Related papers: Constraint tableaux for two-dimensional fuzzy logi…
This paper proposes two kinds of fuzzy abductive inference in the framework of fuzzy rule base. The abductive inference processes described here depend on the semantic of the rule. We distinguish two classes of interpretation of a fuzzy…
This article is the first part of series of articles that aim to present the foundations for fuzzy variational calculus for functions taking values in the space of linearly correlated fuzzy numbers $\mathbb{R}_{\mathcal{F}(A)}$. Recall that…
We introduce proper display calculi for intuitionistic, bi-intuitionistic and classical linear logics with exponentials, which are sound, complete, conservative, and enjoy cut-elimination and subformula property. Based on the same design,…
Systems of fuzzy relation equations and inequalities in which an unknown fuzzy relation is on the one side of the equation or inequality are linear systems. They are the most studied ones, and a vast literature on linear systems focuses on…
The highly influential framework of conceptual spaces provides a geometric way of representing knowledge. Instances are represented by points in a similarity space and concepts are represented by convex regions in this space. After pointing…
In this paper a formulation of U(1) gauge theory on a fuzzy torus is discussed. The theory is regulated in both the infrared and ultraviolet. It can be thought of as a non-commutative version of lattice gauge theory on a periodic lattice.…
One-dimensional fragment of first-order logic is obtained by restricting quantification to blocks of existential (universal) quantifiers that leave at most one variable free. We investigate this fragment over words and trees, presenting a…
Ordered logics and type systems have been used in a variety of applications including computational linguistics, memory allocation, stream processing, logical frameworks, parametricity, and enforcing security protocols. In most…
We propose some analogue of the Narain lattice for CHL string. The symmetries of this lattice are the symmetries of the perturbative spectrum. We explain in this language the known results about the possible gauge groups in compactified…
Lower and upper bounds for a given function are important in many mathematical and engineering contexts, where they often serve as a base for both analysis and application. In this short paper, we derive piecewise linear and quadratic…
In this talk we will report on few results of discrete physics on the fuzzy sphere . In particular non-trivial field configurations such as monopoles and solitons are constructed on fuzzy ${\bf S}^2$ using the language of K-theory, i.e…
We formalise the self-referential definition of physical laws using monotone operators on a lattice of theories, resolving the pathologies of naive set-theoretic formulations. By invoking Tarski fixed point theorem, we identify physical…
We survey systematic approaches to basis-restricted fragments of propositional logic and modal logics, with an emphasis on how expressive power and computational complexity depend on the allowed operators. The propositional case is…
The paper introduces fuzzy linguistic logic programming, which is a combination of fuzzy logic programming, introduced by P. Vojtas, and hedge algebras in order to facilitate the representation and reasoning on human knowledge expressed in…
We provide a denotational semantics for first-order logic that captures the two-level view of the computation process typical for constraint programming. At one level we have the usual program execution. At the other level an automatic…
Based on ideas of quantum theory of open systems we propose the consistent approach to the formulation of logic of plausible propositions. To this end we associate with every plausible proposition diagonal matrix of its likelihood and…
The concept of a fuzzy number is generalized to the case of a finite carrier set of partially ordered elements, more precisely, a lattice, when a membership function also takes values in a partially ordered set (a lattice). Zadeh's…
Programming with logic for sophisticated applications must deal with recursion and negation, which together have created significant challenges in logic, leading to many different, conflicting semantics of rules. This paper describes a…
The categorified theories known as "doctrines" specify a category equipped with extra structure, analogous to how ordinary theories specify a set with extra structure. We introduce a new framework for doctrines based on double category…
We present a comprehensive programme analysing the decomposition of proof systems for non-classical logics into proof systems for other logics, especially classical logic, using an algebra of constraints. That is, one recovers a proof…