Rewriting and Well-Definedness within a Proof System

Term rewriting has a significant presence in various areas, not least in automated theorem proving where it is used as a proof technique. Many theorem provers employ specialised proof tactics for rewriting. This results in an interleaving between deduction and computation (i.e., rewriting) steps. If the logic of reasoning supports partial functions, it is necessary that rewriting copes with potentially ill-defined terms. In this paper, we provide a basis for integrating rewriting with a deductive proof system that deals with well-definedness. The definitions and theorems presented in this paper are the theoretical foundations for an extensible rewriting-based prover that has been implemented for the set theoretical formalism Event-B.Comment: In Proceedings PAR 2010, arXiv:1012.455

Metaphoric coherence: Distinguishing verbal metaphor from `anomaly\u27

Theories and computational models of metaphor comprehension generally circumvent the question of metaphor versus “anomaly” in favor of a treatment of metaphor versus literal language. Making the distinction between metaphoric and “anomalous” expressions is subject to wide variation in judgment, yet humans agree that some potentially metaphoric expressions are much more comprehensible than others. In the context of a program which interprets simple isolated sentences that are potential instances of cross‐modal and other verbal metaphor, I consider some possible coherence criteria which must be satisfied for an expression to be “conceivable” metaphorically. Metaphoric constraints on object nominals are represented as abstracted or extended along with the invariant structural components of the verb meaning in a metaphor. This approach distinguishes what is preserved in metaphoric extension from that which is “violated”, thus referring to both “similarity” and “dissimilarity” views of metaphor. The role and potential limits of represented abstracted properties and constraints is discussed as they relate to the recognition of incoherent semantic combinations and the rejection or adjustment of metaphoric interpretations

Formalization of the fundamental group in untyped set theory using auto2

We present a new framework for formalizing mathematics in untyped set theory using auto2. Using this framework, we formalize in Isabelle/FOL the entire chain of development from the axioms of set theory to the definition of the fundamental group for an arbitrary topological space. The auto2 prover is used as the sole automation tool, and enables succinct proof scripts throughout the project.Comment: 17 pages, accepted for ITP 201

The Hidden Web, XML and Semantic Web: A Scientific Data Management Perspective

The World Wide Web no longer consists just of HTML pages. Our work sheds light on a number of trends on the Internet that go beyond simple Web pages. The hidden Web provides a wealth of data in semi-structured form, accessible through Web forms and Web services. These services, as well as numerous other applications on the Web, commonly use XML, the eXtensible Markup Language. XML has become the lingua franca of the Internet that allows customized markups to be defined for specific domains. On top of XML, the Semantic Web grows as a common structured data source. In this work, we first explain each of these developments in detail. Using real-world examples from scientific domains of great interest today, we then demonstrate how these new developments can assist the managing, harvesting, and organization of data on the Web. On the way, we also illustrate the current research avenues in these domains. We believe that this effort would help bridge multiple database tracks, thereby attracting researchers with a view to extend database technology.Comment: EDBT - Tutorial (2011