ABSTRACT. Reasoning is fundamental to the foundations of information and knowledge systems, enabling these systems to derive reliable conclusions from complex data. Research in FoIKS focuses on the development of logical, non-monotonic, and probabilistic reasoning methods for addressing uncertainty and incomplete information—capabilities that are essential for intelligent agents and robust knowledge-based systems. Effective reasoning empowers information systems to adapt, update, and validate knowledge as new data becomes available.

For LLM-based agents, reasoning is indispensable, as it facilitates planning, decision-making, problem-solving, and adaptation to dynamic environments in a manner that is both human-like and interpretable. Robust reasoning enables these agents to operate autonomously, tackle complex tasks through reflection, and provide justifications for their actions. These abilities are critical for tasks that require multi-step logic, effective tool use, and proficient interaction with humans or other agents.

This talk will examine whether these two perspectives on reasoning share common ground, highlighting recent research in LLM-related reasoning and discussing realistic expectations for future developments.

ABSTRACT. Recent research has provided a framework for measuring similarity of incomplete database instances without considering the presence of complete key information to tackle the challenge of identifying similar tuples across database instances by purely relying on the tuples themselves. The framework proposes a straight forward approach for an approximate algorithm to reach sufficiently good results with computational efficiency. Introducing more advanced methods for nearest neighbour searches, such as locality sensitive hashing (LSH), is an opportunity to build on top of the original framework and further enhance the already achieved results. Hence, this paper proves the superiority of an LSH integrated framework over the original one based on extensive experiments in which the same and sometimes even higher quality is reached in combination with significant advances regarding total processing time. Further, using an LSH integrated approach broadens the application space of the framework for more types of data as well as detecting partial instance matches, which highlights how promising this approach is for future work.

ABSTRACT. We initiate an investigation how the fundamental concept of independence can be represented effectively in the presence of incomplete information in relational databases. The concepts of possible and certain independence are proposed, and first results regarding the axiomatisability and computational complexity of implication problems associated with these concepts are established. In addition, several results for the data and the combined complexity of model checking are presented. The findings help reduce computational overheads associated with the processing of updates and answering of queries.

ABSTRACT. We introduce a two-sort weighted modal logic for possibilistic reasoning with fuzzy formal contexts. The syntax of the logic includes two types of weighted modal operators corresponding to classical necessity ($\Box$) and sufficiency ($\boxminus$) modalities and its formulas are interpreted in fuzzy formal contexts based on possibility theory. We present its axiomatization that is sound with respect to the class of all fuzzy formal contexts. In addition, both the necessity and sufficiency fragments of the logic are also individually complete with respect to the class of all fuzzy contexts. We highlight the expressive power of the logic with some illustrative examples. As a formal context is the basic construct of formal concept analysis (FCA), we generalize three main notions in FCA, i.e., formal concepts, object oriented concepts, and property oriented concepts, to their corresponding $c$-cut concepts in fuzzy formal contexts. Then, we show that our logical language can represent all three of these generalized notions. Finally, we demonstrate the possibility of extending our logic to reasoning with multi-relational fuzzy contexts, in which the Boolean combinations of different fuzzy relations are allowed.

ABSTRACT. Hemaspaandra~et~al.~[JCSS 2010] conjectured that satisfiability for multi-modal logic using only the Boolean connectives XOR and 1 restricted to the frame classes T, S4, and S5 is solvable in polynomial time. We prove that this claim is false for S5, showing that the problem is, in fact, NP-hard.