Belief propagation (BP) is an iterative method to perform approximate inference on arbitrary graphical models. Whether BP converges and if the solution is a unique fixed point depends on both the structure and the parametrization of the model. To understand this dependence it is interesting to find \emph{all} fixed points. In this work, we formulate a set of polynomial equations, the solutions of which correspond to BP fixed points. To solve such a nonlinear system we present the numerical polynomial-homotopy-continuation (NPHC) method. Experiments on binary Ising models and on error-correcting codes show how our method is capable of obtaining all BP fixed points. On Ising models with fixed parameters we show how the structure influences both the number of fixed points and the convergence properties. We further asses the accuracy of the marginals and weighted combinations thereof. Weighting marginals with their respective partition function increases the accuracy in all experiments. Contrary to the conjecture that uniqueness of BP fixed points implies convergence, we find graphs for which BP fails to converge, even though a unique fixed point exists. Moreover, we show that this fixed point gives a good approximation, and the NPHC method is able to obtain this fixed point.

Belief revision deals with the problem of changing a declaratively specified repository under potentially conflicting information. Usually, the problem is approached by providing postulates that specify intended constraints for the revision and constructing concrete revision operators fulfilling them. In the last 30 years since the start of formal belief revision with the work of AGM (Alchourron, Gaerdenfors, and Makinson) roughly four construction principles were investigated and mutually interrelated: partial-meet, epistemic entrenchment, safe/kernel, and the possible worlds (model based) construction. The aim of this paper is to raise into the focus another construction principle relying on the idea of reinterpretation: Conflicts are explained by different use of symbols and conflict resolution is handled by choosing appropriate bridging axioms that relate the different readings. The main purpose of the paper is to argue that the reinterpretation-based approach is sufficiently general by showing how to equivalently formulate classical revision operators such as the operators of Weber, a natural variant of Weber, the operator of Satoh (skeptical operator of Delgrande and Schaub) and the operator of Borgida with reinterpretation operators.

The Belief-Desire-Intention (BDI) architecture is a practical approach for modelling large-scale intelligent systems. In the BDI setting, a complex system is represented as a network of interacting agents - or components - each one modelled based on its beliefs, desires and intentions. However, current BDI implementations are not well-suited for modelling more realistic intelligent systems which operate in environments pervaded by different types of uncertainty. Furthermore, existing approaches for dealing with uncertainty typically do not offer syntactical or tractable ways of reasoning about uncertainty. This complicates their integration with BDI implementations, which heavily rely on fast and reactive decisions. In this paper, we advance the state-of-the-art w.r.t. handling different types of uncertainty in BDI agents. The contributions of this paper are, first, a new way of modelling the beliefs of an agent as a set of epistemic states. Each epistemic state can use a distinct underlying uncertainty theory and revision strategy, and commensurability between epistemic states is achieved through a stratification approach. Second, we present a novel syntactic approach to revising beliefs given unreliable input. We prove that this syntactic approach agrees with the semantic definition, and we identify expressive fragments that are particularly useful for resource-bounded agents. Third, we introduce full operational semantics that extend CAN, a popular semantics for BDI, to establish how reasoning about uncertainty can be tightly integrated into the BDI framework. Fourth, we provide comprehensive experimental results to highlight the usefulness and feasibility of our approach, and explain how the generic epistemic state can be instantiated into various representations.

To guide their behavior, humans and animals rely on previously learned knowledge about the world. Since the world is complex and models of the world are never perfect, the question arises whether we should trust our internal world model that we have built from past data or whether we should readjust it when we receive a new data sample. In noisy environments, a single data sample may not be reliable and in general we need to average over several data samples. However, when a structural change occurs in the environment, the most recent data samples are the most informative ones and we should put more weight on recent data samples than on earlier ones. Indeed, both humans and animals adaptively adjust the relative contribution of old and newly acquired data during learning (Behrens et al., 2007; Nassar et al., 2012; Krugel et al., 2009; Pearce and Hall, 1980) and rapidly adapt to changing environments (Pearce and Hall, 1980; Wilson et al., 1992; Holland, 1997).

Belief Propagation (BP) is an iterative message-passing algorithm for performing inference in graphical models Convergent message-passing algorithms. There has (GMs), such as Markov Random Fields (MRFs). BP calculates been much research on finding variations to the update equations the marginal distribution for each unobserved node, of BP that guarantee convergence. These algorithms conditional on any observed nodes (Pearl 1988). It achieves are often similar in structure to the nonconvergent algorithms, this by propagating the information from a few observed yet it can be proven that the value of the variational nodes throughout the network by iteratively passing information problem (or its dual) improves at each iteration (Hazan and between neighboring nodes. It is known that when Shashua 2008; Heskes 2006; Meltzer, Globerson, and Weiss the graphical model has a tree structure, then BP converges 2009). Another body of recent papers have suggested to to the true marginals (according to exact probabilistic inference) solve the convergence problems of MMinference by linearizing after a finite number of iterations.

Math word problems provide a natural abstraction to a range of natural language understanding problems that involve reasoning about quantities, such as interpreting election results, news about casualties, and the financial section of a newspaper. Units associated with the quantities often provide information that is essential to support this reasoning. This paper proposes a principled way to capture and reason about units and shows how it can benefit an arithmetic word problem solver. This paper presents the concept of Unit Dependency Graphs (UDGs), which provides a compact representation of the dependencies between units of numbers mentioned in a given problem. Inducing the UDG alleviates the brittleness of the unit extraction system and allows for a natural way to leverage domain knowledge about unit compatibility, for word problem solving. We introduce a decomposed model for inducing UDGs with minimal additional annotations, and use it to augment the expressions used in the arithmetic word problem solver of (Roy and Roth 2015) via a constrained inference framework. We show that introduction of UDGs reduces the error of the solver by over 10 %, surpassing all existing systems for solving arithmetic word problems. In addition, it also makes the system more robust to adaptation to new vocabulary and equation forms .

Math word problems provide a natural abstraction to a range of natural language understanding problems that involve reasoning about quantities, such as interpreting election results, news about casualties, and the financial section of a newspaper. Units associated with the quantities often provide information that is essential to support this reasoning. This paper proposes a principled way to capture and reason about units and shows how it can benefit an arithmetic word problem solver. This paper presents the concept of Unit Dependency Graphs (UDGs), which provides a compact representation of the dependencies between units of numbers mentioned in a given problem. Inducing the UDG alleviates the brittleness of the unit extraction system and allows for a natural way to leverage domain knowledge about unit compatibility, for word problem solving. We introduce a decomposed model for inducing UDGs with minimal additional annotations, and use it to augment the expressions used in the arithmetic word problem solver of (Roy and Roth 2015) via a constrained inference framework. We show that introduction of UDGs reduces the error of the solver by over 10 %, surpassing all existing systems for solving arithmetic word problems. In addition, it also makes the system more robust to adaptation to new vocabulary and equation forms .

Math word problems provide a natural abstraction to a range of natural language understanding problems that involve reasoning about quantities, such as interpreting election results, news about casualties, and the financial section of a newspaper. Units associated with the quantities often provide information that is essential to support this reasoning. This paper proposes a principled way to capture and reason about units and shows how it can benefit an arithmetic word problem solver. This paper presents the concept of Unit Dependency Graphs (UDGs), which provides a compact representation of the dependencies between units of numbers mentioned in a given problem. Inducing the UDG alleviates the brittleness of the unit extraction system and allows for a natural way to leverage domain knowledge about unit compatibility, for word problem solving. We introduce a decomposed model for inducing UDGs with minimal additional annotations, and use it to augment the expressions used in the arithmetic word problem solver of (Roy and Roth 2015) via a constrained inference framework. We show that introduction of UDGs reduces the error of the solver by over 10 %, surpassing all existing systems for solving arithmetic word problems. In addition, it also makes the system more robust to adaptation to new vocabulary and equation forms .

Math word problems provide a natural abstraction to a range of natural language understanding problems that involve reasoning about quantities, such as interpreting election results, news about casualties, and the financial section of a newspaper. Units associated with the quantities often provide information that is essential to support this reasoning. This paper proposes a principled way to capture and reason about units and shows how it can benefit an arithmetic word problem solver. This paper presents the concept of Unit Dependency Graphs (UDGs), which provides a compact representation of the dependencies between units of numbers mentioned in a given problem. Inducing the UDG alleviates the brittleness of the unit extraction system and allows for a natural way to leverage domain knowledge about unit compatibility, for word problem solving. We introduce a decomposed model for inducing UDGs with minimal additional annotations, and use it to augment the expressions used in the arithmetic word problem solver of (Roy and Roth 2015) via a constrained inference framework. We show that introduction of UDGs reduces the error of the solver by over 10 %, surpassing all existing systems for solving arithmetic word problems. In addition, it also makes the system more robust to adaptation to new vocabulary and equation forms .

Math word problems provide a natural abstraction to a range of natural language understanding problems that involve reasoning about quantities, such as interpreting election results, news about casualties, and the financial section of a newspaper. Units associated with the quantities often provide information that is essential to support this reasoning. This paper proposes a principled way to capture and reason about units and shows how it can benefit an arithmetic word problem solver. This paper presents the concept of Unit Dependency Graphs (UDGs), which provides a compact representation of the dependencies between units of numbers mentioned in a given problem. Inducing the UDG alleviates the brittleness of the unit extraction system and allows for a natural way to leverage domain knowledge about unit compatibility, for word problem solving. We introduce a decomposed model for inducing UDGs with minimal additional annotations, and use it to augment the expressions used in the arithmetic word problem solver of (Roy and Roth 2015) via a constrained inference framework. We show that introduction of UDGs reduces the error of the solver by over 10 %, surpassing all existing systems for solving arithmetic word problems. In addition, it also makes the system more robust to adaptation to new vocabulary and equation forms .