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We postulate the intuitive idea of reducts of fuzzy contexts based on formal concept analysis and rough set theory. For a complete residuated lattice $L$, it is shown that reducts of $L$-contexts in formal concept analysis are…
Defeasible rules are used in providing computable representations of legal documents and, more recently, have been suggested as a basis for explainable AI. Such applications draw attention to the scalability of implementations. The…
In this paper we establish a link between fuzzy and preferential semantics for description logics and Self-Organising Maps, which have been proposed as possible candidates to explain the psychological mechanisms underlying category…
It is well-known that relatively pseudocomplemented lattices can serve as an algebraic semantics of intuitionistic logic. To extend the concept of relative pseudocomplementation to non-distributive lattices, the first author introduced…
It is shown that propositional calculuses of both quantum and classical logics are non-categorical. We find that quantum logic is in addition to an orthomodular lattice also modeled by a weakly orthomodular lattice and that classical logic…
In this paper, we introduce Interval Real Logic (IRL), a two-sorted logic that interprets knowledge such as sequential properties (traces) and event properties using sequences of real-featured data. We interpret connectives using fuzzy…
The purpose of this paper is to present a fresh idea on how symbolic learning might be realized via analogical reasoning. For this, we introduce directed analogical proportions between logic programs of the form "$P$ transforms into $Q$ as…
Logical relations built on top of an operational semantics are one of the most successful proof methods in programming language semantics. In recent years, more and more expressive notions of operationally-based logical relations have been…
Short-circuit evaluation denotes the semantics of propositional connectives in which the second argument is evaluated only if the first argument does not suffice to determine the value of the expression. In programming, short-circuit…
A theorem of Lurie and Pridham establishes a correspondence between formal moduli problems and differential graded Lie algebras in characteristic zero, thereby formalising a well-known principle in deformation theory. We introduce a variant…
In this work we discuss logical structures related to indistinguishable particles. Most of the framework used to develop these structures was presented in [17, 28] and in [20, 14, 15, 16]. We use these structures and constructions to…
We consider the problem of answering queries about formulas of first-order logic based on background knowledge partially represented explicitly as other formulas, and partially represented as examples independently drawn from a fixed…
Fuzzy rule-based systems have been mostly used in interpretable decision-making because of their interpretable linguistic rules. However, interpretability requires both sensible linguistic partitions and small rule-base sizes, which are not…
Multilattices are generalisations of lattices introduced by Mihail Benado. He replaced the existence of unique lower (resp. upper) bound by the existence of maximal lower (resp. minimal upper) bound(s). A multilattice will be called pure if…
The roundoff errors in computer simulations of continuous dynamical systems, caused by finiteness of machine arithmetic, can lead to qualitative discrepancies between phase portraits of the resulting spatially discretized systems and the…
In this study we follow a new framework for the theory that offers us, other than traditional, a new angle to observe and investigate some relations between finite sets, F-lattice L and their elements. The theory is based on the Fuzzy…
Short-circuit evaluation denotes the semantics of propositional connectives in which the second argument is evaluated only if the first argument does not suffice to determine the value of the expression. Short-circuit evaluation is widely…
We investigate the Platonic Representation Hypothesis (PRH) through a tripartite statistical framework of representations: signal, bias, and noise. {1) Signal:} We propose that Platonic alignment arises from the universal relationship…
This paper develops a category-theoretic approach to uncertainty, informativeness and decision-making problems. It is based on appropriate first order fuzzy logic in which not only logical connectives but also quantifiers have fuzzy…
Incomplete information is a problem in many aspects of actual environments. Furthermore, in many sceneries the knowledge is not represented in a crisp way. It is common to find fuzzy concepts or problems with some level of uncertainty.…