Some Remarks on the Definability of Transitive Closure in First-order Logic and Datalog

نویسنده

  • Uwe Keller
چکیده

In the last WSML phone conference we had a brief discussion about the expressivity of First-order Logic and Datalog resp. the relation between the expressiveness of those two languages. In particular, there has been some confusion around the description of the transitive closure R of some binary relation R. In this short document, we want to clarify the situation and hope to remedy the confusion.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Characterizing weighted MSO for trees by branching transitive closure logics

We introduce the branching transitive closure operator on weighted monadic second-order logic formulas where the branching corresponds in a natural way to the branching inherent in trees. For arbitrary commutative semirings, we prove that weighted monadic second order logics on trees is equivalent to the definability by formulas which start with one of the following operators: (i) a branching t...

متن کامل

Hierarchies in Transitive Closure Logic, Stratified Datalog and Infinitary Logic

We establish a general hierarchy theorem for quantiier classes in the innnitary logic L ! 1! on nite structures. In particular, it is shown that no innnitary formula with bounded number of universal quantiiers can express the negation of a transitive closure. This implies the solution of several open problems in nite model theory: On nite structures, positive transitive closure logic is not clo...

متن کامل

Definability and Compression

A compression algorithm takes a finite structure of a class K as input and produces a finite structure of a different class K’ as output. Given a property P on the class K defined in a logicL, we study the definability of property P on the class K’. We consider two compression schemas on unary ordered structures (words), compression by runlength encoding and the classical Lempel-Ziv. First-orde...

متن کامل

Datalog

An important limitation of relational calculus/algebra is that it cannot express queries involving “paths” through an instance, such as taking the transitive closure over a binary relation. Datalog extends conjunctive queries with recursion to support such queries. A Datalog program consists of a set of rules, each of which is a conjunctive query. Recursion is introduced by allowing the same re...

متن کامل

Definability and model checking: the role of orders and compositionality

Finite model theory and descriptive complexity theory are concerned with assessing the expressive power of logics over finite models and with relating the descriptive resources needed for defining a class of structures to the computational complexity of the corresponding decision problem. In recent years, also the model theory and computational handling (e.g. of the model checking problem) of f...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2004