Related papers: First-order Logic: Modality and Intensionality
Heyting-Lewis Logic is the extension of intuitionistic propositional logic with a strict implication connective that satisfies the constructive counterparts of axioms for strict implication provable in classical modal logics. Variants of…
This paper develops the model theory of normal modal logics based on partial "possibilities" instead of total "worlds," following Humberstone (1981) instead of Kripke (1963). Possibility semantics can be seen as extending to modal logic the…
Intensional sets, i.e., sets given by a property rather than by enumerating elements, are widely recognized as a key feature to describe complex problems (see, e.g., specification languages such as B and Z). Notwithstanding, very few tools…
In this thesis (modal) dependence logic is investigated. It was introduced in 2007 by Jouko V\"a\"aan\"anen as an extension of first-order (resp. modal) logic by the dependence operator =(). For first-order (resp. propositional) variables…
We define the notion of a model of higher-order modal logic in an arbitrary elementary topos $\mathcal{E}$. In contrast to the well-known interpretation of (non-modal) higher-order logic, the type of propositions is not interpreted by the…
Semantic knowledge graphs are foundational to implementing the FAIR Principles, yet RDF/OWL representations often lack the semantic flexibility and cognitive interoperability required in scientific domains. We present a novel framework for…
In this paper, we present a first-order frame condition for interpretability logic and show that the condition is not modally definable. Yet, the frame-condition holds both on ILM and on ILP frames and, hence, is of potential importance for…
This paper describes the first-order logical environment FOLE. Institutions in general, and logical environments in particular, give equivalent heterogeneous and homogeneous representations for logical systems. As such, they offer a…
Neuro-symbolic AI attempts to integrate neural and symbolic architectures in a manner that addresses strengths and weaknesses of each, in a complementary fashion, in order to support robust strong AI capable of reasoning, learning, and…
The definition is a common form of human expert knowledge, a building block of formal science and mathematics, a foundation for database theory and is supported in various forms in many knowledge representation and formal specification…
Automating the translation of natural language to first-order logic (FOL) is crucial for knowledge representation and formal methods, yet remains challenging. We present a systematic evaluation of fine-tuned LLMs for this task, comparing…
We study two extensions of FO2[<], first-order logic interpreted in finite words, in which formulas are restricted to use only two variables. We adjoin to this language two-variable atomic formulas that say, "the letter $a$ appears between…
In this work we describe preferential Description Logics of typicality, a nonmonotonic extension of standard Description Logics by means of a typicality operator T allowing to extend a knowledge base with inclusions of the form T(C) v D,…
Contemporary semantic description of logic is based on the ontology of all possible interpretations, an insufficiently clear metaphysical concept. In this article, logic is described as the internal organization of language. Logical…
Transformer architectures have achieved great success in solving natural language tasks, which learn strong language representations from large-scale unlabeled texts. In this paper, we seek to go further beyond and explore a new logical…
This article initiates the semantic study of distribution-free normal modal logic systems, laying the semantic foundations and anticipating further research in the area. The article explores roughly the same area, though taking a different…
The proof theory and semantics of intuitionistic modal logics have been studied by Simpson in terms of Prawitz-style labelled natural deduction systems and Kripke models. An alternative to model-theoretic semantics is provided by…
We study the system IFP of intuitionistic fixed point logic, an extension of intuitionistic first-order logic by strictly positive inductive and coinductive definitions. We define a realizability interpretation of IFP and use it to extract…
Inquisitive team logic is a variant of inquisitive logic interpreted in team semantics, which has been argued to provide a natural setting for the regimentation of dependence claims. With respect to sentences, this logic is known to be…
Explainable artificial intelligence has rapidly emerged since lawmakers have started requiring interpretable models for safety-critical domains. Concept-based neural networks have arisen as explainable-by-design methods as they leverage…