von Neumann-Morgenstern and Savage Theorems for Causal Decision Making

Causal thinking and decision making under uncertainty are fundamental aspects of intelligent reasoning. Decision making under uncertainty has been well studied when information is considered at the associative (probabilistic) level. The classical Theorems of von Neumann-Morgenstern and Savage provide a formal criterion for rational choice using purely associative information. Causal inference often yields uncertainty about the exact causal structure, so we consider what kinds of decisions are possible in those conditions. In this work, we consider decision problems in which available actions and consequences are causally connected. After recalling a previous causal decision making result, which relies on a known causal model, we consider the case in which the causal mechanism that controls some environment is unknown to a rational decision maker. In this setting we state and prove a causal version of Savage's Theorem, which we then use to develop a notion of causal games with its respective causal Nash equilibrium. These results highlight the importance of causal models in decision making and the variety of potential applications.Comment: Submitted to Journal of Causal Inferenc

An Imprecise Probability Approach for Abstract Argumentation based on Credal Sets

Some abstract argumentation approaches consider that arguments have a degree of uncertainty, which impacts on the degree of uncertainty of the extensions obtained from a abstract argumentation framework (AAF) under a semantics. In these approaches, both the uncertainty of the arguments and of the extensions are modeled by means of precise probability values. However, in many real life situations the exact probabilities values are unknown and sometimes there is a need for aggregating the probability values of different sources. In this paper, we tackle the problem of calculating the degree of uncertainty of the extensions considering that the probability values of the arguments are imprecise. We use credal sets to model the uncertainty values of arguments and from these credal sets, we calculate the lower and upper bounds of the extensions. We study some properties of the suggested approach and illustrate it with an scenario of decision making.Comment: 8 pages, 2 figures, Accepted in The 15th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU 2019

Stochastic Reasoning with Action Probabilistic Logic Programs

In the real world, there is a constant need to reason about the behavior of various entities. A soccer goalie could benefit from information available about past penalty kicks by the same player facing him now. National security experts could benefit from the ability to reason about behaviors of terror groups. By applying behavioral models, an organization may get a better understanding about how best to target their efforts and achieve their goals. In this thesis, we propose action probabilistic logic (or ap-) programs, a formalism designed for reasoning about the probability of events whose inter-dependencies are unknown. We investigate how to use ap-programs to reason in the kinds of scenarios described above. Our approach is based on probabilistic logic programming, a well known formalism for reasoning under uncertainty, which has been shown to be highly flexible since it allows imprecise probabilities to be specified in the form of intervals that convey the inherent uncertainty in the knowledge. Furthermore, no independence assumptions are made, in contrast to many of the probabilistic reasoning formalisms that have been proposed. Up to now, all work in probabilistic logic programming has focused on the problem of entailment, i.e., verifying if a given formula follows from the available knowledge. In this thesis, we argue that other problems also need to be solved for this kind of reasoning. The three main problems we address are: Computing most probable worlds: what is the most likely set of actions given the current state of affairs?; answering abductive queries: how can we effect changes in the environment in order to evoke certain desired actions?; and Reasoning about promises: given the importance of promises and how they are fulfilled, how can we incorporate quantitative knowledge about promise fulfillment in ap-programs? We address different variants of these problems, propose exact and heuristic algorithms to scalably solve them, present empirical evaluations of their performance, and discuss their application in real world scenarios

A logic for reasoning about upper probabilities

We present a propositional logic %which can be used to reason about the uncertainty of events, where the uncertainty is modeled by a set of probability measures assigning an interval of probability to each event. We give a sound and complete axiomatization for the logic, and show that the satisfiability problem is NP-complete, no harder than satisfiability for propositional logic.Comment: A preliminary version of this paper appeared in Proc. of the 17th Conference on Uncertainty in AI, 200