Computer-supported learning is an increasingly important form of study since it allows for independent learning and individualized instruction. In this paper, we discuss a novel approach to developing an intelligent tutoring system for teaching textbook-style mathematical proofs. We characterize the particularities of the domain and discuss common ITS design models. Our approach is motivated by phenomena found in a corpus of tutorial dialogs that were collected in a Wizard-of-Oz experiment. We show how an intelligent tutor for textbook-style mathematical proofs can be built on top of an adapted assertion-level proof assistant by reusing representations and proof search strategies originally developed for automated and interactive theorem proving. The resulting prototype was successfully evaluated on a corpus of tutorial dialogs and yields good results.

We develop a novel absorption technique for large collections of factual assertions about individual objects. These assertions are commonly accompanied by implicit background knowledge and form a knowledge base. Both the assertions and the background knowledge are expressed in a suitable language of Description Logic and queries over such knowledge bases can be expressed as assertion retrieval queries. The proposed absorption technique significantly improves the performance of such queries, in particular in cases where a large number of object features are known for the objects represented in such a knowledge base. In addition to the absorption technique we present the results of a preliminary experimental evaluation that validates the efficacy of the proposed optimization.

A large and complex knowledge base that models some aspect of the real world can rarely be fully specified. Two examples of such underspecification are that (i) some of the cardinality constraints are omitted; (ii) some properties of all individual instances of a class are specialized across a class hierarchy, but specific references to which particular values are specialized are omitted. Such knowledge bases are of great practical interest as they are the basis of an empirically tested knowledge acquisition system that has been used to construct a knowledge base from a significant portion of a biology textbook. In this paper, we formalize an underspecified knowledge base using answer set programming, and give a set of rules called UMAP that support inheritance reasoning in such a knowledge base.

Answering queries in information systems that allow for ex- pressive inferencing is currently a field of intense research. This problem is often referred to as ontology-based data ac- cess (OBDA). We focus on conjunctive query entailment un- der logical rules known as tuple-generating dependencies, existential rules or Datalog+/-. One of the most expressive decidable classes of existential rules known today is that of greedy bounded treewidth sets (gbts). We propose an algo- rithm for this class, which is worst-case optimal for data and combined complexities, with or without bound on the pred- icate arity. A beneficial feature of this algorithm is that it allows for separation between offline and online processing steps: the knowledge base can be compiled independently from queries, which are evaluated against the compiled form. Moreover, very simple adaptations of the algorithm lead to worst-case-optimal complexities for specific subclasses of gbts which have lower complexities, such as guarded rules.

Seven years on from OWL becoming a W3C recommendation, and two years on from the more recent OWL 2 W3C recommendation, OWL has still experienced only patchy uptake on the Web. Although certain OWL features (like owl:sameAs) are very popular, other features of OWL are largely neglected by publishers in the Linked Data world. This may suggest that despite the promise of easy implementations and the proposal of tractable profiles suggested in OWL's second version, there is still no "right" standard fragment for the Linked Data community. In this paper, we (1) analyse uptake of OWL on the Web of Data, (2) gain insights into the OWL fragment that is actually used/usable on the Web, where we arrive at the conclusion that this fragment is likely to be a simplified profile based on OWL RL, (3) propose and discuss such a new fragment, which we call OWL LD (for Linked Data).

Fuzzy rule based models have a capability to approximate any continuous function to any degree of accuracy on a compact domain. The majority of FLC design process relies on heuristic knowledge of experience operators. In order to make the design process automatic we present a genetic approach to learn fuzzy rules as well as membership function parameters. Moreover, several statistical information criteria such as the Akaike information criterion (AIC), the Bhansali-Downham information criterion (BDIC), and the Schwarz-Rissanen information criterion (SRIC) are used to construct optimal fuzzy models by reducing fuzzy rules. A genetic scheme is used to design Takagi-Sugeno-Kang (TSK) model for identification of the antecedent rule parameters and the identification of the consequent parameters. Computer simulations are presented confirming the performance of the constructed fuzzy logic controller.

Knowledge-based support vector machines (KBSVMs) incorporate advice from domain experts, which can improve generalization significantly. A major limitation that has not been fully addressed occurs when the expert advice is imperfect, which can lead to poorer models. We propose a model that extends KBSVMs and is able to not only learn from data and advice, but also simultaneously improve the advice. The proposed approach is particularly effective for knowledge discovery in domains with few labeled examples. The proposed model contains bilinear constraints, and is solved using two iterative approaches: successive linear programming and a constrained concave-convex approach. Experimental results demonstrate that these algorithms yield useful refinements to expert advice, as well as improve the performance of the learning algorithm overall.

Hybrid MKNF knowledge bases are one of the most prominent tightly integrated combinations of open-world ontology languages with closed-world (non-monotonic) rule paradigms. The definition of Hybrid MKNF is parametric on the description logic (DL) underlying the ontology language, in the sense that non-monotonic rules can extend any decidable DL language. Two related semantics have been defined for Hybrid MKNF: one that is based on the Stable Model Semantics for logic programs and one on the Well-Founded Semantics (WFS). Under WFS, the definition of Hybrid MKNF relies on a bottom-up computation that has polynomial data complexity whenever the DL language is tractable. Here we define a general query-driven procedure for Hybrid MKNF that is sound with respect to the stable model-based semantics, and sound and complete with respect to its WFS variant. This procedure is able to answer a slightly restricted form of conjunctive queries, and is based on tabled rule evaluation extended with an external oracle that captures reasoning within the ontology. Such an (abstract) oracle receives as input a query along with knowledge already derived, and replies with a (possibly empty) set of atoms, defined in the rules, whose truth would suffice to prove the initial query. With appropriate assumptions on the complexity of the abstract oracle, the general procedure maintains the data complexity of the WFS for Hybrid MKNF knowledge bases. To illustrate this approach, we provide a concrete oracle for EL+, a fragment of the light-weight DL EL++. Such an oracle has practical use, as EL++ is the language underlying OWL 2 EL, which is part of the W3C recommendations for the Semantic Web, and is tractable for reasoning tasks such as subsumption. We show that query-driven Hybrid MKNF preserves polynomial data complexity when using the EL+ oracle and WFS.

Inference techniques play a central role in many cognitive systems. They transform low-level observations of the environment into high-level, actionable knowledge which then gets used by mechanisms that drive action, problem-solving, and learning. This paper presents an initial effort at combining results from AI and psychology into a pragmatic and scalable computational reasoning system. Our approach combines a numeric notion of plausibility with first-order logic to produce an incremental inference engine that is guided by heuristics derived from the psychological literature. We illustrate core ideas with detailed examples and discuss the advantages of the approach with respect to cognitive systems.

Our approach to mind-design derives from the view of language as a mirror of mind — a view compatible with the linguistic orientation of the Turing Test, and more concretely, with the remarkably tight coupling between linguistic structure and semantic entailment demonstrated by Richard Montague. Additional evidence for the power of this perspective comes from recent work in Natural Logic (NLog), in a sense a method of "reading off" certain obvious inferences directly from linguistic structure. Thus much of our past emphasis has been on developing a knowledge representation, Episodic Logic (EL), matching the expressivity of language, and inference machinery for this representation. More recently we have been striving to create broad bases of general world knowledge and lexical knowledge, while also adapting the latest version of our EPILOG inference engine to the kinds of obvious inferences that are the forte of NLog. At this point our knowledge collections range from sets of a few dozen core lexical axioms to millions of general "factoids" and quantified axioms derived from many of these, all expressed in EL. At the same time we have shown that EPILOG easily handles NLog-like inferences as well as ones beyond the scope of NLog.