Related papers: Rough concepts
This article is an exploratory account of the the non-monotonic behaviour of conceptual associations in the light of context. Computational approximations of conceptual space are furnished by semantic space models which are emerging from…
All current investigations to analyze the derivational complexity of term rewrite systems are based on a single termination method, possibly preceded by transformations. However, the exclusive use of direct criteria is problematic due to…
Logically constrained term rewriting is a relatively new formalism where rules are equipped with constraints over some arbitrary theory. Although there are many recent advances with respect to rewriting induction, completion, complexity…
Factorizing datasets is an interesting process in a multitude of approaches, but many times it is not possible or efficient the computation of a factorization of the dataset. A method to obtain independent subcontexts of a formal context…
Conceptual combination performs a fundamental role in creating the broad range of compound phrases utilized in everyday language. This article provides a novel probabilistic framework for assessing whether the semantics of conceptual…
This vision paper articulates a long-term research agenda for formal methods at the intersection with artificial intelligence, outlining multiple conceptual and technical dimensions and reporting on our ongoing work toward realising this…
We recently performed cognitive experiments on conjunctions and negations of two concepts with the aim of investigating the combination problem of concepts. Our experiments confirmed the deviations (conceptual vagueness, underextension,…
Formal Concept Analysis makes the fundamental observation that any finite lattice $(L, \leq)$ is determined up to isomorphism by the restriction of the relation ${\leq} \subseteq L \times L$ to the set $J(L) \times M(L)$, where $J(L)$ is…
We propose stratified institutions (a decade old generalised version of the theory of institutions of Goguen and Burstall) as a fully abstract model theoretic approach to modal logic. This allows for a uniform treatment of model theoretic…
We explain how recent developments in the fields of realisability models for linear logic -- or geometry of interaction -- and implicit computational complexity can lead to a new approach of implicit computational complexity. This…
In the context of general rough sets, the act of combining two things to form another is not straightforward. The situation is similar for other theories that concern uncertainty and vagueness. Such acts can be endowed with additional…
Optical systems are becoming increasingly important by resolving many bottlenecks in today's communication, electronics, and biomedical systems. However, given the continuous nature of optics, the inability to efficiently analyze optical…
Formal concept analysis (FCA) is a well-founded method for data analysis and has many applications in data mining. Pattern structures is an extension of FCA for dealing with complex data such as sequences or graphs. However the…
Automating the extraction of concept hierarchies from free text is advantageous because manual generation is frequently labor- and resource-intensive. Free result, the whole procedure for concept hierarchy learning from free text entails…
We study the complexity of reasoning tasks for logics in team semantics. Our main focus is on the data complexity of model checking but we also derive new results for logically defined counting and enumeration problems. Our approach is…
We introduce and elaborate a novel formalism for the manipulation and analysis of proofs as objects in a global manner. In this first approach the formalism is restricted to first-order problems characterized by condensed detachment. It is…
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…
In this paper, we present a comprehensive system for the treatment of the topic of limits--conceptually, computationally, and formally. The system addresses fundamental linguistic flaws in the standard presentation of limits, which attempts…
The construction of a consistent theory for structuring and representing how concepts combine and interact is one of the main challenges for the scholars involved in cognitive studies. All traditional approaches are still facing serious…
Large language models (LLMs) have demonstrated remarkable success across a wide range of tasks; however, they still encounter challenges in reasoning tasks that require understanding and inferring relationships between distinct pieces of…