Widely adopted for more than 20 years in industrial fields, business rules offer the opportunity to non-IT users to define decision-making policies in a simple and intuitive way. When used conjointly with probabilistic graphical models (PGM) their expressiveness increase by introducing the notion of probabilistic production rules (PPR). In this paper we will present a new model for PPR and suggest a way to handle the combinatorial explosion due to the number of parents of aggregators in PGM such as Bayesian Networks and Probabilistic Relational Models in an industrial context where marginals should be computed rapidly.

Jakob Bernoulli, working in the late 17th century, identified a gap in contemporary probability theory. He cautioned that it was inadequate to specify force of proof (probability of provability) for some kinds of uncertain arguments. After 300 years, this gap remains in present-day probability theory. We present axioms analogous to Kolmogorov's axioms for probability, specifying uncertainty that lies in an argument's inference/implication itself rather than in its premise and conclusion. The axioms focus on arguments spanning two Boolean algebras, but generalize the obligatory: "force of proof of A implies B is the probability of B or not A" in the case that the Boolean algebras are identical. We propose a categorical framework that relies on generalized probabilities (objects) to express uncertainty in premises, to mix with arguments (morphisms) to express uncertainty embedded directly in inference/implication. There is a direct application to Shafer's evidence theory (Dempster-Shafer theory), greatly expanding its scope for applications. Therefore, we can offer this framework not only as an optimal solution to a difficult historical puzzle, but also to advance the frontiers of contemporary artificial intelligence. Keywords: force of proof, probability of provability, Ars Conjectandi, non additive probabilities, evidence theory.

Many problems in AI (in reasoning, planning, learning, perception and robotics) require the agent to operate with incomplete or uncertain information. e objective of this track is to present and discuss a broad and diverse range of current work on uncertain reasoning, including theoretical and applied research based on di erent paradigms. Begun in 1996, this track, (meeting for its 23rd year) is the oldest of the special tracks in FLAIRS conferences. Like its predecessors, this track seeks to bring together researchers working on broad issues related to reasoning under uncertainty.

This meeting at FLAIRS-27 will mark the nineteenth in the series. Like the previous tracks, the special track seeks to bring together researchers working on broad issues related to reasoning under uncertainty. Papers on all aspects of uncertain reasoning were invited.

Introduction to the papers presented at the 2013 FLAIRS Conference Special Track on Uncertain Reasoning.

This paper examines the use of Bayesian Networks to tackle one of the tougher problems in requirements engineering, translating user requirements into system requirements. The approach taken is to model domain knowledge as Bayesian Network fragments that are glued together to form a complete view of the domain specific system requirements. User requirements are introduced as evidence and the propagation of belief is used to determine what are the appropriate system requirements as indicated by user requirements. This concept has been demonstrated in the development of a system specification and the results are presented here.

The quality criteria of system P have been guiding qualitative uncertain reasoning now for more than two decades. Different semantical approaches have been presented to provide semantics for system P. The aim of the present paper is to investigate the semantical structures underlying system P in more detail, namely, on the level of the models. In particular, we focus on the approach via conditional objects which relies on Boolean intervals, without making any use of qualitative or quantitative information. Indeed, our studies confirm the singular position of conditional objects, but we are also able to establish semantical relationships via novel variants of model theories.

Many problems in AI require an intelligent agent to operate with incomplete or uncertain information, e.g., in reasoning, planning, learning, perception and robotics. We hope that the variety and richness of this track will help to promote cross fertilization among the different approaches for uncertain reasoning, and in this way foster the development of new ideas and paradigms. Like the previous tracks, the special track seeks to bring together researchers working on broad issues related to reasoning under uncertainty. Papers on all aspects of uncertain reasoning were invited. Papers of particular interest included uncertain reasoning formalisms, calculi and methodologies; reasoning with probability, possibility, fuzzy logic, belief function, vagueness, granularity, rough sets, and probability logics; modeling and reasoning using imprecise and indeterminate information, such as Choquet capacities, comparative orderings, convex sets of measures, and interval-valued probabilities; exact, approximate and qualitative uncertain reasoning; graphical models of uncertainty; multiagent uncertain reasoning and decision making; decision-theoretic planning and Markov decision process; temporal reasoning and uncertainty; belief change and merging; nonmonotonic and conditional logics; similarity-based reasoning; and practical applications of uncertain reasoning.

Many problems in AI (in reasoning, planning, learning, perception and robotics) require an agent to operate with incomplete or uncertain information. The objective of this track is to present and discuss a broad and diverse range of current work on uncertain reasoning, including theoretical and applied research based on different paradigms. We hope that the variety and richness of this track will help to promote cross fertilization among the different approaches for uncertain reasoning, and in this way foster the development of new ideas and paradigms. The Special Track on Uncertain Reasoning is the oldest track in FLAIRS conferences, running annually since 1996. This meeting will mark the 16th in the series.

The Special Track on Uncertain Reasoning (UR) is the oldest FLAIRS special track, running annually since 1996. The UR'09 Special Track at the 2009 FLAIRS Conference is the 14th in the series. UR'09 seeks to bring together researchers working on broad issues related to reasoning under uncertainty. Topics pertaining to the special track included, but were not limited to, uncertain reasoning formalisms, calculi and methodologies; reasoning with probability, possibility, fuzzy logic, belief function, vagueness, granularity, argumentation, rough sets, and probability logics; modeling and reasoning using imprecise and indeterminate information, such as Choquet capacities, comparative orderings, convex sets of measures, and interval-valued probabilities; exact, approximate, and qualitative uncertain reasoning; graphical models of uncertainty; multi-agent uncertain reasoning and decision making; decision-theoretic planning and Markov decision process; temporal reasoning and uncertainty; epistemic logics; nonmonotonic and conditional logics; similarity-based reasoning; construction of models from elicitation, data mining, and knowledge discovery; uncertain reasoning in information retrieval, filtering, fusion, diagnosis, prediction, and situation assessment; and practical applications of uncertain reasoning. Through rigorous reviews by the program committee, UR'09 accepted 9 full papers and 4 posters from 18 submissions, which are included in this proceedings.