332,374 research outputs found
The complexity of concept languages
The basic feature of Terminological Knowledge Representation Systems is to represent knowledge by means of taxonomies, here called terminologiesand to provide a specialized reasoning engine to do inferences on these structures. The taxonomy is built through a representation language called concept language (or description logic), which is given well-defined set-theoretic semantics. The efficiency of reasoning has often been advocated as a primary motivation for the use of such systems. Deduction methods and computational properties of reasoning problems in concept languages are the subject of this paper. The main contributions of the paper are: (1) a complexity analysis of concept satisfiability and subsumption for a wide class of concept languages; (2) the algorithms for these inferences that comply with the worst-case complexity of the reasoning task they perform
The complexity of existential quantification in concept languages
Much of the research on concept languages, also called terminological languages, has focused on the computational complexity of subsumption. The intractability results can be divided into two groups. First, it has been shown that extending the basic language FL- with constructs containing some form of logical disjunction leads to co-NP-hard subsumption problems. Second, adding negation to FL- makes subsumption PSPACE-complete. The main result of this paper is that extending FL- with unrestricted existential quantification makes subsumption NP-complete. This is the first proof of intractability for a concept language containing no construct expressing disjunction--whether explicitly or implicitly. Unrestricted existential quantification is therefore, alongside disjunction, a source of computational complexity in concept languages
The complexity of concept languages
The basic feature of Terminological Knowledge Representation Systems is to represent knowledge by means of taxonomies, here called terminologies , and to provide a specialized reasoning engine to do inferences on these structures. The taxonomy is built through a representation language called concept language (or description logic), which is given well-defined set-theoretic semantics. The efficiency of reasoning has often been advocated as a primary motivation for the use of such systems. Deduction methods and computational properties of reasoning problems in concept languages are the subject of this paper. The main contributions of the paper are: (1) a complexity analysis of concept satisfiability and subsumption for a wide class of concept languages; (2) the algorithms for these inferences that comply with the worst-case complexity of the reasoning task they perform
A Fundamental Scale of Descriptions for Analyzing Information Content of Communication Systems
The complexity of a system description is a function of the entropy of its
symbolic description. Prior to computing the entropy of the system description,
an observation scale has to be assumed. In natural language texts, typical
scales are binary, characters, and words. However, considering languages as
structures built around certain preconceived set of symbols, like words or
characters, is only a presumption. This study depicts the notion of the
Description Fundamental Scale as a set of symbols which serves to analyze the
essence a language structure. The concept of Fundamental Scale is tested using
English and MIDI music texts by means of an algorithm developed to search for a
set of symbols, which minimizes the system observed entropy, and therefore best
expresses the fundamental scale of the language employed. Test results show
that it is possible to find the Fundamental Scale of some languages. The
concept of Fundamental Scale, and the method for its determination, emerges as
an interesting tool to facilitate the study of languages and complex systems.Comment: 29 pages, 2 Tables, 5 Figure
Digraph Complexity Measures and Applications in Formal Language Theory
We investigate structural complexity measures on digraphs, in particular the
cycle rank. This concept is intimately related to a classical topic in formal
language theory, namely the star height of regular languages. We explore this
connection, and obtain several new algorithmic insights regarding both cycle
rank and star height. Among other results, we show that computing the cycle
rank is NP-complete, even for sparse digraphs of maximum outdegree 2.
Notwithstanding, we provide both a polynomial-time approximation algorithm and
an exponential-time exact algorithm for this problem. The former algorithm
yields an O((log n)^(3/2))- approximation in polynomial time, whereas the
latter yields the optimum solution, and runs in time and space O*(1.9129^n) on
digraphs of maximum outdegree at most two. Regarding the star height problem,
we identify a subclass of the regular languages for which we can precisely
determine the computational complexity of the star height problem. Namely, the
star height problem for bideterministic languages is NP-complete, and this
holds already for binary alphabets. Then we translate the algorithmic results
concerning cycle rank to the bideterministic star height problem, thus giving a
polynomial-time approximation as well as a reasonably fast exact exponential
algorithm for bideterministic star height.Comment: 19 pages, 1 figur
On the Structure and Complexity of Rational Sets of Regular Languages
In a recent thread of papers, we have introduced FQL, a precise specification
language for test coverage, and developed the test case generation engine
FShell for ANSI C. In essence, an FQL test specification amounts to a set of
regular languages, each of which has to be matched by at least one test
execution. To describe such sets of regular languages, the FQL semantics uses
an automata-theoretic concept known as rational sets of regular languages
(RSRLs). RSRLs are automata whose alphabet consists of regular expressions.
Thus, the language accepted by the automaton is a set of regular expressions.
In this paper, we study RSRLs from a theoretic point of view. More
specifically, we analyze RSRL closure properties under common set theoretic
operations, and the complexity of membership checking, i.e., whether a regular
language is an element of a RSRL. For all questions we investigate both the
general case and the case of finite sets of regular languages. Although a few
properties are left as open problems, the paper provides a systematic semantic
foundation for the test specification language FQL
Queries, rules and definitions as epistemic statements in concept languages
Concept languages have been studied in order to give a formal account of the basic features of frame-based languages. The focus of research in concept languages was initially on the semantical reconstruction of frame-based systems and the computational complexity of reasoning. More recently, attention has been paid to the formalization of other aspects of frame-based languages, such as non-monotonic reasoning and procedural rules, which are necessary in order to bring concept languages closer to implemented systems. In this paper we discuss the above issues in the framework of concept languages enriched with an epistemic operator. In particular, we show that the epistemic operator both introduces novel features in the language, such as sophisticated query formulation and closed world reasoning, and makes it possible to provide a formal account for some aspects of the existing systems, such as rules and definitions, that cannot be characterized in a standard first-order framework
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