Related papers: Fuzzy Propositional Logic Associated with Quantum …
We survey several problems related to logical aspects of quantum structures. In particular, we consider problems related to completions, decidability and axiomatizability, and embedding problems. The historical development is described, as…
We consider the quantum computational process as viewed by an insider observer: this is equivalent to an isomorphism between the quantum computer and a quantum space, namely the fuzzy sphere. The result is the formulation of a reversible…
This paper addresses fundamental issues on the nature of the concepts and structures of fuzzy logic, focusing, in particular, on the conceptual and functional differences that exist between probabilistic and possibilistic approaches. A…
A construction of a fuzzy logic controller based on an analogy between fuzzy conditional rule of inference and marginal probability in terms of the conditional probability function has been proposed.
We investigate an unsuspected connection between logical connectives with non-harmonious deduction rules, such as Prior's tonk, and quantum computing. We argue that these connectives model the information-erasure, the non-reversibility, and…
We give an axiomatic formulation of quantum structures like semilogics and quasilogics which generalize the boolean semirings of events and fuzzy logics. The notions of distributions, states, representations observables and semiobservables…
A probabilistic propositional logic, endowed with an epistemic component for asserting (non-)compatibility of diagonizable and bounded observables, is presented and illustrated for reasoning about the random results of projective…
In fuzzy propositional logic, to a proposition a partial truth in [0,1] is assigned. It is well known that under certain circumstances, fuzzy logic collapses to classical logic. In this paper, we will show that under dual conditions, fuzzy…
In this paper we show several similarities among logic systems that deal simultaneously with deductive and quantitative inference. We claim it is appropriate to call the tasks those systems perform as Quantitative Logic Reasoning. Analogous…
Computer vision applications are omnipresent nowadays. The current paper explores the use of fuzzy logic in computer vision, stressing its role in handling uncertainty, noise, and imprecision in image data. Fuzzy logic is able to model…
The approach described here allows to use the fuzzy Object Based Representation of imprecise and uncertain knowledge. This representation has a great practical interest due to the possibility to realize reasoning on classification with a…
The increasing rise in artificial intelligence has made the use of imprecise language in computer programs like ChatGPT more prominent. Fuzzy logic addresses this form of imprecise language by introducing the concept of fuzzy sets, where…
This paper explores the integration of hypothetical reasoning into an efficient implementation of the fuzzy logic language Bousi~Prolog. To this end, we first analyse what would be expected from a logic inference system, equipped with what…
This work proposes a formulation of propositional logic, named Eigenlogic, using quantum observables as propositions. The eigenvalues of these operators are the truth-values and the associated eigenvectors the interpretations of the…
This paper mainly focuses on (1) a generalized treatment of fuzzy sets of type $n$, where $n$ is an integer larger than or equal to $1$, with an example, mathematical discussions, and real-life interpretation of the given mathematical…
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…
Most fuzzy systems including fuzzy decision support and fuzzy control systems provide out-puts in the form of fuzzy sets that represent the inferred conclusions. Linguistic interpretation of such outputs often involves the use of linguistic…
Intuitionistic fuzzy Banach algebra is introduced and a few properties of it is studied. The properties of invertible elements and relation among invertible elements, open set, closed set are emphasized. Topological divisors of zero is…
We present a way to apply quantum logic to the study of quantum programs. This is made possible by using an extension of the usual propositional language in order to make transformations performed on the system appear explicitly. This way,…
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.…