Logical properties of nonmonotonic causal theories and the action language C+

The formalism of nonmonotonic causal theories (Giunchiglia, Lee, Lifschitz, McCain, Turner, 2004) provides a general-purpose formalism for nonmonotonic reasoning and knowledge representation, as well as a higher level, special-purpose notation, the action language C+, for specifying and reasoning about the e ects of actions and the persistence (`inertia') of facts over time. In this paper we investigate some logical properties of these formalisms. There are two motivations. From the technical point of view, we seek to gain additional insights into the properties of the languages when viewed as a species of conditional logic. From the practical point of view, we are seeking to nd conditions under which two di erent causal theories, or two di erent action descriptions in C+, can be said to be equivalent, with the further aim of helping to decide between alternative formulations when constructing practical applications. A condensed version of this paper appeared as `Some logical properties of nonmonotonic causal theories', Proc. Eighth International Conference on Logic Programming and Non-Monotonic Reasoning, LNCS, Springer

Nonmonotonic Probabilistic Logics between Model-Theoretic Probabilistic Logic and Probabilistic Logic under Coherence

Recently, it has been shown that probabilistic entailment under coherence is weaker than model-theoretic probabilistic entailment. Moreover, probabilistic entailment under coherence is a generalization of default entailment in System P. In this paper, we continue this line of research by presenting probabilistic generalizations of more sophisticated notions of classical default entailment that lie between model-theoretic probabilistic entailment and probabilistic entailment under coherence. That is, the new formalisms properly generalize their counterparts in classical default reasoning, they are weaker than model-theoretic probabilistic entailment, and they are stronger than probabilistic entailment under coherence. The new formalisms are useful especially for handling probabilistic inconsistencies related to conditioning on zero events. They can also be applied for probabilistic belief revision. More generally, in the same spirit as a similar previous paper, this paper sheds light on exciting new formalisms for probabilistic reasoning beyond the well-known standard ones.Comment: 10 pages; in Proceedings of the 9th International Workshop on Non-Monotonic Reasoning (NMR-2002), Special Session on Uncertainty Frameworks in Nonmonotonic Reasoning, pages 265-274, Toulouse, France, April 200

Probabilistic Default Reasoning with Conditional Constraints

We propose a combination of probabilistic reasoning from conditional constraints with approaches to default reasoning from conditional knowledge bases. In detail, we generalize the notions of Pearl's entailment in system Z, Lehmann's lexicographic entailment, and Geffner's conditional entailment to conditional constraints. We give some examples that show that the new notions of z-, lexicographic, and conditional entailment have similar properties like their classical counterparts. Moreover, we show that the new notions of z-, lexicographic, and conditional entailment are proper generalizations of both their classical counterparts and the classical notion of logical entailment for conditional constraints.Comment: 8 pages; to appear in Proceedings of the Eighth International Workshop on Nonmonotonic Reasoning, Special Session on Uncertainty Frameworks in Nonmonotonic Reasoning, Breckenridge, Colorado, USA, 9-11 April 200

On Properties of Update Sequences Based on Causal Rejection

We consider an approach to update nonmonotonic knowledge bases represented as extended logic programs under answer set semantics. New information is incorporated into the current knowledge base subject to a causal rejection principle enforcing that, in case of conflicts, more recent rules are preferred and older rules are overridden. Such a rejection principle is also exploited in other approaches to update logic programs, e.g., in dynamic logic programming by Alferes et al. We give a thorough analysis of properties of our approach, to get a better understanding of the causal rejection principle. We review postulates for update and revision operators from the area of theory change and nonmonotonic reasoning, and some new properties are considered as well. We then consider refinements of our semantics which incorporate a notion of minimality of change. As well, we investigate the relationship to other approaches, showing that our approach is semantically equivalent to inheritance programs by Buccafurri et al. and that it coincides with certain classes of dynamic logic programs, for which we provide characterizations in terms of graph conditions. Therefore, most of our results about properties of causal rejection principle apply to these approaches as well. Finally, we deal with computational complexity of our approach, and outline how the update semantics and its refinements can be implemented on top of existing logic programming engines.Comment: 59 pages, 2 figures, 3 tables, to be published in "Theory and Practice of Logic Programming

Representing First-Order Causal Theories by Logic Programs

Nonmonotonic causal logic, introduced by Norman McCain and Hudson Turner, became a basis for the semantics of several expressive action languages. McCain's embedding of definite propositional causal theories into logic programming paved the way to the use of answer set solvers for answering queries about actions described in such languages. In this paper we extend this embedding to nondefinite theories and to first-order causal logic.Comment: 29 pages. To appear in Theory and Practice of Logic Programming (TPLP); Theory and Practice of Logic Programming, May, 201

A general approach to temporal reasoning about action and change

Reasoning about actions and change based on common sense knowledge is one of the most important and difficult tasks in the artificial intelligence research area. A series of such tasks are identified which motivate the consideration and application of reasoning formalisms. There follows a discussion of the broad issues involved in modelling time and constructing a logical language. In general, worlds change over time. To model the dynamic world, the ability to predict what the state of the world will be after the execution of a particular sequence of actions, which take time and to explain how some given state change came about, i.e. the causality are basic requirements of any autonomous rational agent. The research work presented herein addresses some of the fundamental concepts and the relative issues in formal reasoning about actions and change. In this thesis, we employ a new time structure, which helps to deal with the so-called intermingling problem and the dividing instant problem. Also, the issue of how to treat the relationship between a time duration and its relative time entity is examined. In addition, some key terms for representing and reasoning about actions and change, such as states, situations, actions and events are formulated. Furthermore, a new formalism for reasoning about change over time is presented. It allows more flexible temporal causal relationships than do other formalisms for reasoning about causal change, such as the situation calculus and the event calculus. It includes effects that start during, immediately after, or some time after their causes, and which end before, simultaneously with, or after their causes. The presented formalism allows the expression of common-sense causal laws at high level. Also, it is shown how these laws can be used to deduce state change over time at low level. Finally, we show that the approach provided here is expressive