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Structured knowledge bases (KBs) are a foundation of many intelligent applications, yet are notoriously incomplete. Language models (LMs) have recently been proposed for unsupervised knowledge base completion (KBC), yet, despite encouraging…
From an inconsistent database non-trivial arguments may be constructed both for a proposition, and for the contrary of that proposition. Therefore, inconsistency in a logical database causes uncertainty about which conclusions to accept.…
Inconsistency handling is an important issue in knowledge management. Especially in ontology engineering, logical inconsistencies may occur during ontology construction. A natural way to reason with an inconsistent ontology is to utilize…
Weighted monadic second-order logic is a weighted extension of monadic second-order logic that captures exactly the behaviour of weighted automata. Its semantics is parameterized with respect to a semiring on which the values that weighted…
Post-hoc explanation methods are widely used to interpret black-box predictions, but their generation is often computationally expensive and their reliability is not guaranteed. We propose epistemic uncertainty as a low-cost proxy for…
Knowledge bases are employed in a variety of applications from natural language processing to semantic web search; alas, in practice their usefulness is hurt by their incompleteness. Embedding models attain state-of-the-art accuracy in…
In ontology-mediated query answering, access to incomplete data sources is mediated by a conceptual layer constituted by an ontology. To correctly compute answers to queries, it is necessary to perform complex reasoning over the constraints…
Knowledge-based question answering (KBQA) is widely used in many scenarios that necessitate domain knowledge. Large language models (LLMs) bring opportunities to KBQA, while their costs are significantly higher and absence of…
This paper addresses the problem of merging uncertain information in the framework of possibilistic logic. It presents several syntactic combination rules to merge possibilistic knowledge bases, provided by different sources, into a new…
Real-valued logics underlie an increasing number of neuro-symbolic approaches, though typically their logical inference capabilities are characterized only qualitatively. We provide foundations for establishing the correctness and power of…
Complexity remains one of the central challenges in science and technology. Although several approaches at defining and/or quantifying complexity have been proposed, at some point each of them seems to run into intrinsic limitations or…
We consider formal verification of recursive programs with resource consumption. We introduce prefix replacement systems with non-negative integer counters which can be incremented and reset to zero as a formal model for such programs. In…
We investigate the problem whether two ALC knowledge bases are indistinguishable by queries over a given vocabulary. We give model-theoretic criteria in terms of (partial) homomorphisms and products and prove that this problem is…
The necessity to manage inconsistency in Description Logics Knowledge Bases (KBs) has come to the fore with the increasing importance gained by the Semantic Web, where information comes from different sources that constantly change their…
Circumscription is one of the main approaches for defining non-monotonic description logics (DLs). While the decidability and complexity of traditional reasoning tasks such as satisfiability of circumscribed DL knowledge bases (KBs) is well…
We introduce derivation depth-a computable metric of the reasoning effort needed to answer a query based on a given set of premises. We model information as a two-layered structure linking abstract knowledge with physical carriers, and…
Knowledge bases are widely used for information management, enabling high-impact applications such as web search, question answering, and natural language processing. They also serve as the backbone for automatic decision systems, e.g., for…
We address the problem of answering Web ontology queries efficiently. An ontology is formalized as a Deductive Ontology Base (DOB), a deductive database that comprises the ontology's inference axioms and facts. A cost-based query…
Representation of defeasible information is of interest in description logics, as it is related to the need of accommodating exceptional instances in knowledge bases. In this direction, in our previous works we presented a datalog…
Automated reasoning about uncertain knowledge has many applications. One difficulty when developing such systems is the lack of a completely satisfactory integration of logic and probability. We address this problem directly. Expressive…