In most learning systems examples are represented as fixed-length "feature vectors", the components of which are either real numbers or nominal values. We propose an extension of the featurevector representation that allows the value of a feature to be a set of strings; for instance, to represent a small white and black dog with the nominal features size and species and the setvalued feature color, one might use a feature vector with size=small, species=canis-familiaris and color=fwhite,blackg. Since we make no assumptions about the number of possible set elements, this extension of the traditional feature-vector representation is closely connected to Blum's "infinite attribute" representation. We argue that many decision tree and rule learning algorithms can be easily extended to setvalued features. We also show by example that many real-world learning problems can be efficiently and naturally represented with set-valued features; in particular, text categorization problems and probl...

Computing the least common subsumer (lcs) is an inference task that can be used to support the "bottom-up " construction of knowledge bases for KR systems based on description logics. Previous work on how to compute the lcs has concentrated on description logics that allow for universal value restrictions, but not for existential restrictions. The main new contribution of this paper is the treatment of description logics with existential restrictions. Our approach for computing the lcs is based on an appropriate representation of concept descriptions by certain trees, and a characterization of subsumption by homomorphisms between these trees. The lcs operation then corresponds to the product operation on trees.

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Computing least common subsumers (Ics) and most specific concepts (msc) are inference tasks that can support the bottom-up construction of knowledge bases in description logics. In description logics with existential restrictions, the most specific concept need not exist if one restricts the attention to concept descriptions or acyclic TBoxes. In this paper, we extend the notions les and msc to cyclic TBoxes. For the description logic EC (which allows for conjunctions, existential restrictions, and the top-concept), we show that the les and msc always exist and can be computed in polynomial time if we interpret cyclic definitions with greatest fixpoint semantics.

The problem of rewriting a concept given a terminology can informally be stated as follows: given a terminology T (i.e., a set of concept definitions) and a concept description C that does not contain concept names defined in T, can this description be rewritten into a "related better " description E by using (some of) the names defined in T? In this paper, we first introduce a general framework for the rewriting problem in description logics, and then concentrate on one specific instance of the framework, namely the minimal rewriting problem (where "better " means shorter, and "related " means equivalent). We investigate the complexity of the decision problem induced by the minimal rewriting problem for the languages FL 0, ALN, ALE, and ALC, and then introduce an algorithm for computing (minimal) rewritings for the language ALE. (In the full paper, a similar algorithm is also developed for ALN.) Finally, we sketch other interesting instances of the framework.

. Description logics, also called terminological logics, are commonly used in knowledgebased systems to describe objects and their relationships. We investigate the learnability of a typical description logic, Classic, and show that Classic sentences are learnable in polynomial time in the exact learning model using equivalence queries and membership queries (which are in essence, "subsumption queries"---we show a prediction hardness result for the more traditional membership queries that convey information about specific individuals). We show that membership queries alone are insufficient for polynomial time learning of Classic sentences. Combined with earlier negative results (Cohen & Hirsh, 1994a) showing that, given standard complexity theoretic assumptions, equivalence queries alone are insufficient (or random examples alone in the PAC setting are insufficient), this shows that both sources of information are necessary for efficient learning in that neither type alone is sufficie...

Methods for computing the least common subsumer (lcs) are usually restricted to rather inexpressive DLs whereas existing knowledge bases are written in very expressive DLs. In order to allow the user to re-use concepts defined in such terminologies and still support the definition of new concepts by computing the lcs, we extend the notion of the lcs of concept descriptions to the notion of the lcs w.r.t. a background terminology.

. For a given TBox of a terminological KR system, the classification algorithm computes (a representation of) the subsumption hierarchy of all concepts introduced in the TBox. In general, this hierarchy does not contain sufficient information to derive all subsumption relationships between conjunctions of these concepts. We show how a method developed in the area of "formal concept analysis " for computing minimal implication bases can be used to determine a minimal representation of the subsumption hierarchy between conjunctions of concepts introduced in a TBox. To this purpose, the subsumption algorithm must be extended such that it yields (sufficient information about) a counterexample in cases where there is no subsumption relationship. For the concept language ALC, this additional requirement does not change the worst-case complexity of the subsumption algorithm. One advantage of the extended hierarchy is that it is a lattice, and not just a partial ordering. 1 Introduction In kn...

We develop, analyze, and evaluate a novel, supervised, specific-to-general learner for a simple temporal logic and use the resulting algorithm to learn visual event definitions from video sequences. First, we introduce a simple, propositional, temporal, event-description language called AMA that is sufficiently expressive to represent many events yet sufficiently restrictive to support learning. We then give algorithms, along with lower and upper complexity bounds, for the subsumption and generalization problems for AMA formulas. We present a positive-examples -- only specific-to-general learning method based on these algorithms. We also present a polynomial-time -- computable "syntactic" subsumption test that implies semantic subsumption without being equivalent to it. A generalization algorithm based on syntactic subsumption can be used in place of semantic generalization to improve the asymptotic complexity of the resulting learning algorithm. Finally

One view of computational learning theory is that of a learner acquiring the knowledge of a teacher. We introduce a formal model of learning capturing the idea that teachers may have gaps in their knowledge. In particular, we consider learning from a teacher who labels examples "+" (a positive instance of the concept being learned), "\Gamma" (a negative instance of the concept being learned), and "?" (an instance with unknown classification), in such a way that knowledge of the concept class and all the positive and negative examples is not sufficient to determine the labelling of any of the examples labelled with "?". The goal of the learner is not to compensate for the ignorance of the teacher by attempting to infer "+" or "\Gamma" labels for the examples labelled with "?", but is rather to learn (an approximation to) the ternary labelling presented by the teacher. Thus, the goal of the learner is still to acquire the knowledge of the teacher, but now the learner must also ...