The Meaning of Distributive Justice for Aristotle’s Theory of Constitutions

Abstract: This paper examines Aristotle’s theory of distributive justice and its meaning for his theory of constitutions. First, it shows that his account of constitutions in Books IV–VI of the Politics is an extension and refinement of his scheme of six constitutions in Book III. Second, it argues for the thesis that the account of justice (τὸ δίκαιον) in distribution of political offices that Aristotle gives in Book III of the Politics links up with and extends the doctrine of justice (δικαιοσύνη) that he develops in Book V of the Nicomachean Ethics. Third, it substantiates the thesis that Aristotle understands the different forms of constitution as embodiments of different conceptions of distributive justice, and argues for the thesis that Aristotle has a clear preference for the aristocratic conception and, as a consequence, for aristocracy. Finally, it supports the thesis that the constitution of the best polis, which Aristotle outlines in Books VII and VIII of the Politics, has to be understood as a true aristocracy and not as a polity (πολιτεία).Keywords: Aristotle’s Politics, Theory of Justice, Distributive Justice, Constitutions doi: http://dx.doi.org/10.20318/fons.2016.2529

Architectural Refinement in HETS

The main objective of this work is to bring a number of improvements to the Heterogeneous Tool Set HETS, both from a theoretical and an implementation point of view. In the first part of the thesis we present a number of recent extensions of the tool, among which declarative specifications of logics, generalized theoroidal comorphisms, heterogeneous colimits and integration of the logic of the term rewriting system Maude. In the second part we concentrate on the CASL architectural refinement language, that we equip with a notion of refinement tree and with calculi for checking correctness and consistency of refinements. Soundness and completeness of these calculi is also investigated. Finally, we present the integration of the VSE refinement method in HETS as an institution comorphism. Thus, the proof manangement component of HETS remains unmodified

The role of logical interpretations on program development

Stepwise refinement of algebraic specifications is a well known formal methodology for program development. However, traditional notions of refinement based on signature morphisms are often too rigid to capture a number of relevant transformations in the context of software design, reuse, and adaptation. This paper proposes a new approach to refinement in which signature morphisms are replaced by logical interpretations as a means to witness refinements. The approach is first presented in the context of equational logic, and later generalised to deductive systems of arbitrary dimension. This allows, for example, refining sentential into equational specifications and the latter into modal ones.The authors express their gratitude to the anonymous referees who raised a number of pertinent questions entailing a more precise characterisation of the paper's contributions and a clarification of their scope. This work was funded by HRDF - European Regional Development Fund through the COMPETE Programme (operational programme for competitiveness) and by National Funds through the FCT (Portuguese Foundation for Science and Technology) within project FCOMP-01-0124-FEDER-028923 (Nasoni) and the project PEst-C/MAT/UI4106/2011 with COMPETE number FCOMP-01-0124-FEDER-022690 (CIDMA-UA). The first author also acknowledges the financial assistance by the projects GetFun, reference FP7-PEOPLE-2012-IRSES, and NOCIONES IDE COMPLETUD, reference FFI2009-09345 (MICINN - Spain). A. Madeira was supported by the FCT within the project NORTE-01-0124-FEDER-000060

An Institution for Event-B

This paper presents a formalisation of the Event-B formal specification language in terms of the theory of institutions. The main objective of this paper is to provide: (1) a mathematically sound semantics and (2) modularisation constructs for Event-B using the specification-building operations of the theory of institutions. Many formalisms have been improved in this way and our aim is thus to define an appropriate institution for Event-B, which we call EVT. We provide a definition of EVT and the proof of its satisfaction condition. A motivating example of a traffic-light simulation is presented to illustrate our approach

Accurate robot simulation through system identification

Robot simulators are useful tools for developing robot behaviours. They provide a fast and efficient means to test robot control code at the convenience of the office desk. In all but the simplest cases though, due to the complexities of the physical systems modelled in the simulator, there are considerable differences between the behaviour of the robot in the simulator and that in the real world environment. In this paper we present a novel method to create a robot simulator using real sensor data. Logged sensor data is used to construct a mathematically explicit model(in the form of a NARMAX polynomial) of the robot’s environment. The advantage of such a transparent model — in contrast to opaque modelling methods such as artificial neural networks — is that it can be analysed to characterise the modelled system, using established mathematical methods In this paper we compare the behaviour of the robot running a particular task in both the simulator and the real-world using qualitative and quantitative measures including statistical methods to investigate the faithfulness of the simulator