Automated Reasoning " ' Probabilistic Reasoning with Maximum Entropy - The System

1 Abstract We present a system for common sense reasoning based on propositional logic, the probability calculus and the concept of model-quantiication. The task of this system PIT (for Probability Induction Tool) is to deliver decisions under incomplete knowledge but to keep the necessary additional assumptions as minimal as possible. Following this task it shows non-monotonic behavior in two ways: Non-monotonic decisions can be the result of reasoning in a single probability model (via conditionalization) or in a set of probability models (via additional principles of rational decisions, justi-ed by model-quantiication). As the concept of model-quantiication delivers a precise semantics we know the corresponding decisions to make sense in many problems of common sense reasoning. We will show this with an example from default reasoning and an example of medical diagnosis. 2 Introduction Propositional logic is a well-researched area of science and allows the speciication of many kinds of exact knowledge. However it lacks the features necessary for modeling most real world situations. Especially there are three features missing from propositional logic for modeling common sense reasoning: The ability to describe uncertain knowledge, the ability to support plausible reasoning under incomplete knowledge and a appropriate modeling of the common sense if-then. On the other hand reasoning with probability models is also well-researched, incorporates reasoning with uncertainty and has a mature concept for the common sense conditional (by "conditionalization"). But as the language is very ne grained (context-sensitive), it lacks the ability to deal with incomplete knowledge. We therefore enrich the probability calculus with additional (context-sensitive, global) constraints (resp. principles) which are able to support rational decisions based on incomplete knowledge. These principles have their common source in the concept of model-quantiication (see section 4.1) and nd their dense representation in the (well-known) principle of Maximum Entropy (see 10]). As this principles form the theoretical base for our system we continue by describing the properties of our language in connection to non-monotonic reasoning (see sec. 3) sketching the diierent principles of model quan-tiication, their relation and their connection to eecient implementations (see section 4) explaining the parts of system and their tasks (see section 5) giving a set of examples for working with the system (see section 6) describing the necessary resources and some url's for additional information (see section 8). 3 The Language and its relation to Nonmonotonic Reasoning Combining propositional logic with probability theory we specify a range of …