This paper describes a resolution based Description Logic reasoning system called DLog. DLog transforms Description Logic axioms into a Prolog program and uses the standard Prolog execution for efficiently answering instance retrieval queries. From the Description Logic point of view, DLog is an ABox reasoning engine for the full SHIQ language. The DLog approach makes it possible to store the individuals in a database instead of memory, which results in better scalability and helps using description logic ontologies directly on top of existing information sources. To appear in Theory and Practice of Logic Programming (TPLP).
The basic idea of KAON2 is to first transform a @math knowledge base into a skolemized first-order clausal form. However, instead of using direct clausification, first a structural transformation @cite_2 is applied on the @math axioms. This transformation eliminates the nested concept descriptions by introducing new concepts; the resulting set of first-order clauses is denoted by @math . In the next step, basic superposition @cite_18 , a refinement of first-order resolution, is applied to saturate @math . The resulting set of clauses is denoted by @math . Clauses @math are then transformed into a disjunctive datalog program @cite_32 entailing the same set of ground facts as the initial DL knowledge base. This program is executed using a disjunctive datalog engine written specifically for KAON2. In this approach, the saturated clauses may still contain (non-nested) function symbols which are eliminated by introducing a new constant @math , standing for @math , for each individual @math in the ABox. This effectively means that KAON2 has to read the of the ABox before attempting to answer any queries.
@cite_18 @cite_32 @cite_2
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In this work, we introduce @math -expansion, a notion borrowed from number theory, as a theoretical framework to study fast construction of polar codes based on a recursive structure of universal partial order (UPO) and polarization weight (PW) algorithm. We show that polar codes can be recursively constructed from UPO by continuously solving several polynomial equations at each recursive step. From these polynomial equations, we can extract an interval for @math , such that ranking the synthetic channels through a closed-form @math -expansion preserves the property of nested frozen sets, which is a desired feature for low-complex construction. In an example of AWGN channels, we show that this interval for @math converges to a constant close to @math when the code block-length trends to infinity. Both asymptotic analysis and simulation results validate our theoretical claims. Abstract Given two infinite binary sequences A , B we say that B can compress at least as well as A if the prefix-free Kolmogorov complexity relative to B of any binary string is at most as much as the prefix-free Kolmogorov complexity relative to A , modulo a constant. This relation, introduced in Nies (2005) [14] and denoted by A ≤ L K B , is a measure of relative compressing power of oracles, in the same way that Turing reducibility is a measure of relative information. The equivalence classes induced by ≤ L K are called L K degrees (or degrees of compressibility) and there is a least degree containing the oracles which can only compress as much as a computable oracle, also called the ‘low for K ’ sets. A well-known result from Nies (2005) [14] states that these coincide with the K-trivial sets, which are the ones whose initial segments have minimal prefix-free Kolmogorov complexity. We show that with respect to ≤ L K , given any non-trivial Δ 2 0 sets X , Y there is a computably enumerable set A which is not K-trivial and it is below X , Y . This shows that the local structures of Σ 1 0 and Δ 2 0 Turing degrees are not elementarily equivalent to the corresponding local structures in the LK degrees. It also shows that there is no pair of sets computable from the halting problem which forms a minimal pair in the LK degrees; this is sharp in terms of the jump, as it is known that there are sets computable from 0 ″ which form a minimal pair in the LK degrees. We also show that the structure of LK degrees below the LK degree of the halting problem is not elementarily equivalent to the Δ 2 0 or Σ 1 0 structures of LK degrees. The proofs introduce a new technique of permitting below a Δ 2 0 set that is not K -trivial, which is likely to have wider applications. Many real-world knowledge-based systems must deal with information coming from different sources that invariably leads to incompleteness, overspecification, or inherently uncertain content. The presence of these varying levels of uncertainty doesn't mean that the information is worthless --- rather, these are hurdles that the knowledge engineer must learn to work with. In this paper, we continue work on an argumentation-based framework that extends the well-known Defeasible Logic Programming (DeLP) language with probabilistic uncertainty, giving rise to the Defeasible Logic Programming with Presumptions and Probabilistic Environments (DeLP3E) model. Our prior work focused on the problem of belief revision in DeLP3E, where we proposed a non-prioritized class of revision operators called AFO (Annotation Function-based Operators) to solve this problem. In this paper, we further study this class and argue that in some cases it may be desirable to define revision operators that take quantitative aspects into account, such as how the probabilities of certain literals or formulas of interest change after the revision takes place. To the best of our knowledge, this problem has not been addressed in the argumentation literature to date. We propose the QAFO (Quantitative Annotation Function-based Operators) class of operators, a subclass of AFO, and then go on to study the complexity of several problems related to their specification and application in revising knowledge bases. Finally, we present an algorithm for computing the probability that a literal is warranted in a DeLP3E knowledge base, and discuss how it could be applied towards implementing QAFO-style operators that compute approximations rather than exact operations. Knowledge base (KB) completion adds new facts to a KB by making inferences from existing facts, for example by inferring with high likelihood nationality(X,Y) from bornIn(X,Y). Most previous methods infer simple one-hop relational synonyms like this, or use as evidence a multi-hop relational path treated as an atomic feature, like bornIn(X,Z) -> containedIn(Z,Y). This paper presents an approach that reasons about conjunctions of multi-hop relations non-atomically, composing the implications of a path using a recursive neural network (RNN) that takes as inputs vector embeddings of the binary relation in the path. Not only does this allow us to generalize to paths unseen at training time, but also, with a single high-capacity RNN, to predict new relation types not seen when the compositional model was trained (zero-shot learning). We assemble a new dataset of over 52M relational triples, and show that our method improves over a traditional classifier by 11 , and a method leveraging pre-trained embeddings by 7 .