Formal language

About: Formal language is a research topic. Over the lifetime, 5763 publications have been published within this topic receiving 154114 citations.

A Formal Framework for Complex Event Processing

Abstract: Complex Event Processing (CEP) has emerged as the unifying field for technologies that require processing and correlating distributed data sources in real-time. CEP finds applications in diverse domains, which has resulted in a large number of proposals for expressing and processing complex events. However, existing CEP languages lack from a clear semantics, making them hard to understand and generalize. Moreover, there are no general techniques for evaluating CEP query languages with clear performance guarantees. In this paper we embark on the task of giving a rigorous and efficient framework to CEP. We propose a formal language for specifying complex events, called CEL, that contains the main features used in the literature and has a denotational and compositional semantics. We also formalize the so-called selection strategies, which had only been presented as by-design extensions to existing frameworks. With a well-defined semantics at hand, we discuss how to efficiently process complex events by evaluating CEL formulas with unary filters. We start by studying the syntactical properties of CEL and propose rewriting optimization techniques for simplifying the evaluation of formulas. Then, we introduce a formal computational model for CEP, called complex event automata (CEA), and study how to compile CEL formulas with unary filters into CEA. Furthermore, we provide efficient algorithms for evaluating CEA over event streams using constant time per event followed by constant-delay enumeration of the results. Finally, we gather the main results of this work to present an efficient and declarative framework for CEP.

Frege and semantics

Abstract: In recent work on Frege, one of the most salient issues has been whether he was prepared to make serious use of semantical notions such as reference and truth. I argue here Frege did make very serious use of semantical concepts. I argue, fi rst, that Frege had reason to be interested in the question how the axioms and rules of his formal theory might be justifi ed and, second, that he explicitly commits himself to off ering a justifi cation that appeals to the notion of reference. I then discuss the justifi cations Frege off ered, focusing on his discussion of inferences involving free variables, in section 17 of Grundgesetze, and his argument, in sections 29–32, that every well-formed expression of his formal language has a unique reference.