Quantitative Behavioural Reasoning for Higher-order Effectful Programs: Applicative Distances (Extended Version)

This paper studies the quantitative refinements of Abramsky's applicative similarity and bisimilarity in the context of a generalisation of Fuzz, a call-by-value $\lambda$-calculus with a linear type system that can express programs sensitivity, enriched with algebraic operations \emph{\`a la} Plotkin and Power. To do so a general, abstract framework for studying behavioural relations taking values over quantales is defined according to Lawvere's analysis of generalised metric spaces. Barr's notion of relator (or lax extension) is then extended to quantale-valued relations adapting and extending results from the field of monoidal topology. Abstract notions of quantale-valued effectful applicative similarity and bisimilarity are then defined and proved to be a compatible generalised metric (in the sense of Lawvere) and pseudometric, respectively, under mild conditions

New Directions in Model Checking Dynamic Epistemic Logic

Dynamic Epistemic Logic (DEL) can model complex information scenarios in a way that appeals to logicians. However, its existing implementations are based on explicit model checking which can only deal with small models, so we do not know how DEL performs for larger and real-world problems. For temporal logics, in contrast, symbolic model checking has been developed and successfully applied, for example in protocol and hardware verification. Symbolic model checkers for temporal logics are very efficient and can deal with very large models. In this thesis we build a bridge: new faithful representations of DEL models as so-called knowledge and belief structures that allow for symbolic model checking. For complex epistemic and factual change we introduce transformers, a symbolic replacement for action models. Besides a detailed explanation of the theory, we present SMCDEL: a Haskell implementation of symbolic model checking for DEL using Binary Decision Diagrams. Our new methods can solve well-known benchmark problems in epistemic scenarios much faster than existing methods for DEL. We also compare its performance to to existing model checkers for temporal logics and show that DEL can compete with established frameworks. We zoom in on two specific variants of DEL for concrete applications. First, we introduce Public Inspection Logic, a new framework for the knowledge of variables and its dynamics. Second, we study the dynamic gossip problem and how it can be analyzed with epistemic logic. We show that existing gossip protocols can be improved, but that no perfect strengthening of "Learn New Secrets" exists

Understanding Whitehead

Originally published in 1962. The central aim of this book is to discuss the development of Alfred North Whitehead's thought and to underscore how it is unique. The book collects nine essays written by Victor Lowe originally published between 1941 and 1961. The essays have been revised for inclusion in this volume

Edmund Husserl between Platonism and Aristotelianism

The volume contains the first collection of essays delaying with the relations between, on the one hand, Husserl's philosophy, and, on the other, the traditions of Platonism and Aristotelianism

Einstein vs. Bergson

On 6 April 1922, Einstein met Bergson to debate the nature of time: is the time the physicist calculates the same time the philosopher reflects on? Einstein claimed that only scientific time is real, while Bergson argued that scientific time always presupposes a living and perceiving subject. On that day, nearly 100 years ago, conflict was inevitable. Is it still inevitable today? How many kinds of time are there

Endogenous development: a model for the process of man-environment transaction

Iran is currently subject to a number of adverse factors affecting good development in the built environment: population explosion, oil- dependent economy, finite resources, war and natural disasters, etc. The object of the study is to research a development model appropriate to the Country's needs for a proactive system of building environment. This model is not specific to Iran and, as the case studies and the discourse of the thesis indicate, is universal. However, the author suggests that the validity of development approaches will not be determined as a result of theoretical and ideological debate but in the realm of practice. Therefore, he has explored diverse ways in which professionals in the built environment can provide an analytical survey of the problems that beset them. An attempt has been made to bring these various elements into perspective and offer a model of 'endogenous development'.The process for achieving a viable, exciting and humane built environment is very complex and calls for contributions from many individuals and small multi -disciplinary groups. Beside professionals contributions (which is accomplished by deduction inference), there is a need for people's participation in design process (which is accomplished either by deduction or by abduction inferences). This participatory approach can also help shifting the process of design towards a wider domain that of the 'production process' (which is accomplished by abduction and induction inferences). Production process is the first paradigm of the model of endogenous development and is a manifestation of a feedback mechanism and acts as an open - ended living system. The second is 'supply- demand' paradigm which shows the relationships between the components of a system or between different systems in surface- structuresThis model is directed at society's development, not just its economic growth, but it does not preclude the possibility of such growth. The reduction of the problems' effect in an endogenous development is viewed more as a way of improving the quality of life than of increasing the standard of living. Nowadays, people are passive recipients in the consumer society and are totally dependent on others for their survival. This style of living is assumed to project an image of economic development and higher productivity, but there is a confrontation of preadjusted commodities which are the products of others. That is because the process of production is not natural (i.e. a closed loop cyclic process via feedback control). It is artificial (i.e. an open -loop linear process via a feed -forward control) which may not help satisfying the user's needs and wants entirely. In the built environment, the great majority have no say in the planning and design of their homes or places of work.Accordingly, endogenous development offers a framework within which the necessity of employing the people's creative power in building their environment is explained. It is based on the assumption that each individual and society's knowledge and experiences play a central and mediating role between professionals' perceptions of the environment and a series of preferences judgements or choices they might make towards and within that environment. Indigenous knowledge and cultural attributes of traditional societies and the organizational capabilities of traditional polities are essential in qualification of the development plans, which are also evaluated and assessed by this proposed framework

Logic and intuition in architectural modelling: philosophy of mathematics for computational design

This dissertation investigates the relationship between the shift in the focus of architectural modelling from object to system and philosophical shifts in the history of mathematics that are relevant to that change. Particularly in the wake of the adoption of digital computation, design model spaces are more complex, multidimensional, arguably more logical, less intuitive spaces to navigate, less accessible to perception and visual comprehension. Such spatial issues were encountered much earlier in mathematics than in architectural modelling, with the growth of analytical geometry, a transition from Classical axiomatic proofs in geometry as the basis of mathematics, to analysis as the underpinning of geometry. Can the computational design modeller learn from the changing modern history, philosophy and psychology of mathematics about the construction and navigation of computational geometrical architectural system model space? The research is conducted through a review of recent architectural project examples and reference to three more detailed architectural modelling case studies. The spatial questions these examples and case studies raise are examined in the context of selected historical writing in the history, philosophy and psychology of mathematics and space. This leads to conclusions about changes in the relationship of architecture and mathematics, and reflections on the opportunities and limitations for architectural system models using computation geometry in the light of this historical survey. This line of questioning was motivated as a response to the experience of constructing digital associative geometry models and encountering the apparent limits of their flexibility as the graph of dependencies grew and the messiness of the digital modelling space increased. The questions were inspired particularly by working on the Narthex model for the Sagrada Família church, which extends to many tens of thousands of relationships and constraints, and which was modelled and repeatedly partially remodelled over a very long period. This experience led to the realisation that the limitations of the model were not necessarily the consequence of poor logical schema definition, but could be inevitable limitations of the geometry as defined, regardless of the means of defining it, the ‘shape’ of the multidimensional space being created. This led to more fundamental questions about the nature of Space, its relationship to geometry and the extent to which the latter can be considered simply as an operational and notational system. This dissertation offers a purely inductive journey, offering evidence through very selective examples in architecture, architectural modelling and in the philosophy of mathematics. The journey starts with some questions about the tendency of the model space to break out and exhibit unpredictable and not always desirable behaviour and the opportunities for geometrical construction to solve these questions is not conclusively answered. Many very productive questions about computational architectural modelling are raised in the process of looking for answers