Related papers: Conceptual Collectives
Embedding large and high dimensional data into low dimensional vector spaces is a necessary task to computationally cope with contemporary data sets. Superseding latent semantic analysis recent approaches like word2vec or node2vec are well…
Many recent language models (LMs) are capable of in-context learning (ICL), manifested in the LMs' ability to perform a new task solely from natural-language instruction. Previous work curating in-context learners assumes that ICL emerges…
With our work, we contribute towards a qualitative analysis of the discourse on controversies in online news media. For this, we employ Formal Concept Analysis and the economics of conventions to derive conceptual controversy maps. In our…
Relational concept analysis (RCA) is an extension of formal concept analysis allowing to deal with several related contexts simultaneously. It has been designed for learning description logic theories from data and used within various…
The IFF approach for the notion of "lattice of theories" uses the idea of a concept lattice from Formal Concept Analysis (Ganter and Wille) and the idea of the truth classification from Information Flow (Barwise and Seligman). The IFF…
Natural language contexts display logical regularities with respect to substitutions of related concepts: these are captured in a functional order-theoretic property called monotonicity. For a certain class of NLI problems where the…
Recent ideas about epistemic modals and indicative conditionals in formal semantics have significant overlap with ideas in modal logic and dynamic epistemic logic. The purpose of this paper is to show how greater interaction between formal…
The highly influential framework of conceptual spaces provides a geometric way of representing knowledge. Instances are represented by points in a high-dimensional space and concepts are represented by regions in this space. In this…
This paper explores how natural-language descriptions of formal languages can be compared to their formal representations and how semantic differences can be explained. This is motivated from educational scenarios where learners describe a…
The emergence of large language models (LLMs) has demonstrated that systems trained solely on text can acquire extensive world knowledge, develop reasoning capabilities, and internalize abstract semantic concepts--showcasing properties that…
This article combines the vocabulary of semiotics and category theory to provide a formal analysis of visualization. It shows how familiar processes of visualization fit the semiotic frameworks of both Saussure and Peirce, and extends these…
The linguistic applications of the Lambek calculus suggest its semantics over algebras of formal languages. A straightforward approach to construct such semantics indeed yields a brilliant completeness theorem (Pentus 1995). However,…
While computer programs and logical theories begin by declaring the concepts of interest, be it as data types or as predicates, network computation does not allow such global declarations, and requires *concept mining* and *concept…
Concept Hierarchies and Formal Concept Analysis are theoretically well grounded and largely experimented methods. They rely on line diagrams called Galois lattices for visualizing and analysing object-attribute sets. Galois lattices are…
Taking a quotient roughly means changing the notion of equality on a given object, set or type. In a quantitative setting, equality naturally generalises to a distance, measuring how much elements are similar instead of just stating their…
We design temporal description logics suitable for reasoning about temporal conceptual data models and investigate their computational complexity. Our formalisms are based on DL-Lite logics with three types of concept inclusions (ranging…
Category theory can be used to state formulas in First-Order Logic without using set membership. Several notable results in logic such as proof of the continuum hypothesis can be elegantly rewritten in category theory. We propose in this…
In recent work, we introduced a new semantics for conditionals, covering a large class of what we call preconditionals. In this paper, we undertake an axiomatic study of preconditionals and subclasses of preconditionals. We then prove that…
Recursive relational specifications are commonly used to describe the computational structure of formal systems. Recent research in proof theory has identified two features that facilitate direct, logic-based reasoning about such…
It is well known by analysts that a concept lattice has an exponential size in the data. Thus, as soon as he works with real data, the size of the concept lattice is a fundamental problem. In this chapter, we propose to investigate factor…