1,721,152 research outputs found
On Normal Forms in Lukasiewicz's Logic
No full textFormulas of n variables of Lukasiewicz sentential calculus can be represented, via McNaughton's theorem, by piecewise linear functions, with integer coefficients, from hypercube [0,1]n to [0,1], called McNaughton functions. As a consequence of McNaughton representation, a canonical form of a formula is obtained. Indeed, up to logical equivalence, any formula can be written as an infimum of finite suprema of formulas associated to McNaughton functions which are truncated functions to [0,1] of the restriction to [0,1]n of single hyperplanes, for short, called simple McNaughton functions. In the present paper the authors concern with the problem of presenting formulas of Lukasiewicz sentential calculus in normal from. The main results are: a) an axiomatic description of some classes of formulas having the property to be canonically mapped one-to-one onto the class of simple Mc Naughton functions; b) a normal form for Lukasiewicz sentential calculus, making use of formulas defined in (a); c) the polynomial complexity of formulas, in normal form, coming from a certain class described as in (a) is proved; d) the results described in (a), (b) and (c) are extended to Rational Lukasiewicz logic
The spectrum problem for Abelian l-groups and MV-algebras
No full textAbstract. This paper deals with the problem of characterizing those topological spaces which are homeomorphic to the prime spectra of MValgebras or Abelian l-groups. As a first main result, we show that a topological space X is the prime spectrum of an MV-algebra if and only if X is spectral, and the lattice K(X) of compact open subsets of X is a closed epimorphic image of the lattice of “cylinder rational polyhedra” (a natural generalization of rational polyhedra) of [0, 1]Y for some set Y . As a second main result we extend our results to Abelian -groups. That is, a topological space X is the prime spectrum of an Abelian l-group if and only if X is generalized spectral, and the lattice K(X) is a closed epimorphic image of the lattice of "cylinder rational cones" (a generalization of rational cones) in RY for some set Y . Finally, we axiomatize, in monadic second order logic, the Belluce lattices of free MV-algebras (equivalently, the lattice of cylinder rational polyhedra) of dimension 1, 2 and infinite, and we study the problem of describing Belluce lattices in certain fragments of second order logic
Finiteness based results in BL-algebras
No full textBL-algebras were introduced by P. Hajek as algebraic structures of Basic Logic. The aim of the paper is a survey of known results about the structure of finite BL-algebras and natural dualities for varieties of BL-algebras. Extending the notion of ordinal sum of BL-algebras, a class of finite BL-algebras, actually BL-comets, which can be seen as a generalization of finite BL-chain, is characterized. Then, just using BL-comets, any finite BL-algebra can be represented as a direct product of BL-comets. This result can be seen as a generalization of the representation of finite MV-algebras as a direct product of finite MV-chains. Then it is shown the existence of a strong duality for each variety generated by one finite non-trivial totally ordered BL-algebra. As an application of the dualities, the injective and the weak injective members of these classes are described
Thermodynamic and kinetic characterization of a beta-hairpin peptide in solution: An extended phase space sampling by molecular dynamics simulations in explicit water
No full textThe folding of the amyloidogenic H1 peptide MKHMAGAAAAGAVV taken from the syrian hamster prion protein is explored in explicit aqueous solution at 300 K using long time scale all-atom molecular dynamics simulations for a total simulation time of 1.1 mu s. The system, initially modeled as an alpha-helix, preferentially adopts a beta-hairpin structure and several unfolding/refolding events are observed, yielding a very short average beta-hairpin folding time of similar to 200 ns. The long time scale accessed by our simulations and the reversibility of the folding allow to properly explore the configurational space of the peptide in solution. The free energy profile, as a function of the principal components (essential eigenvectors) of motion, describing the main conformational transitions, shows the characteristic features of a funneled landscape, with a downhill surface toward the beta-hairpin folded basin. However, the analysis of the peptide thermodynamic stability, reveals that the beta-hairpin in solution is rather unstable. These results are in good agreement with several experimental evidences, according to which the isolated H1 peptide adopts very rapidly in water beta-sheet structure, leading to amyloid fibril precipitates [Nguyen et al., Biochemistry 1995;34:4186-4192; Inouye et al., J Struct Biol 1998;122:247-255]. Moreover, in this article we also characterize the diffusion behavior in conformational space, investigating its relations with folding/unfolding conditions. (c) 2005 Wiley-Liss, Inc
Tropicalization through the lens of Łukasiewicz logic, with a topos theoretic perspective
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Ultramatricial algebras over commutative chain semirings and application to MV-algebras
No full textAbstract
In this paper, we give a complete description of strongly projective semimodules over a semiring which is a finite direct product of matrix semirings over commutative chain semirings. We then classify ultramatricial algebras over commutative chain semirings by their ordered SK0-groups. Consequently, we get that there is a one-one correspondence between isomorphism classes of ultramatricial algebras A whose SK0(A) is lattice-ordered over a given commutative chain semiring and isomorphism classes of countable MV-algebras
An approach to stochastic processes via non-classical logic
No full textWithin the infinitary variety of σ-complete Riesz MV-algebras RMVσ, we introduce the algebraic analogue of a random variable as a homomorphism defined on the free algebra in RMVσ. After a preliminary study of the proposed notion, we use it to define stochastic processes in the framework of non-classical logic (Łukasiewicz logic, more precisely) and we define stochastic independence
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