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Subatomic logic is a recent innovation in structural proof theory where atoms are no longer the smallest entity in a logical formula, but are instead treated as binary connectives. As a consequence, we can give a subatomic proof system for…

We introduce a multi-type display calculus for Propositional Dynamic Logic (PDL). This calculus is complete w.r.t. PDL, and enjoys Belnap-style cut-elimination and subformula property.

Multiple logic-based reconstructions of conceptual data modelling languages such as EER, UML Class Diagrams, and ORM exist. They mainly cover various fragments of the languages and none are formalised such that the logic applies…

This paper proposes new semantics for nondeterministic program execution, replacing the standard relational semantics for propositional dynamic logic (PDL). Under these new semantics, program execution is represented as fundamentally…

In real-world continual learning (CL) scenarios, tasks often exhibit intricate and unpredictable semantic shifts, posing challenges for fixed prompt management strategies which are tailored to only handle semantic shifts of uniform degree…

Learning first-order logic programs (LPs) from relational facts which yields intuitive insights into the data is a challenging topic in neuro-symbolic research. We introduce a novel differentiable inductive logic programming (ILP) model,…

The class of Unambiguous Star-Free Regular Languages (UL) was defined by Schutzenberger as the class of languages defined by Unambiguous Polynomials. UL has been variously characterized (over finite words) by logics such as TL[X_a,Y_a],…

Diffusion language models (DLMs) offer a structural alternative to autoregressive generation: denoising can update tokens in arbitrary orders or in parallel rather than along a fixed left-to-right chain. In practice, fast DLM decoding…

Continuous representations of logic formulae allow us to integrate symbolic knowledge into data-driven learning algorithms. If such embeddings are semantically consistent, i.e. if similar specifications are mapped into nearby vectors, they…

This paper presents matching logic, a first-order logic (FOL) variant for specifying and reasoning about structure by means of patterns and pattern matching. Its sentences, the patterns, are constructed using variables, symbols, connectives…

Uniform interpolation is the property that, for any formula and set of atoms, there exists the strongest consequence omitting those atoms. It plays a central role in knowledge representation and reasoning tasks such as knowledge update and…

Definite descriptions are expressions of the form "the unique $x$ satisfying property $C$," which allow reference to objects through their distinguishing characteristics. They play a crucial role in ontology and query languages, offering an…

Differentiable logic networks (DLNs) have shown promising results in tabular domains by combining accuracy, interpretability, and computational efficiency. In this work, we apply DLNs to the domain of TSC for the first time, focusing on…

While neural models show remarkable accuracy on individual predictions, their internal beliefs can be inconsistent across examples. In this paper, we formalize such inconsistency as a generalization of prediction error. We propose a…

We study approximation of non-autonomous linear differential equations with variable delay over infinite intervals. We use piecewise constant argument to obtain a corresponding discrete difference equation. The study of numerical…

Logic-based approaches to AI have the advantage that their behavior can in principle be explained with the help of proofs of the computed consequences. For ontologies based on Description Logic (DL), we have put this advantage into practice…

Ontology is a popular method for knowledge representation in different domains, including the legal domain, and description logics (DL) is commonly used as its description language. To handle reasoning based on inconsistent DL-based legal…

Real-world large-scale datasets usually contain noisy labels and are imbalanced. Therefore, we propose derivative manipulation (DM), a novel and general example weighting approach for training robust deep models under these adverse…

In the Declarative Networking paradigm, Datalog-like languages are used to express distributed computations. Whereas recently formal operational semantics for these languages have been developed, a corresponding declarative semantics has…

The logical semantics of normal logic programs has traditionally been based on the notions of Clark's completion and two-valued or three-valued canonical models, including supported, stable, regular, and well-founded models. Two-valued…