Changing a semantics: opportunism or courage?

The generalized models for higher-order logics introduced by Leon Henkin, and their multiple offspring over the years, have become a standard tool in many areas of logic. Even so, discussion has persisted about their technical status, and perhaps even their conceptual legitimacy. This paper gives a systematic view of generalized model techniques, discusses what they mean in mathematical and philosophical terms, and presents a few technical themes and results about their role in algebraic representation, calibrating provability, lowering complexity, understanding fixed-point logics, and achieving set-theoretic absoluteness. We also show how thinking about Henkin's approach to semantics of logical systems in this generality can yield new results, dispelling the impression of adhocness. This paper is dedicated to Leon Henkin, a deep logician who has changed the way we all work, while also being an always open, modest, and encouraging colleague and friend.Comment: 27 pages. To appear in: The life and work of Leon Henkin: Essays on his contributions (Studies in Universal Logic) eds: Manzano, M., Sain, I. and Alonso, E., 201

Transforming process models: executable rewrite rules versus a formalized java program

Abstract. In the business process management community, transformations for process models are usually programmed using imperative languages (such as Java). The underlying mapping rules tend to be documented using informal visual rules whereas they tend to be formalized using mathematical set constructs. In the Graph and Model Transformation communities, special purpose languages and tools (such as GrGen 1) are being developed to support the direct execution of such mapping rules. As part of our ongoing effort to bridge these two communities, we have implemented a transformation from petri-nets to statecharts (PN2SC) using both approaches. By relying on technical comparison criteria and by making the solutions available for online replay, we illustrate that rule-based approaches require less specification effort due to their more declarative specification style and automatic performance optimizations. From a tool perspective, GrGen has better visualization and debugging support whereas Java tools support evolution better.

Comparing Expressiveness of Set Constructor Symbols

In this paper we consider the relative expressive power of two very common operators applicable to sets and multisets: the with and the union operators. For such operators we prove that they are not mutually expressible by means of existentially quantified formulae. In order to prove our results, canonical forms for set-theoretic and multiset-theoretic formulae are established and a particularly natural axiomatization of multisets is given and studied