My paper “Three characterization of strict coherence for infinite-valued events” has been published online on the *Review of Symbolic Logic. * If you are interest, please follow this link

# Tag: De Finetti

## ECSQARU 2019

The 15th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU 2019) will be held in Belgrade (Serbia), on September 18-20, 2019, at the Serbian Academy of Sciences and Arts in Belgrade.

The biennial ECSQARU conferences constitute a major forum for advances in the theory and practice of reasoning under uncertainty, with a focus on bringing symbolic and quantitative aspects together. Contributions come from researchers interested in advancing the scientific knowledge and from practitioners using uncertainty techniques in real-world applications. The scope of the ECSQARU conferences encompasses fundamental issues, representation, inference, learning, and decision making in qualitative and numeric uncertainty paradigms.

Submission infos are here available

## IPMU 2018

My contribute paper titled* “Logics for strict coherence and Carnap-regular probability *functions” has been recently accepted to be presented at the 17th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems – IPMU 2018. that will take place in Cádiz, Spain.

## Layers of zero probability and stable coherence over Łukasiewicz events

*Tommaso Flaminio, Lluis Godo*

The notion of stable coherence has been recently introduced to characterize coherent assignments to conditional many-valued events by means of hyperreal-valued states. In a nutshell, an assignment, or book, β on a finite set of conditional events is stably coherent if there exists a coherent variant β′ of β such that β′ maps all antecedents of conditional events to a strictly positive hyperreal number, and such that β and β′ differ by an infinitesimal. In this paper, we provide a characterization of stable coherence in terms of layers of zero probability for books on Łukasiewicz logic events.

**Keywords:** Layers of zero probability, Conditional probability, Stable coherence MV-algebras.

, Volume 21, Issue 1, pp. 113–123.

## On the complexity of Strictly Coherent Books

Given an book on formulas (i.e., a partial map on **SL** to rational numbers of [0,1]), deciding if it is coherent is an **NP**-complete problem. The proof essentially uses Carathéodory theorem which characterizes the points of a convex set: given a convex set **C**=cl-co(**X**) whose affine dimension is *n*, then *x* belongs to C *if and only if* there is a finite subset **Y** of **X** of cardinality at most *n+1*, such that *x* is a convex combination of the elements of **Y**. Indeed a book is coherent if and only if it belongs to cl-co(**H**) being **H** the set of logical valuations.

Moving from coherence to strict-coherence essentially boils down, in geometrical terms, to providing a characterization, *á la* Carathéodory, for the *relative interior* of cl-co(**H**). Steinitz theorem gives a (unfortunately useless) direction: if a point *x* belongs to relint cl-co(**H**), then there exists a finite subset **K** of **H** of cardinality at most *2n* such that *x* belongs to relint cl-co(**K**). The converse direction (which is *key* for the decidability of a strictly coherent book) is trivially false: consider a cube **C** in R3 and pick a point *x* lying in the relint of a face of **C**. Then *x* belongs to the relative interior of a square, but not to the relint of the cube.

In the last weeks I’m just trying to extend (in certain sense) Steinitz theorem to obtain a characterization of the relative interior of a convex set. I don’t know if I will get it, but I like very much the drawings.