Search results for " logic"
showing 10 items of 1720 documents
Gradation of Fuzzy Preconcept Lattices
2021
Noticing certain limitations of concept lattices in the fuzzy context, especially in view of their practical applications, in this paper, we propose a more general approach based on what we call graded fuzzy preconcept lattices. We believe that this approach is more adequate for dealing with fuzzy information then the one based on fuzzy concept lattices. We consider two possible gradation methods of fuzzy preconcept lattice—an inner one, called D-gradation and an outer one, called M-gradation, study their properties, and illustrate by a series of examples, in particular, of practical nature.
Conjunction, Disjunction and Iterated Conditioning of Conditional Events
2013
Starting from a recent paper by S. Kaufmann, we introduce a notion of conjunction of two conditional events and then we analyze it in the setting of coherence. We give a representation of the conjoined conditional and we show that this new object is a conditional random quantity, whose set of possible values normally contains the probabilities assessed for the two conditional events. We examine some cases of logical dependencies, where the conjunction is a conditional event; moreover, we give the lower and upper bounds on the conjunction. We also examine an apparent paradox concerning stochastic independence which can actually be explained in terms of uncorrelation. We briefly introduce the…
Online Induction of Probabilistic Real Time Automata
2012
Probabilistic real time automata (PRTAs) are a representation of dynamic processes arising in the sciences and industry. Currently, the induction of automata is divided into two steps: the creation of the prefix tree acceptor (PTA) and the merge procedure based on clustering of the states. These two steps can be very time intensive when a PRTA is to be induced for massive or even unbounded data sets. The latter one can be efficiently processed, as there exist scalable online clustering algorithms. However, the creation of the PTA still can be very time consuming. To overcome this problem, we propose a genuine online PRTA induction approach that incorporates new instances by first collapsing…
How to simulate free will in a computational device
1999
Since we believe that human brain is not a purely deterministic device merely reacting to the environment but rather it is capable to a free will, Theoretical Computer Science has also tried to develop a system of notions generalizing determinism. Nondeterministic and probabilistic algorithms were the first generalizations. Nondeterministic machines constitute an important part of the Theory of Computation. Nondeterminism is a useful way to describe possible choices. In real life there are many regulations restricting our behavior. These regulations nearly always leave some freedom for us how to react. Such regulations are best described in terms of nondeterministic algorithms. Nondetermini…
Truth and Historicism in Kuhn’s Thesis of Methodological Incommensurability
2013
Methodological incommensurability is a Thomas Kuhn’s thesis affirming that there are not shared, objective methodological rules or neutral scientific standards for theory comparison and choice. This thesis has often been interpreted as a relativistic and irrationalist claim on the incomparability of scientific theories. Since every paradigm refers to its standards, problem-field and aims, theory choice is subjective and arbitrary. Moreover it seems that, in his latest works, Kuhn abandons this aspect of incommensurability to focus on semantic incommensurability. On the contrary I will argue against the interpretation of methodological incommensurability as a source of epistemological relati…
Noetherian type in topological products
2010
The cardinal invariant "Noetherian type" of a topological space $X$ (Nt(X)) was introduced by Peregudov in 1997 to deal with base properties that were studied by the Russian School as early as 1976. We study its behavior in products and box-products of topological spaces. We prove in Section 2: 1) There are spaces $X$ and $Y$ such that $Nt(X \times Y) < \min\{Nt(X), Nt(Y)\}$. 2) In several classes of compact spaces, the Noetherian type is preserved by the operations of forming a square and of passing to a dense subspace. The Noetherian type of the Cantor Cube of weight $\aleph_\omega$ with the countable box topology, $(2^{\aleph_\omega})_\delta$, is shown in Section 3 to be closely related …
Extension theory and the calculus of butterflies
2016
Abstract This paper provides a unified treatment of two distinct viewpoints concerning the classification of group extensions: the first uses weak monoidal functors, the second classifies extensions by means of suitable H 2 -actions. We develop our theory formally, by making explicit a connection between (non-abelian) G-torsors and fibrations. Then we apply our general framework to the classification of extensions in a semi-abelian context, by means of butterflies [1] between internal crossed modules. As a main result, we get an internal version of Dedecker's theorem on the classification of extensions of a group by a crossed module. In the semi-abelian context, Bourn's intrinsic Schreier–M…
Fuzzy Multi-Criteria Decision Making: An entropy-based approach to assess tourism sustainability
2019
In this article, we propose a method for ranking tourist destinations and evaluating their performances under a sustainability perspective: a fuzzy multiple criteria decision-making method is applied for determining sustainability performance values and ranking destinations accordingly. We select a set of sustainability evaluation criteria and use a fuzzy analytic hierarchy process to weight the selected criteria. We also optimize each evaluator’s membership function support by means of a fuzzy entropy maximization criteria. A case study is illustrated and results are compared with two data envelopment analysis–based models. The simplicity of the proposed approach along with the easy reada…
A fuzzy evaluation of tourism sustainability
2019
For many years the sustainability assessment of tourist destinations has been based on the carrying capacity, which is a measure that takes into account the preservation of a geographical area (by measuring the number of tourists, the visitor flow and the environmental thresholds) along with its tourist fruition (by assessing the quality of the experience perceived by visitors). Unfortunately, its definition lacks clarity, and its dependence upon qualitative variables makes it unable to provide a unique criterion for its assessment. In this paper we propose a fuzzy approach that takes into account the inherent uncertainty and vagueness of the involved variables to assess a destination’s sus…
Projective unification in transitive modal logics
2018
We show that a transitive normal modal logic L enjoys projective unification (i.e. each unifiable formula is projective) if and only if L contains K4D1 ( D1 : ( x → y ) ∨ ( y → x ) ). It means, in particular, that K4D1 (and any of its extensions) is almost structurally complete, i.e. the logic is complete with respect to all non-passive admissible rules. We also characterize non-unifiable formulas and provide an explicit form of the basis for all passive rules over K4G + ( x → x )