Related papers: Two-sorted Modal Logic for Formal and Rough Concep…
Assumption-based Argumentation (ABA) is a well-known structured argumentation formalism, whereby arguments and attacks between them are drawn from rules, defeasible assumptions and their contraries. A common restriction imposed on ABA…
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…
Long-sequence transformers are designed to improve the representation of longer texts by language models and their performance on downstream document-level tasks. However, not much is understood about the quality of token-level predictions…
In flowchart languages, predicates play an interesting double role. In the textual representation, they are often presented as conditions, i.e., expressions which are easily combined with other conditions (often via Boolean combinators) to…
Among the various forms of reasoning studied in the context of artificial intelligence, qualitative reasoning makes it possible to infer new knowledge in the context of imprecise, incomplete information without numerical values. In this…
Conceptual Graphs (CG) are a graph-based knowledge representation and reasoning formalism; fuzzy Conceptual Graphs (fCG) constitute an extension that enriches their expressiveness, exploiting the fuzzy set theory so as to relax their…
Analytic proof calculi are introduced for box and diamond fragments of basic modal fuzzy logics that combine the Kripke semantics of modal logic K with the many-valued semantics of G\"odel logic. The calculi are used to establish…
Soft set theory and rough set theory are mathematical tools to deal with uncertainties. In [3], authors combined these concepts and introduced soft rough sets. In this paper, we introduce the concepts of soft rough graphs, vertex and edge…
We develop and investigate a general theory of representations of second-order functionals, based on a notion of a right comodule for a monad on the category of containers. We show how the notion of comodule representability naturally…
We present a proof system for a multimodal logic, based on our previous work on a multimodal Martin-Loef type theory. The specification of modes, modalities, and implications between them is given as a mode theory, i.e. a small 2-category.…
In order to address complex systems, apply pattern recongnition on their evolution could play an key role to understand their dynamics. Global patterns are required to detect emergent concepts and trends, some of them with qualitative…
This paper brings together two lines of research: factor-based models of case-based reasoning (CBR) and the logical specification of classifiers. Logical approaches to classifiers capture the connection between features and outcomes in…
Formal Concept Analysis has proven to be an effective method of restructuring complete lattices and various algebraic domains. In this paper, the notions of attribute continuous formal context and continuous formal concept are introduced by…
In this paper we attempt to physically interpret the Modal Kochen- Specker (MKS) theorem. In order to do so, we analyze the features of the possible properties of quantum systems arising from the elements in an orthomodular lattice and…
It is a classic result in modal logic that the category of modal algebras is dually equivalent to the category of descriptive frames. The latter are Kripke frames equipped with a Stone topology such that the binary relation is continuous.…
The notion of class is ubiquitous in computer science and is central in many formalisms for the representation of structured knowledge used both in knowledge representation and in databases. In this paper we study the basic issues…
Representation theorems for formal systems often take the form of an inductive translation that satisfies certain invariants, which are proved inductively. Theory morphisms and logical relations are common patterns of such inductive…
We investigate the formal semantics of a simple imperative language that has both classical and quantum constructs. More specifically, we provide an operational semantics, a denotational semantics and two Hoare-style proof systems: an…
The paper aims to develop a framework for coalgebraic fuzzy geometric logic by adding modalities to the language of fuzzy geometric logic. Using the methods of coalgebra, the modal operators are introduced in the language of fuzzy geometric…
Algebraic theories with dependency between sorts form the structural core of Martin-L\"of type theory and similar systems. Their denotational semantics are typically studied using categorical techniques; many different categorical…