31,692 research outputs found
Kolmogorov Complexity in perspective. Part II: Classification, Information Processing and Duality
We survey diverse approaches to the notion of information: from Shannon
entropy to Kolmogorov complexity. Two of the main applications of Kolmogorov
complexity are presented: randomness and classification. The survey is divided
in two parts published in a same volume. Part II is dedicated to the relation
between logic and information system, within the scope of Kolmogorov
algorithmic information theory. We present a recent application of Kolmogorov
complexity: classification using compression, an idea with provocative
implementation by authors such as Bennett, Vitanyi and Cilibrasi. This stresses
how Kolmogorov complexity, besides being a foundation to randomness, is also
related to classification. Another approach to classification is also
considered: the so-called "Google classification". It uses another original and
attractive idea which is connected to the classification using compression and
to Kolmogorov complexity from a conceptual point of view. We present and unify
these different approaches to classification in terms of Bottom-Up versus
Top-Down operational modes, of which we point the fundamental principles and
the underlying duality. We look at the way these two dual modes are used in
different approaches to information system, particularly the relational model
for database introduced by Codd in the 70's. This allows to point out diverse
forms of a fundamental duality. These operational modes are also reinterpreted
in the context of the comprehension schema of axiomatic set theory ZF. This
leads us to develop how Kolmogorov's complexity is linked to intensionality,
abstraction, classification and information system.Comment: 43 page
Introduction to the 26th International Conference on Logic Programming Special Issue
This is the preface to the 26th International Conference on Logic Programming
Special IssueComment: 6 page
kLog: A Language for Logical and Relational Learning with Kernels
We introduce kLog, a novel approach to statistical relational learning.
Unlike standard approaches, kLog does not represent a probability distribution
directly. It is rather a language to perform kernel-based learning on
expressive logical and relational representations. kLog allows users to specify
learning problems declaratively. It builds on simple but powerful concepts:
learning from interpretations, entity/relationship data modeling, logic
programming, and deductive databases. Access by the kernel to the rich
representation is mediated by a technique we call graphicalization: the
relational representation is first transformed into a graph --- in particular,
a grounded entity/relationship diagram. Subsequently, a choice of graph kernel
defines the feature space. kLog supports mixed numerical and symbolic data, as
well as background knowledge in the form of Prolog or Datalog programs as in
inductive logic programming systems. The kLog framework can be applied to
tackle the same range of tasks that has made statistical relational learning so
popular, including classification, regression, multitask learning, and
collective classification. We also report about empirical comparisons, showing
that kLog can be either more accurate, or much faster at the same level of
accuracy, than Tilde and Alchemy. kLog is GPLv3 licensed and is available at
http://klog.dinfo.unifi.it along with tutorials
Reducing fuzzy answer set programming to model finding in fuzzy logics
In recent years, answer set programming (ASP) has been extended to deal with multivalued predicates. The resulting formalisms allow for the modeling of continuous problems as elegantly as ASP allows for the modeling of discrete problems, by combining the stable model semantics underlying ASP with fuzzy logics. However, contrary to the case of classical ASP where many efficient solvers have been constructed, to date there is no efficient fuzzy ASP solver. A well-known technique for classical ASP consists of translating an ASP program P to a propositional theory whose models exactly correspond to the answer sets of P. In this paper, we show how this idea can be extended to fuzzy ASP, paving the way to implement efficient fuzzy ASP solvers that can take advantage of existing fuzzy logic reasoners
A Boxology of Design Patterns for Hybrid Learning and Reasoning Systems
We propose a set of compositional design patterns to describe a large variety
of systems that combine statistical techniques from machine learning with
symbolic techniques from knowledge representation. As in other areas of
computer science (knowledge engineering, software engineering, ontology
engineering, process mining and others), such design patterns help to
systematize the literature, clarify which combinations of techniques serve
which purposes, and encourage re-use of software components. We have validated
our set of compositional design patterns against a large body of recent
literature.Comment: 12 pages,55 reference
Integration of Logic and Probability in Terminological and Inductive Reasoning
This thesis deals with Statistical Relational Learning (SRL), a research area combining principles and ideas from three important subfields of Artificial Intelligence: machine learn- ing, knowledge representation and reasoning on uncertainty. Machine learning is the study of systems that improve their behavior over time with experience; the learning process typi- cally involves a search through various generalizations of the examples, in order to discover regularities or classification rules. A wide variety of machine learning techniques have been developed in the past fifty years, most of which used propositional logic as a (limited) represen- tation language. Recently, more expressive knowledge representations have been considered, to cope with a variable number of entities as well as the relationships that hold amongst them. These representations are mostly based on logic that, however, has limitations when reason- ing on uncertain domains. These limitations have been lifted allowing a multitude of different formalisms combining probabilistic reasoning with logics, databases or logic programming, where probability theory provides a formal basis for reasoning on uncertainty.
In this thesis we consider in particular the proposals for integrating probability in Logic Programming, since the resulting probabilistic logic programming languages present very in- teresting computational properties. In Probabilistic Logic Programming, the so-called "dis- tribution semantics" has gained a wide popularity. This semantics was introduced for the PRISM language (1995) but is shared by many other languages: Independent Choice Logic, Stochastic Logic Programs, CP-logic, ProbLog and Logic Programs with Annotated Disjunc- tions (LPADs). A program in one of these languages defines a probability distribution over normal logic programs called worlds. This distribution is then extended to queries and the probability of a query is obtained by marginalizing the joint distribution of the query and the programs. The languages following the distribution semantics differ in the way they define the distribution over logic programs.
The first part of this dissertation presents techniques for learning probabilistic logic pro- grams under the distribution semantics. Two problems are considered: parameter learning and structure learning, that is, the problems of inferring values for the parameters or both the structure and the parameters of the program from data. This work contributes an algorithm for parameter learning, EMBLEM, and two algorithms for structure learning (SLIPCASE and SLIPCOVER) of probabilistic logic programs (in particular LPADs). EMBLEM is based on the Expectation Maximization approach and computes the expectations directly on the Binary De- cision Diagrams that are built for inference. SLIPCASE performs a beam search in the space of LPADs while SLIPCOVER performs a beam search in the space of probabilistic clauses and a greedy search in the space of LPADs, improving SLIPCASE performance. All learning approaches have been evaluated in several relational real-world domains.
The second part of the thesis concerns the field of Probabilistic Description Logics, where we consider a logical framework suitable for the Semantic Web. Description Logics (DL) are a family of formalisms for representing knowledge. Research in the field of knowledge repre- sentation and reasoning is usually focused on methods for providing high-level descriptions of the world that can be effectively used to build intelligent applications.
Description Logics have been especially effective as the representation language for for- mal ontologies. Ontologies model a domain with the definition of concepts and their properties and relations. Ontologies are the structural frameworks for organizing information and are used in artificial intelligence, the Semantic Web, systems engineering, software engineering, biomedical informatics, etc. They should also allow to ask questions about the concepts and in- stances described, through inference procedures. Recently, the issue of representing uncertain information in these domains has led to probabilistic extensions of DLs.
The contribution of this dissertation is twofold: (1) a new semantics for the Description Logic SHOIN(D) , based on the distribution semantics for probabilistic logic programs, which embeds probability; (2) a probabilistic reasoner for computing the probability of queries from uncertain knowledge bases following this semantics. The explanations of queries are encoded in Binary Decision Diagrams, with the same technique employed in the learning systems de- veloped for LPADs. This approach has been evaluated on a real-world probabilistic ontology
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