Representing defeasibility is an important issue in common sense reasoning. In reasoning about action and change, this issue becomes more difficult because domain and action related defeasible information may conflict with general inertia rules. Furthermore, different types of defeasible information may also interfere with each other during the reasoning. In this paper, we develop a prioritized logic programming approach to handle defeasibilities in reasoning about action. In particular, we propose three action languages AT ^ 0 , AT ^ 1 and AT ^ 2 which handle three types of defeasibilities in action domains named defeasible constraints, defeasible observations and actions with defeasible and abnormal effects respectively. Each language with a higher superscript can be viewed as an extension of the language with a lower superscript. These action languages inherit the simple syntax of A language but their semantics is developed in terms of transition systems where transition functions are defined based on prioritized logic programs. By illustrating various examples, we show that our approach eventually provides a powerful mechanism to handle various defeasibilities in temporal prediction and postdiction. We also investigate semantic properties of these three action languages and characterize classes of action domains that present more desirable solutions in reasoning about action within the underlying action languages.
An early effort on handling defeasible causal rules in reasoning about action was due to the author's previous work @cite_2 , in which the author identified the restriction of McCain and Turner's causal theory of actions @cite_11 and claimed that in general a causal rule should be treated as a defeasible rule in order to solve the ramification problem properly. In @cite_2 , constraints ) and ) simply correspond to defaults @math and @math respectively. By combining Reiter's default theory @cite_10 and Winslett's PMA @cite_21 the author developed a causality-based minimal change principle for reasoning about action and change which subsumes McCain and Turner's causal theory.
@cite_11 @cite_10 @cite_21 @cite_2
2017479918 2156092566 2150014546 2542071751
Recent research on reasoning about action has shown that the traditional logic form of domain constraints is problematic to represent ramifications of actions that are related to causality of domains. To handle this problem properly, as proposed by some researchers, it is necessary to describe causal relations of domains explicitly in action theories. In this paper, we address this problem from a new point of view. Specifically, unlike other researchers viewing causal relations as some kind of inference rules, we distinguish causal relations between defeasible and non-defeasible cases. It turns out that a causal theory in our formalism can be specified by using Reiter's default logic. Based on this idea, we propose a causality-based minimal change approach for representing effects of actions, and argue that our approach provides more plausible solutions for the ramification and qualification problems compared with other related work. We also describe a logic programming approximation to compute causal theories of actions which provides an implementational basis for our approach. In this dissertation I present a formal approach to defeasible reasoning. This mathematical approach is based on the notion of specificity introduced by Poole and the general theory of warrant as presented by Pollock. General background information on the subject of Nonmonotonic Reasoning is presented and some of the shortcomings of existing systems are analyzed. We believe that the approach presented here represents a definite improvement over past systems. The main contribution of this thesis is a formally precise, elegant, clean, well-defined system which exhibits a correct behavior when applied to the benchmark examples in the literature. Model-theoretic semantical issues have been addressed. The investigation on the theoretical issues has aided the study of how this kind of reasoner can be realized on a computer. An interpreter of a restricted language, an extension of Horn clauses with defeasible rules, has been implemented. Finally, the implementation details are discussed. Michotte's theory of ampliation suggests that causal relationships are perceived by objects animated under appropriate spatiotemporal conditions. We extend the theory of ampliation and propose that the immediate perception of complex causal relations is also dependent on a set of structural and temporal rules. We designed animated representations, based on Michotte's rules, for showing complex causal relationships or causal semantics. In this paper we describe a set of animations for showing semantics such as causal amplification, causal strength, causal dampening, and causal multiplicity. In a two part study we compared the effectiveness of both the static and animated representations. The first study (N=44) asked participants to recall passages that were previously displayed using both types of representations. Participants were 8 more accurate in recalling causal semantics when they were presented using animations instead of static graphs. In the second study (N=112) we evaluated the intuitiveness of the representations. Our results showed that while users were as accurate with the static graphs as with the animations, they were 9 faster in matching the correct causal statements in the animated condition. Overall our results show that animated diagrams that are designed based on perceptual rules such as those proposed by Michotte have the potential to facilitate comprehension of complex causal relations. Motivated by online recommendation and advertising systems, we consider a causal model for stochastic contextual bandits with a latent low-dimensional confounder. In our model, there are @math observed contexts and @math arms of the bandit. The observed context influences the reward obtained through a latent confounder variable with cardinality @math ( @math ). The arm choice and the latent confounder causally determines the reward while the observed context is correlated with the confounder. Under this model, the @math mean reward matrix @math (for each context in @math and each arm in @math ) factorizes into non-negative factors @math ( @math ) and @math ( @math ). This insight enables us to propose an @math -greedy NMF-Bandit algorithm that designs a sequence of interventions (selecting specific arms), that achieves a balance between learning this low-dimensional structure and selecting the best arm to minimize regret. Our algorithm achieves a regret of @math at time @math , as compared to @math for conventional contextual bandits, assuming a constant gap between the best arm and the rest for each context. These guarantees are obtained under mild sufficiency conditions on the factors that are weaker versions of the well-known Statistical RIP condition. We further propose a class of generative models that satisfy our sufficient conditions, and derive a lower bound of @math . These are the first regret guarantees for online matrix completion with bandit feedback, when the rank is greater than one. We further compare the performance of our algorithm with the state of the art, on synthetic and real world data-sets.