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An algebraic treatment of imprecise probabilities

Montagna F.

Demonstratio Mathematica

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2011

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Vol. 44, nr 3

497-509

EN

This is a survey paper about an algebraic approach to imprecise probabilities. In the first part of it, we outline the work by Walley on imprecise probabilities and the more algebraic approach of Fedel et al.. Then, in the second part we will present some work in progress about a general treatment of upper and lower probabilities over many-valued events and of upper and lower previsions of gambles, by means of Universal Algebra.

2

A multicriteria approach to support the design of comlex systems

Norese M. F., Montagna F., Riva S.

Foundations of Computing and Decision Sciences

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2008

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Vol. 33, No. 1

53-70

EN

Numerous design problems exist when the product is so complex that it has to be decomposed and given to specialists from different disciplines. Multidisciplinary interaction is difficult and therefore specific methodologies are proposed for the design of systems and for the coordination of the involved organizational groups. The concept of interaction between disciplines is related to the original work context, the design coordination, but can be extended to all situations in which different sectors are involved, tin technical, administrative or management contexts. A collaboration between the Thales Alenia Space Italia enterprise and the university made it possible to define the problem of supporting the design of complex systems, in relation to the firm's design processes, and to test some innovative approaches. I One of these approaches integrates methods of Problem structuring and Multicriteria analysis. The results, in relation to a specific space-mission case study, are presented and analysed.

3

Probabilistic variants of Renyi-Ulam game and many-valued logic

Marini C., Montagna F.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

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2005

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Vol. 9, No 3

317-335

EN

In this paper we discuss some generalizations of Renyi-Ulam game with lies: some of them are simply probabilistic variants of it, some others differ from it by the presence of more than one number to guess. In the last part of the paper, we also discuss the relationship between such variants and many-valued logic. This paper is just a survey of known results, but in its last part it also contains some plans for future research.

4

Analytic Calculi for Monoidal T-norm Based Logic

Baaz M., Ciabattoni A., Montagna F.

Fundamenta Informaticae

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2004

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Vol. 59, nr 4

315--332

EN

Monoidal t-norm based logic MTL is the logic of left continuous t-norms. We introduce two analytic calculi for first-order MTL. These are obtained by lifting two sequent calculi for different fragments of this logic to the hypersequent level with subsequent addition of Avron's communication rule. Our calculi enable to prove the mid(hyper)sequent theorem. As corollaries follow Herbrand's theorem for first-order MTL, the decidability of its ∀∃-fragment and admissibility of Skolemization.