional belief bases that induces a variety of different revision scenarios quite naturally and particularly allows for taking background beliefs into account. As a proof of concept, we instantiate this framework by ranking-theoretic reasoning based on so-called c-revisions. We illustrate the constructive usefulness of our approach, as well as its integrating power.
This talk presents a broad view on inductive reasoning by embedding it in theories of epistemic states, conditionals, and belief revision. More precisely, we consider nonmonotonic inductive reasoning as a specific case of belief revision on epistemic states which include conditionals as a basic means for representing beliefs. We present a general framework for inductive reasoning from conditional belief bases that induces a variety of different revision scenarios quite naturally and particularly allows for taking background beliefs into account. As a proof of concept, we instantiate this framework by ranking-theoretic reasoning based on so-called c-revisions. We illustrate the constructive usefulness of our approach, as well as its integrating power.
This talk is based on the paper "Inductive Reasoning, Conditionals, and Belief Dynamics" by Gabriele Kern-Isberner and Wolfgang Spohn, Journal of Applied Logics, Special Issue on Foundations, Applications, and Theory of Inductive Logic, Guest Editors Martin Adamcík and Matthias Thimm, Volume 11, Number 1: January 2024, p. 89–127. https://www.collegepublications.co.uk/ifcolog/?00063
This seminar series is currently organized by Jonas Haldimann and Giovanni Casini. For questions, or if you are interested in giving a talk, please contact us at jonas@haldimann.de or giovanni.casini@isti.cnr.it.