This paper presents a simple framework for Horn-clause abduction, with probabilities associated with hypotheses. The framework incorporates assumptions about the rule base and independence assumptions amongst hypotheses. It is shown how any probabilistic knowledge representable in a discrete Bayesian belief network can be represented in this framework. The main contribution is in finding a relationship between logical and probabilistic notions of evidential reasoning. This provides a useful representation language in its own right, providing a compromise between heuristic and epistemic adequacy. It also shows how Bayesian networks can be extended beyond a propositional language. This paper also shows how a language with only (unconditionally) independent hypotheses can represent any probabilistic knowledge, and argues that it is better to invent new hypotheses to explain dependence rather than having to worry about dependence in the language. Scholar, Canadian Institute for Advanced...

Inspired by game theory representations, Bayesian networks, influence diagrams, structured Markov decision process models, logic programming, and work in dynamical systems, the independent choice logic (ICL) is a semantic framework that allows for independent choices (made by various agents, including nature) and a logic program that gives the consequence of choices. This representation can be used as a specification for agents that act in a world, make observations of that world and have memory, as well as a modelling tool for dynamic environments with uncertainty. The rules specify the consequences of an action, what can be sensed and the utility of outcomes. This paper presents a possible-worlds semantics for ICL, and shows how to embed influence diagrams, structured Markov decision processes, and both the strategic (normal) form and extensive (game-tree) form of games within the Thanks to Craig Boutilier and Holger Hoos for detailed comments on this paper. This work was supporte...

Abstract. We give a logic programming based account of probability and describe a declarative language P-log capable of reasoning which combines both logical and probabilistic arguments. Several non-trivial examples illustrate the use of P-log for knowledge representation. 1

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This paper shows how we can combine logical representations of actions and decision theory in such a manner that seems natural for both. In particular we assume an axiomatization of the domain in terms of situation calculus, using what is essentially Reiter's solution to the frame problem, in terms of the completion of the axioms defining the state change. Uncertainty is handled in terms of the independent choice logic, which allows for independent choices and a logic program that gives the consequences of the choices.

In probabilistic reasoning, the problems of existence and identity are important to many different queries; for example, the probability that something that fits some description exists, the probability that some description refers to an object you know about or to a new object, or the probability that an object fulfils some role. Many interesting queries reduce to reasoning about the role of objects. Being able to talk about the existence of parts and sub-parts and the relationships between these parts, allows for probability distributions over complex descriptions. Rather than trying to define a new language, this paper shows how the integration of multiple objects, ontologies and roles can be achieved cleanly. This solves two main problems: reasoning about existence and identity while preserving the clarity principle that specifies that probabilities must be over well defined propositions, and the correspondence problem that means that we don’t need to search over all possible correspondences between objects said to exist and things in the world.

Statistical techniques for NLP typically do not take advantage of existing domain knowledge and require large amounts of tagged training data. This paper presents a partial remedy to these shortcomings by introducing a richer class of statistical models, graphical models, along with techniques for: 1) establishing the form of the model in this class that best describes a given set of training data, 2) estimating the parameters of graphical models from untagged data, 3) combining constraints formulated in propositional logic with those derived from training data to produce a graphical model, and 4) simultaneously resolving interdependent ambiguities. The paper also describes how these tools can be used to produce a broad-coverage lexicon represented as a probabilistic model, and presents a method for using such a lexicon to simultaneously disambiguate all words in a sentence. Introduction The specification and acquisition of lexical knowledge is a central problem in n...

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We are working on a logic to combine the advantages of first-order logic, but using Bayesian decision theory (or more generally game theory) as a basis for handing uncertainty. This forms a logic for multiple agents under uncertainty. These agents act asynchronously, can have their own goals, have noisy sensors, and imperfect effectors. Recently we have developed the independent choice logic that incorporates all of these features. In this paper we discuss two different representations of time within this framework: the situation calculus and what is essentially the event calculus. We show how they both can be used, and compare the different ontological commitments made by each. Uncertainty is handled in terms of a logic which allows for independent choices and a logic program that gives the consequences of the choices. There are probabilities over the choices by nature. As part of the This work was supported by Institute for Robotics and Intelligent Systems, Project IC-7 and Natural Sciences and Engineering Research Council of Canada Operating Grant OGPOO44121. 1 consequences are a specification of the utility of (final) states. In the situation calculus, agents adopt programs and programs lead to situations in possible worlds (which correspond to the possible outcomes of complete histories) ; given a probability distribution over possible worlds, we can get the expected utility of a program. In the event calculus view, actions are propositions and agents adopt policies which are logic programs to imply what the agent will do based on what it observes. Again the expected value of a policy can be computed. The aim is to choose the plan or policy that maximizes the expected utility. This paper overviews both approaches, and explains why I think the event calculus i...

There have been many proposals for first-order belief networks (i.e., where we quantify over individuals) but these typically only let us reason about the individuals that we know about. There are many instances where we have to quantify over all of the individuals in a population. When we do this the population size often matters and we need to reason about all of the members of the population (but not necessarily individually). This paper presents an algorithm to reason about multiple individuals, where we may know particular facts about some of them, but want to treat the others as a group. Combining unification with variable elimination lets us reason about classes of individuals without needing to ground out the theory.