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

The prospects for mathematical logic in the twenty-first century

The four authors present their speculations about the future developments of mathematical logic in the twenty-first century. The areas of recursion theory, proof theory and logic for computer science, model theory, and set theory are discussed independently.Comment: Association for Symbolic Logi

A temporal logic for micro- and macro-step-based real-time systems: Foundations and applications

Many systems include components interacting with each other that evolve at possibly very different speeds. To deal with this situation many formal models adopt the abstraction of “zero-time transitions”, which do not consume time. These, however, have several drawbacks in terms of naturalness and logic consistency, as a system is modeled to be in different states at the same time. We propose a novel approach that exploits concepts from non-standard analysis and pairs them with the traditional “next” operator of temporal logic to introduce a notion of micro- and macro-steps; our approach is enacted in an extension of the TRIO metric temporal logic, called X-TRIO. We study the expressiveness and decidability properties of the new logic. Decidability is achieved through translation of a meaningful subset of X-TRIO into Linear Temporal Logic, a traditional way to support automated verification. We illustrate the usefulness and the generality of our approach by applying it to provide a formal semantics of timed Petri nets, which allows for their automated verification. We also give an overview of a formal semantics of Stateflow/Simulink diagrams, defined in terms of X-TRIO, which has been applied to the automated verification of a robotic cell

Noninterfering schedulers: when possibilistic noninterference implies probabilistic noninterference

We develop a framework for expressing and analyzing the behavior of probabilistic schedulers. There, we define noninterfering schedulers by a probabilistic interpretation of Goguen and Meseguer’s seminal notion of noninterference. Noninterfering schedulers are proved to be safe in the following sense: if a multi-threaded program is possibilistically noninterfering, then it is also probabilistically noninterfering when run under this scheduler

Mathematical Logic: Proof theory, Constructive Mathematics

The workshop “Mathematical Logic: Proof Theory, Constructive Mathematics” was centered around proof-theoretic aspects of current mathematics, constructive mathematics and logical aspects of computational complexit

A formally verified compiler back-end

This article describes the development and formal verification (proof of semantic preservation) of a compiler back-end from Cminor (a simple imperative intermediate language) to PowerPC assembly code, using the Coq proof assistant both for programming the compiler and for proving its correctness. Such a verified compiler is useful in the context of formal methods applied to the certification of critical software: the verification of the compiler guarantees that the safety properties proved on the source code hold for the executable compiled code as well

An interval logic for higher-level temporal reasoning

Prior work explored temporal logics, based on classical modal logics, as a framework for specifying and reasoning about concurrent programs, distributed systems, and communications protocols, and reported on efforts using temporal reasoning primitives to express very high level abstract requirements that a program or system is to satisfy. Based on experience with those primitives, this report describes an Interval Logic that is more suitable for expressing such higher level temporal properties. The report provides a formal semantics for the Interval Logic, and several examples of its use. A description of decision procedures for the logic is also included