The Methodology of Political Theory

This article examines the methodology of a core branch of contemporary political theory or philosophy: “analytic” political theory. After distinguishing political theory from related fields, such as political science, moral philosophy, and legal theory, the article discusses the analysis of political concepts. It then turns to the notions of principles and theories, as distinct from concepts, and reviews the methods of assessing such principles and theories, for the purpose of justifying or criticizing them. Finally, it looks at a recent debate on how abstract and idealized political theory should be, and assesses the significance of disagreement in political theory. The discussion is carried out from an angle inspired by the philosophy of science

A theory of hyperfinite sets

We develop an axiomatic set theory -- the Theory of Hyperfinite Sets THS, which is based on the idea of existence of proper subclasses of big finite sets. We demonstrate how theorems of classical continuous mathematics can be transfered to THS, prove consistency of THS and present some applications.Comment: 28 page

Towards Realizability Checking of Contracts using Theories

Virtual integration techniques focus on building architectural models of systems that can be analyzed early in the design cycle to try to lower cost, reduce risk, and improve quality of complex embedded systems. Given appropriate architectural descriptions and compositional reasoning rules, these techniques can be used to prove important safety properties about the architecture prior to system construction. Such proofs build from "leaf-level" assume/guarantee component contracts through architectural layers towards top-level safety properties. The proofs are built upon the premise that each leaf-level component contract is realizable; i.e., it is possible to construct a component such that for any input allowed by the contract assumptions, there is some output value that the component can produce that satisfies the contract guarantees. Without engineering support it is all too easy to write leaf-level components that can't be realized. Realizability checking for propositional contracts has been well-studied for many years, both for component synthesis and checking correctness of temporal logic requirements. However, checking realizability for contracts involving infinite theories is still an open problem. In this paper, we describe a new approach for checking realizability of contracts involving theories and demonstrate its usefulness on several examples.Comment: 15 pages, to appear in NASA Formal Methods (NFM) 201

What makes industries believe in formal methods

The introduction of formal methods in the design and development departments of an industrial company has far reaching and long lasting consequences. In fact it changes the whole environment of methods, tools and skills that determine the design culture of that company. A decision to replace current design practice by formal methods, therefore, appears a vital one and is not lightly taken. The past has shown that efforts to introduce formal methods in industry has faced a lot of controversy and opposition at various hierarchical levels in companies, resulting in a marginal spread of such methods. This paper revisits the requirements for formal description techniques and identifies some critical success and inhibiting factors associated with the introduction of formal methods in the industrial practice. One of the inhibiting factors is the often encountered lack of appropriateness of the formal model to express and manipulate the design concerns that determine the world of the engineer. This factor motivated our research in the area of architectural and implementation design concepts. The last two sections of this paper report on some results of this research

Abstract Canonical Inference

An abstract framework of canonical inference is used to explore how different proof orderings induce different variants of saturation and completeness. Notions like completion, paramodulation, saturation, redundancy elimination, and rewrite-system reduction are connected to proof orderings. Fairness of deductive mechanisms is defined in terms of proof orderings, distinguishing between (ordinary) "fairness," which yields completeness, and "uniform fairness," which yields saturation.Comment: 28 pages, no figures, to appear in ACM Trans. on Computational Logi