Extensions of Pure Datalog

An important question of knowledge management is how we can support domain experts in formulating their domain knowledge and in making this expertise available via knowledge based systems. Critiquing systems are a special kind of knowledge based system. These systems provide context sensitive advice, and rationale to an artifact (for example charts, Web pages and so on) designed by a user. This is realized by delivering so called critiques, which contain relevant information for the user to the task at hand. We present a visual programming language called VisualCiLa, which allows design experts to formulate such critiques. It is based on a special subset of first order logic and a special form of text construction. VisualCiLa is built on top of a pipe-, filter and collector-metaphor and allows users to plug critiques together by placing tiles on a spreadsheet. Furthermore, VisualCiLa supports users in simulating the inference mechanism, which is represented by the flow of objects through the pipes. Filters and collectors visualize the functionality of inference and support the debugging process of such critiques. We believe that this language is a framework which allows design experts to formulate, to test, and to debug their expertise as critiquing knowledge.

Many temporal and modal logic languages can be regarded as subsets of first order logic, i.e. the semantics of a temporal logic formula is given as a first order condition on points of the underlying models (Kripke structures). Often the set of possible models is restricted to models which are trees. A temporal logic language is (first order) expressively complete, if for every first order condition for a node of a tree there exists an equivalent temporal formula which expresses the same condition. In this paper expressive completeness of the temporal logic language with the set of operators U (until), S (since), and X k (k-next) is proved, and the result is extended to various other tree-like structures.

Approximate Model Checking Using a Subset of First-order Logic

Attribute-value based representations, standard in today's data mining systems, have a limited expressiveness. Inductive Logic Programming provides an interesting alternative, particularly for learning from structured examples whose parts, each with its own attributes, are related to each other by means of first-order predicates. Several subsets of first-order logic (FOL) with different expressive power have been proposed in Inductive Logic Programming (ILP). The challenge lies in the fact that the more expressive the subset of FOL the learner works with, the more critical the dimensionality of the learning task. The Datalog language is expressive enough to represent realistic learning problems when data is given directly in a relational database, making it a suitable tool for data mining. Consequently, it is important to elaborate techniques that will dynamically decrease the dimensionality of learning tasks expressed in Datalog, just as Feature Subset Selection (FSS) techniques do it in attribute-value learning. The idea of re-using these techniques in ILP runs immediately into a problem as ILP examples have variable size and do not share the same set of literals. We propose here the first paradigm that brings Feature Subset Selection to the level of ILP, in languages at least as expressive as Datalog. The main idea is to first perform a change of representation, which approximates the original relational problem by a multi-instance problem. The representation obtained as the result is suitable for FSS techniques which we adapted from attribute-value learning by taking into account some of the characteristics of the data due to the change of representation. We present the simple FSS proposed for the task, the requisite change of representation, and the entire method combining those two algorithms. The method acts as a filter, preprocessing the relational data, prior to the model building, which outputs relational examples with empirically relevant literals. We discuss experiments in which the method was successfully applied to two real-world domains.

The Semantic Web (SW) has been envisioned to enable software tools or Web Services, respectively, to process information provided on the Web automatically. For this purpose, languages for representing the semantics of data by means of ontologies have been proposed such as RDF(S) and OWL. While the semantics of RDF(S) requires a non-standard model-theory that goes beyond first order logics, OWL is intended to model subsets of first order logics. OWL consists of three variants that are layered on each other. The less expressive variants OWL-Light and OWL-DL correspond to the Description Logics \(\mathcal{SHIF}\)(D) and \(\mathcal{SHOIN}\)(D) [1], respectively, and thus to subsets of First Order Logics [2].KeywordsLogic ProgramDescription LogicInformation IntegrationReasoning AlgorithmDistribute Information RetrievalThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

In the process of information semantic integration for product design and manufacturing, it is very important to express the product information semantic. Description logics (DLs) are a family of state-of-the-art knowledge representation languages, and a decidable subset of first-order logic. Firstly, by analyzing the characteristics of product information, proposed a semantic information description framework based on description logics for product information integration, which is divided into three levels: basic description logic, classic extended logic and unusual extended logic. Then, in the framework, reducer was taken for example to illustrate the application of their description logic in product design and manufacturing formal semantic information. Finally, based on description logic, discussed reasoning problems of product design and manufacturing information.

The logic of Counters, Lambdas, and Uninterpreted functions (CLU) is a subset of first-order logic satisfying the twin properties that 1) the validity of a CLU formula can be decided by generating a Boolean formula and using a Boolean satisfiability (SAT) checker to show the formula is unsatisfiable, and 2) it has sufficient expressive power to construct models of a variety of interesting software and hardware systems. We describe this logic and show its modeling capabilities.

Although there is an increasing amount of experimental research on learning concepts expressed in first-order logic, there are still relatively few formal results on the polynomial learnability of first-order representations from examples. Most previous analyses in the pac-model have focused on subsets of Prolog, and only a few highly restricted subsets have been shown to be learnable. In this paper, we will study instead the learnability of the restricted first-order logics known as “description logics”, also sometimes called “terminological logics” or “KL-ONE-type languages”. Description logics are also subsets of predicate calculus, but are expressed using a different syntax, allowing a different set of syntactic restrictions to be explored. We first define a simple description logic, summarize some results on its expressive power, and then analyze its learnability. It is shown that the full logic cannot be tractably learned. However, syntactic restrictions exist that enable tractable learning from positive examples alone, independent of the size of the vocabulary used to describe examples. The learnable sublanguage appears to be incomparable in expressive power to any subset of first-order logic previously known to be learnable.