Related papers: Impossibility in Belief Merging
Efforts to ensure the safe development of artificial general intelligence (AGI) often rely on consensus-based alignment approaches grounded in axiomatic formalism, interpretability, and empirical validation. However, these methods may be…
Facing an unknown situation, a person may not be able to firmly elicit his/her preferences over different alternatives, so he/she tends to express uncertain preferences. Given a community of different persons expressing their preferences…
This paper presents four theorems that connect continuity postulates in mathematical economics to solvability axioms in mathematical psychology, and ranks them under alternative supplementary assumptions. Theorem 1 connects notions of…
We propose a doxastic \L ukasiewicz logic \textbf{B\L} that is sound and complete with respect to the class of Kripke-based models in which atomic propositions and accessibility relations are both infinitely valued in the standard…
In this work we generalize standard Decision Theory by assuming that two outcomes can also be incomparable. Two motivating scenarios show how incomparability may be helpful to represent those situations where, due to lack of information,…
We consider a population of Bayesian agents who share a common prior over some finite state space and each agent is exposed to some information about the state. We ask which distributions over empirical distributions of posteriors beliefs…
We present a logical framework that enables us to define a formal theory of computational trust in which this notion is analysed in terms of epistemic attitudes towards the possible objects of trust and in relation to existing evidence in…
The fact that the famous Godel incompleteness theorem and the archetype of all logical paradoxes, that of the Liar, are related closely is, of course, not only well known, but is a part of the common knowledge of logician community.…
Most questionnaires offer ordered responses whose order is poorly studied via belief functions. In this paper, we study the consequences of a frame of discernment consisting of ordered elements on belief functions. This leads us to redefine…
We construct a probabilistic coherence measure for information sets which determines a partial coherence ordering. This measure is applied in constructing a criterion for expanding our beliefs in the face of new information. A number of…
We further develop the formal foundations of Paraconsistent Belief Revision (PBR) by introducing Logics of Formal Inconsistency (LFIs) specifically designed to support the development of epistemic entrenchment-based models for belief…
We discuss conditionalisation for Accept-Desirability models in an abstract decision-making framework, where uncertain rewards live in a general linear space, and events are special projection operators on that linear space. This abstract…
We develop a framework that leverages the smoothed complexity analysis by Spielman and Teng to circumvent paradoxes and impossibility theorems in social choice, motivated by modern applications of social choice powered by AI and ML. For…
These lectures deal with the problem of inductive inference, that is, the problem of reasoning under conditions of incomplete information. Is there a general method for handling uncertainty? Or, at least, are there rules that could in…
We study algorithmic complexity and expressive power of fusion grammars, a novel formalism introduced in [Kreowski, Kuske, and Lye 2017], which extends hyperedge replacement grammars. In the first part of the work, we prove that the…
We address the problem of belief change in (nonmonotonic) logic programming under answer set semantics. Unlike previous approaches to belief change in logic programming, our formal techniques are analogous to those of distance-based belief…
A model for a subject's beliefs about a phenomenon may exhibit symmetry, in the sense that it is invariant under certain transformations. On the other hand, such a belief model may be intended to represent that the subject believes or knows…
In earlier work, we introduced flexible inference and decision-theoretic metareasoning to address the intractability of normative inference. Here, rather than pursuing the task of computing beliefs and actions with decision models composed…
The stability rule for belief, advocated by Leitgeb [Annals of Pure and Applied Logic 164, 2013], is a rule for rational acceptance that captures categorical belief in terms of $\textit{probabilistically stable propositions}$: propositions…
In real-world applications, knowledge bases consisting of all the information at hand for a specific domain, along with the current state of affairs, are bound to contain contradictory data coming from different sources, as well as data…