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Reasoning over streams of input data is an essential part of human intelligence. During the last decade {\em stream reasoning} has emerged as a research area within the AI-community with many potential applications. In fact, the increased…
AI support of collaborative interactions entails mediating potential misalignment between interlocutor beliefs. Common preference alignment methods like DPO excel in static settings, but struggle in dynamic collaborative tasks where the…
Ethical and explainable artificial intelligence is an interdisciplinary research area involving computer science, philosophy, logic, the social sciences, etc. For an ethical autonomous system, the ability to justify and explain its decision…
Retrieval-Augmented Generation (RAG) enhances large language models by incorporating external knowledge, yet suffers from critical limitations in high-stakes domains -- namely, sensitivity to noisy or contradictory evidence and opaque,…
We consider the notion of a vacuous reduct semantics for abstract argumentation frameworks, which, given two abstract argumentation semantics {\sigma} and {\tau}, refines {\sigma} (base condition) by accepting only those {\sigma}-extensions…
An abstract argumentation framework is a commonly used formalism to provide a static representation of a dialogue. However, the order of enunciation of the arguments in an argumentative dialogue is very important and can affect the outcome…
Monitoring and analyzing process traces is a critical task for modern companies and organizations. In scenarios where there is a gap between trace events and reference business activities, this entails an interpretation problem, amounting…
Assumption-based argumentation (ABA) is a central structured argumentation formalism. As shown recently, answer set programming (ASP) enables efficiently solving NP-hard reasoning tasks of ABA in practice, in particular in the commonly…
We elaborate upon the formal foundations of hybrid Answer Set Programming (ASP) and extend its underlying logical framework with aggregate functions over constraint values and variables. This is achieved by introducing the construct of…
This paper presents a novel framework for structured argumentation, named extend argumentative decision graph ($xADG$). It is an extension of argumentative decision graphs built upon Dung's abstract argumentation graphs. The $xADG$…
Despite the recent, widespread focus on eXplainable AI (XAI), explanations computed by XAI methods tend to provide little insight into the functioning of Neural Networks (NNs). We propose a novel framework for obtaining (local) explanations…
This thesis concerns the development of a framework that facilitates the design and analysis of formal systems. Specifically, this framework provides a specification language which supports the concise and direct description of formal…
Different types of reasoning impose different structural demands on representational systems, yet no systematic account of these demands exists across psychology, AI, and philosophy of mind. I propose a framework identifying four structural…
This paper seeks to apply categorical logic to the design of artificial intelligent agents that reason symbolically about objects more richly structured than sets. Using Johnstone's sequent calculus of terms- and formulae-in-context, we…
Broadly speaking, there are two kinds of semantics-aware assistant systems for mathematics: proof assistants express the semantic in logic and emphasize deduction, and computer algebra systems express the semantics in programming languages…
We present a novel approach to construction of a formal semantics for a programming language. Our approach, using a parametric denotational semantics, allows the semantics to be easily extended to support new language features, and…
The rule $\mathrm{Defeated}(x) \leftarrow \mathrm{Attacks}(y,x),\, \neg \, \mathrm{Defeated}(y)$, evaluated under the well-founded semantics (WFS), yields a unique 3-valued (skeptical) solution of an abstract argumentation framework (AF).…
We present a simple technique for semantic, open logical relations arguments about languages with recursive types, which, as we show, follows from a principled foundation in categorical semantics. We demonstrate how it can be used to give a…
Non-monotonic logic programming is the basis for a declarative problem solving paradigm known as answer set programming (ASP). Departing from the seminal definition by Gelfond and Lifschitz in 1988 for simple normal logic programs, various…
An answer set is a plain set of literals which has no further structure that would explain why certain literals are part of it and why others are not. We show how argumentation theory can help to explain why a literal is or is not contained…