Related papers: Algebraic hierarchy of logics unifying fuzzy logic…

The class of quasi-N4-lattices (QN4-lattices) was introduced as a common generalization of quasi-Nelson algebras and N4-lattices, in such a way that N4-lattices are precisely the QN4-lattices satisfying the double negation law (~~x = x) and…

We present a logic for reasoning about graded inequalities which generalizes the ordinary inequational logic used in universal algebra. The logic deals with atomic predicate formulas of the form of inequalities between terms and formalizes…

Differentiable logics are a family of quantitative logics originated in the machine learning literature. Because of their origin, differentiable logics often come equipped with analytic properties that guarantee that they are…

Non-classical negations may fail to be contradictory-forming operators in more than one way, and they often fail also to respect fundamental meta-logical properties such as the replacement property. Such drawbacks are witnessed by intricate…

The multi-valued logic of {\L}ukasiewicz is a substructural logic that has been widely studied and has many interesting properties. It is classical, in the sense that it admits the axiom schema of double negation, [DNE]. However, our…

The present work presents some results about the categorial relation between logics and its categories of structures. A (propositional, finitary) logic is a pair given by a signature and Tarskian consequence relation on its formula algebra.…

There are two kinds of bisimulation, namely crisp and fuzzy, between fuzzy structures such as fuzzy automata, fuzzy labeled transition systems, fuzzy Kripke models and fuzzy interpretations in description logics. Fuzzy bisimulations between…

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…

Lukasiewicz logic is a "fuzzy" logic in which truth value can be real numbers in the unit interval. There are connectives for min, max, addition and complement (1-x). The "value" of a closed formula in a fuzzy (relational model) is defined…

In the paper we define the convergence of compact fuzzy sets as a convergence of alpha-cuts in the topology of compact subsets of a metric space. Furthermore we define typical convergences of fuzzy variables and show relations with…

We extend the epistemic logic with De Morgan negation by Fagin et al. (Artif. Intell. 79, 203-240, 1995) by adding operators for universal and common knowledge in a group of agents, and with a formalization of information update using a…

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…

Taking an algebraic perspective on the basic structures of Rough Concept Analysis as the starting point, in this paper we introduce some varieties of lattices expanded with normal modal operators which can be regarded as the natural rough…

The causal structure of space-time offers a natural notion of an opposite or orthogonal in the logical sense, where the opposite of a set is formed by all points non time-like related with it. We show that for a general space-time the…

We define a stable model semantics for fuzzy propositional formulas, which generalizes both fuzzy propositional logic and the stable model semantics of classical propositional formulas. The syntax of the language is the same as the syntax…

Recently, description logic LE-ALC was introduced for reasoning in the semantic environment of enriched formal contexts, and a polynomial-time tableaux algorithm was developed to check the consistency of knowledge bases with acyclic TBoxes.…

Within the Hamiltonian framework, the propositions about a classical physical system are described in the Borel {\sigma}-algebra of a symplectic manifold (the phase space) where logical connectives are the standard set operations.…

We propose a new version of generalized probabilistic propositional logic, namely, discrete-continuous logic (DCL) in which every generalized proposition (GP) is represented as 2x2 nondiagonal positive matrix with unit trace. We demonstrate…

We consider the role of the diffeomorphism constraint in the quantization of lattice formulations of diffeomorphism invariant theories of connections. It has been argued that in working with abstract lattices, one automatically takes care…

In the last years, the adoption of active systems has increased in many fields of computer science, such as databases, sensor networks, and software engineering. These systems are able to automatically react to events, by collecting…