Abstract. We introduce a new framework for the study of reasoning. The Learning (in order) to Reason approach developed here views learning as an integral part of the inference process, and suggests that learning and reasoning should be studied together. The Learning to Reason framework combines the interfaces to the world used by known learning models with the reasoning task and a performance criterion suitable for it. In this framework, the intelligent agent is given access to its favorite learning interface, and is also given a grace period in which it can interact with this interface and construct a representation KB of the world W. The reasoning performance is measured only after this period, when the agent is presented with queries � from some query language, relevant to the world, and has to answer whether W implies �. The approach is meant to overcome the main computational difficulties in the traditional treatment of reasoning which stem from its separation from the “world”. Since the agent interacts with the world when constructing its knowledge representation it can choose a representation that is useful for the task at hand. Moreover, we can now make explicit the dependence of the reasoning performance on the environment the agent interacts with. We show how previous results from learning theory and reasoning fit into this framework and

Independence { the study of what is relevant to a given problem of reasoning { has received an increasing attention from the AI community. In this paper, we consider two basic forms of independence, namely, a syntactic one and a semantic one. We show features and drawbacks of them. In particular, while the syntactic form of independence is computationally easy to check, there are cases in which things that intuitively are not relevant are not recognized as such. We also consider the problem of forgetting, i.e., distilling from a knowledge base only the part that is relevant to the set of queries constructed from a subset of the alphabet. While such process is computationally hard, it allows for a simpli - cation of subsequent reasoning, and can thus be viewed as a form of compilation: once the relevant part of a knowledge base has been extracted, all reasoning tasks to be performed can be simpli ed.

Formal AI systems traditionally represent knowledge using logical formulas.

The Learning to Reason framework combines the study of Learning and Reasoning into a single task. Within it, learning is done specifically for the purpose of reasoning with the learned knowledge. Computational considerations show that this is a useful paradigm; in some cases learning and reasoning problems that are intractable when studied separately become tractable when performed as a task of Learning to Reason. In this paper we study Learning to Reason problems where the interaction with the world supplies the learner only partial information in the form of partial assignments. Several natural interpretations of partial assignments are considered and learning and reasoning algorithms using these are developed. The results presented exhibit a tradeoff between learnability, the strength of the oracles used in the interface, and the range of reasoning queries the learner is guaranteed to answer correctly.

We investigate the space e#ciency of a Propositional Knowledge Representation (PKR) formalism. Intuitively, the space e#ciency of a formalism F in representing a certain piece of knowledge #, is the size of the shortest formula of F that represents #. In this paper we assume that knowledge is either a set of propositional interpretations (models) or a set of propositional formulae (theorems). We provide a formal way of talking about the relative ability of PKR formalisms to compactly represent a set of models or a set of theorems. We introduce two new compactness measures, the corresponding classes, and show that the relative space e#ciency of a PKR formalism in representing models/theorems is directly related to such classes. In particular, we consider formalisms for nonmonotonic reasoning, such as circumscription and default logic, as well as belief revision operators and the stable model semantics for logic programs with negation. One interesting result is that formalisms ...

Characteristic models are an alternative, model based, representation for Horn expressions. It has been shown that these two representations are incomparable and each has its advantages over the other. It is therefore natural to ask what is the cost of translating, back and forth, between these representations. Interestingly, the same translation questions arise in database theory, where it has applications to the design of relational databases. We study the complexity of these problems and prove some positive and negative results. Our main result is that the two translation problems are equivalent under polynomial reductions, and that they are equivalent to the corresponding decision problem. Namely, translating is equivalent to deciding whether a given set a models is the set of characteristic models for a given Horn expression. We also relate these problems to translating between the CNF and DNF representations of monotone functions, a well known problem for which no pol...

For humans, looking at how concrete examples behave is an intuitive way of deriving conclusions. The drawback with this method is that it does not necessarily give the correct results. However, under certain conditions example-based deduction can be used to obtain a correct and complete inference procedure. This is the case for Boolean formulae (reasoning with models) and for certain types of database integrity constraints (the use of Armstrong relations). We show that these approaches are closely related, and use the relationship to prove new results about the existence and sizes of Armstrong relations for Boolean dependencies. Furthermore, we exhibit close relations between the questions of finding keys in relational databases and that of finding abductive explanations. Further applications of the correspondence between these two approaches are also discussed. 1 Introduction One of the major tasks in database systems as well as artificial intelligence systems is to express some know...

Abstract. We propose a notion of deterministic association rules for ordered data. We prove that our proposed rules can be formally justified by a purely logical characterization, namely, a natural notion of empirical Horn approximation for ordered data which involves background Horn conditions; these ensure the consistency of the propositional theory obtained with the ordered context. The main proof resorts to a concept lattice model in the framework of Formal Concept Analysis, but adapted to ordered contexts. We also discuss a general method to mine these rules that can be easily incorporated into any algorithm for mining closed sequences, of which there are already some in the literature. 1

The paper introduces LogAn-H --- a system for learning first-order function-free Horn expressions from interpretations. The system is based on an interactive algorithm (that asks questions) that was proved correct in previous work. The current paper shows how the algorithm can be implemented in a practical system by reducing some inefficiencies.

Motivation: The problem addressed in this paper is the prediction of splice site locations in human DNA. The aims of the proposed approach are explicit splicing rule description, high recognition quality, and robust and stable `one shot' data processing.