Introduction to linear logic and ludics, part II

This paper is the second part of an introduction to linear logic and ludics, both due to Girard. It is devoted to proof nets, in the limited, yet central, framework of multiplicative linear logic and to ludics, which has been recently developped in an aim of further unveiling the fundamental interactive nature of computation and logic. We hope to offer a few computer science insights into this new theory

Interaction Graphs: Full Linear Logic

Interaction graphs were introduced as a general, uniform, construction of dynamic models of linear logic, encompassing all Geometry of Interaction (GoI) constructions introduced so far. This series of work was inspired from Girard's hyperfinite GoI, and develops a quantitative approach that should be understood as a dynamic version of weighted relational models. Until now, the interaction graphs framework has been shown to deal with exponentials for the constrained system ELL (Elementary Linear Logic) while keeping its quantitative aspect. Adapting older constructions by Girard, one can clearly define "full" exponentials, but at the cost of these quantitative features. We show here that allowing interpretations of proofs to use continuous (yet finite in a measure-theoretic sense) sets of states, as opposed to earlier Interaction Graphs constructions were these sets of states were discrete (and finite), provides a model for full linear logic with second order quantification

On paths-based criteria for polynomial time complexity in proof-nets

Girard's Light linear logic (LLL) characterized polynomial time in the proof-as-program paradigm with a bound on cut elimination. This logic relied on a stratification principle and a "one-door" principle which were generalized later respectively in the systems L^4 and L^3a. Each system was brought with its own complex proof of Ptime soundness. In this paper we propose a broad sufficient criterion for Ptime soundness for linear logic subsystems, based on the study of paths inside the proof-nets, which factorizes proofs of soundness of existing systems and may be used for future systems. As an additional gain, our bound stands for any reduction strategy whereas most bounds in the literature only stand for a particular strategy.Comment: Long version of a conference pape

Propositions as Sessions

Continuing a line of work by Abramsky (1994), by Bellin and Scott (1994), and by Caires and Pfenning (2010), among others, this paper presents CP, a calculus in which propositions of classical linear logic correspond to session types. Continuing a line of work by Honda (1993), by Honda, Kubo, and Vasconcelos (1998), and by Gay and Vasconcelos (2010), among others, this paper presents GV, a linear functional language with session types, and presents a translation from GV into CP. The translation formalises for the first time a connection between a standard presentation of session types and linear logic, and shows how a modification to the standard presentation yield a language free from deadlock, where deadlock freedom follows from the correspondence to linear logic. Note. Please read this paper in colour! The paper uses colour to highlight the relation of types to terms and source to target. 1

Coherence for Frobenius pseudomonoids and the geometry of linear proofs

We prove coherence theorems for Frobenius pseudomonoids and snakeorators in monoidal bicategories. As a consequence we obtain a 3d notation for proofs in nonsymmetric multiplicative linear logic, with a geometrical notion of equivalence, and without the need for a global correctness criterion or thinning links. We argue that traditional proof nets are the 2d projections of these 3d diagrams

Random Effect Models For Repairable System Reliability

The practical motivation for the work described in this thesis arose from the development of a new Jaguar car engine. Development tests on prototype engines led to multiple failure time data which are modelled as a non-homogeneous Poisson process in its log-linear form. Initial analysis of the data using failure time plots showed considerable differences between prototype engines and suggested the use of models incorporating random effects for the engine effects. These models were fitted using the method of maximum likelihood. Two random effects have been considered: a proportional effect and a time dependent effect. In each case a simulation study showed the method of maximum likelihood to produce good estimates of the parameters and standard errors. There is also shown to be a bias in the estimate of the random effect, especially in smaller samples. The likelihood ratio test has been shown to be valid in assessing the statistical significance of the random effect, and a simulation exercise has demonstrated this in practical terms. Applying this test to the models fitted to the Jaguar data gives the proportional random effect to be significant while the time dependent random effect is not found to be significantly different from zero. This test has also been demonstrated to be of use in distinguishing between the two models and again the proportional random effect model is found to be more suitable for the Jaguar data. Residual analysis is performed to aid model validation Covariates are included, in various forms, in the proportional random effect model and the inclusion of these in the time dependent model is briefly discussed. The use of these models is demonstrated for the Jaguar data by including the type of test an engine performed as a covariate. The covariate models have also been used to compare engine phases. A framework for extending the models for interval censored data is developed. Finally this thesis discusses possible extensions of the work summarised in the previous paragraphs. This includes work on alternative models, Bayesian methods and experimental design.Jaguar Cars Limite

Job type as an intervening variable in the prediction of managerial success, using measures of cognitive abilities, personality, and self-perceived leadership style

This research is a predictive study of managerial success by specific job type in a single British company. Seventy-four managers, at the same level, in specific jobs differentiated by degree of task structure, completed a battery of tests of cognitive abilities, personality, and self-perceived leadership. Three years later their status was checked to determine if they had been promoted or not. Differences examined in Successful managers between job types, Unsuccessful managers between job types, and between Successful and Unsuccessful managers within job type, for all managers as a whole regardless of job differences. The basic hypothesis of the research, that a situational approach to the prediction of managerial success differentiating managers by job type, would yield results than predictions of managerial success regard for job differences was supported. Significant differences in cognitive abilities, personality, self-perceived leadership style were found between Successful managers in the two job functions, and classification of Successfuls and Unsuccessfuls by discriminant analysis was more accurate for managers within specific job types than for the total sample of managers regard for job differences