Probability intervals are an attractive tool for reasoning under uncertainty. Unlike belief functions, though, they lack a natural probability transformation to be used for decision making in a utility theory framework. In this paper we propose the use of the intersection probability, a transform derived originally for belief functions in the framework of the geometric approach to uncertainty, as the most natural such transformation. We recall its rationale and definition, compare it with other candidate representives of systems of probability intervals, discuss its credal rationale as focus of a pair of simplices in the probability simplex, and outline a possible decision making framework for probability intervals, analogous to the Transferable Belief Model for belief functions.

The Dempster-Shafer (DS) Theory (DST) or the Theory of Evidence is considered by many researchers as an appropriate tool to represent various 2 ANDRZEJ MATUSZEWSKI, MIECZYS lAW A. K lOPOTEK aspects of human dealing with uncertain knowledge, especially for representation ofpartial ignorance. However, one particular obstacle in applying DST is its relationship to frequencies [12]. Though, in general a belief function may be derived from frequencies under some particular database representation [5], there exist serious difficulties in finding factorizations of belief functions from data. In probability theory and in classical statistics the factorizations are usually related to notion of (conditional) independence and such possibility istested accordingly. However, in DST conditional belief distributions prove to be non-proper belief functions (that is ones connected with negative "frequencies").This makes statistical testing of potential conditional independencies practically impossible, as no coherent interpretation could be found so far for negative belief function values.

Agents can be thought of as following a social behaviour, depending on the context in which they are interacting. We devise a computationally grounded  mechanism to represent and reason about others in social terms, reflecting the local perspective of an agent (first-person view), to support both stereotypical and empathetic reasoning. We use a hierarchy of agent models to discriminate which behaviours of others are plausible, and decide which behaviour for ourselves is socially acceptable, i.e. conforms to the social context. To this aim, we investigate the implications of considering agents capable of various degrees of theory of mind, and discuss a scenario showing how this affects behaviour.

The Dempster-Shafer theory of belief functions is an important approach to deal with uncertainty in AI.In the theory, belief functions are defined on Boolean algebras of events. In many applications of belief functions in real world problems, however, the objects that we manipulateis no more a Boolean algebra but a distributive lattice. In this paper, we extend the Dempster-Shafer theory to the setting of distributive lattices, which has a mathematical theory as attractive as in that of Boolean algebras.Moreover, we apply this more general theory to a simple epistemic logic the first-degree-entailment fragment of relevance logic R , provide a sound and complete axiomatization for reasoning about belief functions for this logic and show that the complexity of the satisfiability problem of a belief formula with respect to the class of the corresponding Dempster-Shafer structures is NP-complete.