Abductive expansion is an AGM-style belief-change operation that accommodates new information by adding explanatory hypotheses rather than incorporating the input outright. In contrast to belief sets, belief bases are finite and non-deductively closed, allowing a distinction between explicit and implicit beliefs. We extend abductive belief-change operations to belief bases relative to a hypothesis space, treating the base as firm beliefs and maintaining a separate space of tentative hypotheses that is conditioned on new inputs. Inspired by partial meet and kernel construction from classical belief revision, we provide concrete instances of three different types of abductive change: expansion, suspension (which corresponds to contraction), and revision. In the form of representation theorems, all these operators are shown to be characterized axiomatically by intuitive postulates. Along the constructions, counterparts of the well-known Levi identity and the Harper identity are exploited.

The latest developments in AI focus on agentic systems where artificial and human agents cooperate to realize global goals. An example is collaborative learning, which aims to train a global model based on data from individual agents. A major challenge in designing such systems is to guarantee safety and alignment with human values, particularly a fair distribution of rewards upon achieving the global goal. Cooperative game theory offers useful abstractions of cooperating agents via value functions, which assign value to each coalition, and via reward functions. With these, the idea of fair allocation can be formalized by specifying fairness axioms and designing concrete mechanisms. Classical cooperative game theory, exemplified by the Shapley value, does not fully capture scenarios like collaborative learning, as it assumes non-replicable resources, whereas data and models can be replicated. Infinite replicability requires a generalized notion of fairness, formalized through new axioms and mechanisms. These must address imbalances in reciprocal benefits among participants, which can lead to strategic exploitation and unfair allocations. The main contribution of this paper is a mechanism and a proof that it fulfills the property of mutual fairness, formalized by the Balanced Reciprocity Axiom. It ensures that, for every pair of players, each benefits equally from the participation of the other.

Smart Materials (SMat) promise to open new opportunities in the area of Intelligent Environments (IE), whether as part of dedicated smart devices or as the fabric constituting everyday appliances and building infrastructure. Through the use of ontologies both IE engineers and the IEs themselves can be aware of, and predict, how novel configurable and changing materials react under different conditions. In contrast to conventional Smart Objects, however, as computational software/hardware-systems, lending themselves to the object-oriented perspective of conventional ontology specification languages, SMat and IE in the wider sense require a perspective focussing on extended spaces and numerical domains. Both are known to be problematic in terms of usability and computational complexity for the traditional object-oriented languages, with even very basic notions already leading into undecidability. Context Logic (CL), in contrast, is a formalism specialized for these domains. This paper demonstrates how terminology from this area involving extended spaces and numerical domains can be modeled in CL.

This paper is concerned with knowledge graph embedding with background knowledge, taking the formal perspective of logics. In knowledge graph embedding, knowledge— expressed as a set of triples of the form (a R b) (“a is R-related to b”)—is embedded into a real-valued vector space. The embedding helps exploiting geometrical regularities of the space in order to tackle typical inductive tasks of machine learning such as link prediction. Recent embedding approaches also consider incorporating background knowledge, in which the intended meanings of the symbols a, R, b are further constrained via axioms of a theory. Of particular interest are theories expressed in a formal language with a neat semantics and a good balance between expressivity and feasibility. In that case, the knowledge graph together with the background can be considered to be an ontology. This paper develops a cone-based theory for embedding in order to advance the expressivity of the ontology: it works (at least) with ontologies expressed in the description logic ALC, which comprises restricted existential and universal quantifiers, as well as concept negation and concept disjunction. In order to align the classical Tarskian Style semantics for ALC with the sub-symbolic representation of triples, we use the notion of a geometric model of an ALC ontology and show, as one of our main results, that an ALC ontology is satisfiable in the classical sense iff it is satisfiable by a geometric model based on cones. The geometric model, if treated as a partial model, can even be chosen to be faithful, i.e., to reflect all and only the knowledge captured by the ontology. We introduce the class of axis-aligned cones and show that modulo simple geometric operations any distributive logic (such as ALC) interpreted over cones employs this class of cones. Cones are also attractive from a machine learning perspective on knowledge graph embeddings since they give rise to applying conic optimization techniques.

This paper presents an embedding of ontologies expressed in the ALC description logic into a real-valued vector space, comprising restricted existential and universal quantifiers, as well as concept negation and concept disjunction. Our main result states that an ALC ontology is satisfiable in the classical sense iff it is satisfiable by a partial faithful geometric model based on cones. The line of work to which we contribute aims to integrate knowledge representation techniques and machine learning. The new cone-model of ALC proposed in this work gives rise to conic optimization techniques for machine learning, extending previous approaches by its ability to model full ALC.

In the database community Polystores is an emerging and promising approach for data federation that aims at designing a unified querying layer over multiple data models. In the Semantic Web community a similar in spirit approach of Ontology-Based Data Access (OBDA) has been recently proposed, attracted a lot of attention, and proved its success in several industrial scenarios. In this paper we discuss a semantic approach to building polystores using the OBDA paradigm. We also present our system Optique that is utilized in an industrial application of performing turbine diagnostics in Siemens.

Real-time processing of data coming from multiple heterogeneous data streams and static databases is a typical task in many industrial scenarios such as diagnostics of large machines. A complex diagnostic task may require a collection of up to hundreds of queries over such data. Although many of these queries retrieve data of the same kind, such as temperature measurements, they access structurally different data sources. In this work we show how Semantic Technologies implemented in our system optique can simplify such complex diagnostics by providing an abstraction layer---ontology---that integrates heterogeneous data. In a nutshell, optique allows complex diagnostic tasks to be expressed with just a few high-level semantic queries. The system can then automatically enrich these queries, translate them into a collection with a large number of low-level data queries, and finally optimise and efficiently execute the collection in a heavily distributed environment. We will demo the benefits of optique on a real world scenario from Siemens.

Resolving conflicts based on ambiguities in the public vocabulary is one of the challenges in semantic integration. Though different suggestions for resolving (ambiguity) conflicts with semantic integration operators exist, there is still a need for clear formalizations of adequacy criteria for the operators. In this article, adequacy criteria for semantic integration similar to rationality postulates of classical belief revision but adjusted to the semantic integration scenario are formalized. The criteria are intended to capture integration settings in which the integration candidates are well developed ontologies with a shared public vocabulary. In such cases, both ontologies have to be preserved in some form in the integration result and have to be recoverable from the integration result. Additionally, the integration result has to be consistent and provide connections between the integrated ontologies. The criteria are applied by evaluating a small collection of integration operators that solve conflicts deriving from ambiguities in the public vocabulary.