Related papers: Modal reduction principles: a parametric shift to …
The present paper establishes systematic connections among the first-order correspondents of Sahlqvist modal reduction principles in various relational semantic settings which include crisp and many-valued Kripke frames, and crisp and…
The present paper proposes a novel way to unify Rough Set Theory and Formal Concept Analysis. Our method stems from results and insights developed in the algebraic theory of modal logic, and is based on the idea that Pawlak's original…
We propose a modal logic tailored to describe graph transformations and discuss some of its properties. We focus on a particular class of graphs called termgraphs. They are first-order terms augmented with sharing and cycles. Termgraphs…
We study the first order theory of structures over graphs i.e. structures of the form ($\mathcal{G},\tau$) where $\mathcal{G}$ is the set of all (isomorphism types of) finite undirected graphs and $\tau$ some vocabulary. We define the…
The main goal of this note is to provide a First-Order Logic with Betweenness (FOLB) axiomatization of the main classes of graphs occurring in Metric Graph Theory, in analogy to Tarski's axiomatization of Euclidean geometry. We provide such…
A well-defined distance on the parameter space is key to evaluating estimators, ensuring consistency, and building confidence sets. While there are typically standard distances to adopt in a continuous space, this is not the case for…
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…
The language of modal logic is capable of expressing first-order conditions on Kripke frames. The classic result by Henrik Sahlqvist identifies a significant class of modal formulas for which first-order conditions -- or Sahlqvist…
We present an extension and generalization of Sahlqvist--Van Benthem correspondence to the case of distribution-free modal logic, with, or without negation and/or implication connectives. We follow a reductionist strategy, reducing the…
For each natural number $n$ we study the modal logic determined by the class of transitive Kripke frames in which there are no cycles of length greater than $n$ and no strictly ascending chains. The case $n=0$ is the G\"odel-L\"ob…
Logical formalisms for reasoning about relations between spatial regions play a fundamental role in geographical information systems, spatial and constraint databases, and spatial reasoning in AI. In analogy with Halpern and Shoham's modal…
Graph transformations definable in logic can be described using the notion of transductions. By understanding transductions as a basic embedding mechanism, which captures the possibility of encoding one graph in another graph by means of…
In this paper we introduce a general framework for the study of limits of relational structures in general and graphs in particular, which is based on a combination of model theory and (functional) analysis. We show how the various…
Frames are the most natural generalization of orthonormal bases that allow the inclusion of redundant systems. In this article, we introduce the concept of frames generated by graphs in finite-dimensional spaces and study their properties.…
We study preservation theorems for modal logics over finite structures with respect to three fundamental semantic relations: embeddings, injective homomorphisms, and homomorphisms. We focus on classes of pointed Kripke models that are…
The Lambek calculus is a substructural logic known to be closely related to the formal language theory: on the one hand, it is used for generating formal languages by means of categorial grammars and, on the other hand, it has formal…
In this paper, we use theory of rough set to study graphs using the concept of orbits. We investigate the indiscernibility partitions and approximations of graphs induced by orbits of graphs. We also study rough membership functions,…
Rational approximations are introduced and studied in granular graded rough sets and generalizations thereof by the first author in recent research papers. The concept of rationality is determined by related ontologies and coherence between…
Graph foundation models (GFMs) seek transferable representations across graph domains but are limited by structural heterogeneity and incompatible node feature spaces. We propose Structure-Centric Graph Foundation Models (SCGFM), which…
Rough set theory is a new mathematical approach to imperfect knowledge. The notion of rough sets is generalized by using an arbitrary binary relation on attribute values in information systems, instead of the trivial equality relation. The…