Is Hartwick’s rule a necessary condition for maximin in Solow’s [1974] model? Until recently this has been an open question; this is surprising given the prominence of the model. Cairns and Yang [2000] as well as Withagen, Asheim and Buchholz (this issue) claim that the answer is in the affirmative and claim to provide a formal proof. The latter team argues that the proof by the former is not c...

The purposes of this paper is to give simple new proofs of some interesting recent results about the relative succinctness of different representations of regular, deterministic and unambiguous context-free languages and to derive some new results about how the relative succinctness of representations change when the representations contain a formal proof that the languages generated are in the...

We present a practical approach to a formal analysis of UMLbased models. This is achieved by an underlying formal representation in Z, which allows us to pose and discharge conjectures to analyse models. We show how our approach allows us to consistency-check UML models, and model analysis by simply drawing snapshot diagrams.

This paper discusses and exemplifies some of the trade-offs that need to be considered when proving properties of formally modelled interactive systems. The properties we are interested in concern the usability of an interactive system, such as showing that things users want to do are easy to do. A simple model of a webbrowsing system is proposed and we show how we can expose usability problems...

Numerous astrophysical observations have shown that classical Newtonian dynamics fails on galactic scales and beyond, if only visible matter is taken into account. The two most popular theoretical concepts dealing with this problem are Dark Matter (DM) and Modified Newtonian Dynamics (MOND). In the first part of this paper it is demonstrated that a generalized MOND equation can be derived in th...

Design patterns represent a highly successful technique in software engineering, giving a reusable ‘best practice’ solution to commonly occurring problems in software design. Taking inspiration from this approach, this paper introduces proof patterns, which aim to provide a common vocabulary for solving formal methods proof obligations by capturing and describing solutions to common patterns of...

syntax trees almost copying the abstract grammar: type term = Var of string | Fn of string * term list;; and express in a direct recursive way the function returning the set of variables in a term: let rec vars tm =

In this article we demonstrate how algorithmic probability theory is applied to situations that involve uncertainty. When people are unsure of their model of reality, then the outcome they observe will cause them to update their beliefs. We argue that classical probability cannot be applied in such cases, and that subjective probability must instead be used. In Experiment 1 we show that, when j...

Cut-introduction is a technique for structuring and compressing formal proofs. In this paper we generalize our cut-introduction method for the introduction of quantified lemmas of the form ∀x.A (for quantifier-free A) to a method generating lemmas of the form ∀x1 . . .∀xn.A. Moreover, we extend the original method to predicate logic with equality. The new method was implemented and applied to t...

Although Kant envisaged a prominent role for logic in the argumentative structure of his Critique of pure reason [12], logicians and philosophers have generally judged Kant’s logic negatively. What Kant called ‘general’ or ‘formal’ logic has been dismissed as a fairly arbitrary subsystem of first order logic, and what he called ‘transcendental logic’ is considered to be not a logic at all: no s...